CHAPTER 1
Overview of Corporate Finance and the Financial Environment
Corporate finance
Forms of business organization
Objective of the firm: Maximize wealth
Determinants of stock pricing
The financial environment
Financial instruments, markets and institutions
Interest rates and yield curves
Why is corporate finance important to all managers?
Corporate finance provides the skills managers need to:
Identify and select the corporate strategies and individual projects that add value to their firm.
Forecast the funding requirements of their company, and devise strategies for acquiring those funds.
Sole proprietorship
Partnership
Corporation
What are some forms of
business organization?
Advantages:
Ease of formation
Subject to few regulations
No corporate income taxes
Disadvantages:
Limited life
Unlimited liability
Difficult to raise capital
Sole Proprietorship
A partnership has roughly the same advantages and disadvantages as a sole proprietorship.
Partnership
Advantages:
Unlimited life
Easy transfer of ownership
Limited liability
Ease of raising capital
Disadvantages:
Double taxation
Cost of set-up and report filing
Corporation
The primary objective should be shareholder wealth maximization, which translates to maximizing stock price.
Should firms behave ethically? YES!
Do firms have any responsibilities to society at large? YES! Shareholders are also members of society.
What should management’s primary objective be?
Is maximizing stock price good for society, employees, and customers?
Employment growth is higher in firms that try to maximize stock price. On average, employment goes up in:
firms that make managers into owners (such as LBO firms)
firms that were owned by the government but that have been sold to private investors
Consumer welfare is higher in capitalist free market economies than in communist or socialist economies.
Fortune lists the most admired firms. In addition to high stock returns, these firms have:
high quality from customers’ view
employees who like working there
Amount of cash flows expected by shareholders
Timing of the cash flow stream
Risk of the cash flows
What three factors affect stock prices?
Sales revenues
Current level
Short-term growth rate in sales
Long-term sustainable growth rate in sales
Operating expenses (., raw materials, labor, etc.)
Necessary investments in operating capital (., buildings, machines, inventory, etc.)
What factors determine of cash flows?
What factors affect the level and
risk of cash flows?
Decisions made by financial managers:
Investment decisions (product lines, production processes, geographic market, use of technology, marketing strategy, etc.)
Financing decisions (choice of debt policy and dividend policy)
The external environment (taxes, regulation, etc.)
What are financial assets?
A financial asset is a contract that entitles the owner to some type of payoff.
Debt
Equity
Derivatives
In general, each financial asset involves two parties, a provider of cash (., capital) and a user of cash.
What are some financial instruments?
Instrument Rate (9/01)
. T-bills %
Banker’s acceptances
Commercial paper
Negotiable CDs
Eurodollar deposits
Commercial loans Tied to prime (%) or LIBOR (%)
(More . .)
Financial Instruments (Continued)
Instrument Rate (9/01)
. T-notes and T-bonds %
Mortgages
Municipal bonds
Corporate (AAA) bonds
Preferred stocks 7 to 9%
Common stocks (expected) 10 to 15%
Who are the providers (savers) and users (borrowers) of capital?
Households: Net savers
Non-financial corporations: Net users (borrowers)
Governments: Net borrowers
Financial corporations: Slightly net borrowers, but almost breakeven
What are three ways that capital is transferred between savers and borrowers?
Direct transfer (., corporation issues commercial paper to insurance company)
Through an investment banking house (., IPO, seasoned equity offering, or debt placement)
Through a financial intermediary (., individual deposits money in bank, bank makes commercial loan to a company)
What are some financial intermediaries?
Commercial banks
Savings & Loans, mutual savings banks, and credit unions
Life insurance companies
Mutual funds
Pension funds
The Top 5 Banking Companies
in the World, 12/1999
$697 billion
Tokyo
Bank of Tokyo
$717 billion
New York
Citigroup
$632 billion
Charlotte
Bank of America
$702 billion
Paris
BNP Paribas
$844 billion
Frankfurt
Deutsche Bank AG
Total assets
Country
Bank Name
What are some types of markets?
A market is a method of exchanging one asset (usually cash) for another asset.
Physical assets vs. financial assets
Spot versus future markets
Money versus capital markets
Primary versus secondary markets
How are secondary markets organized?
By “location”
Physical location exchanges
Computer/telephone networks
By the way that orders from buyers and sellers are matched
Open outcry auction
Dealers (., market makers)
Electronic communications networks (ECNs)
Physical Location vs. Computer/telephone Networks
Physical location exchanges: ., NYSE, AMEX, CBOT, Tokyo Stock Exchange
Computer/telephone: ., Nasdaq, government bond markets, foreign exchange markets
Auction Markets
NYSE and AMEX are the two largest auction markets for stocks.
NYSE is a modified auction, with a “specialist.”
Participants have a seat on the exchange, meet face-to-face, and place orders for themselves or for their clients; ., CBOT.
Market orders vs. limit orders
Dealer Markets
“Dealers” keep an inventory of the stock (or other financial asset) and place bid and ask “advertisements,” which are prices at which they are willing to buy and sell.
Computerized quotation system keeps track of bid and ask prices, but does not automatically match buyers and sellers.
Examples: Nasdaq National Market, Nasdaq SmallCap Market, London SEAQ, German Neuer Markt.
Electronic Communications Networks (ECNs)
ECNs:
Computerized system matches orders from buyers and sellers and automatically executes transaction.
Examples: Instinet (US, stocks), Eurex (Swiss-German, futures contracts), SETS (London, stocks).
Over the Counter (OTC) Markets
In the old days, securities were kept in a safe behind the counter, and passed “over the counter” when they were sold.
Now the OTC market is the equivalent of a computer bulletin board, which allows potential buyers and sellers to post an offer.
No dealers
Very poor liquidity
What do we call the price, or cost, of debt capital?
The interest rate
What do we call the price, or cost, of equity capital?
Required Dividend Capital
return yield gain
= + .
What four factors affect the cost
of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
Real versus Nominal Rates
r*
= Real risk-free rate.
T-bond rate if no inflation;
1% to 4%.
= Any nominal rate.
= Rate on Treasury securities.
r
rRF
r = r* + IP + DRP + LP + MRP.
Here:
r = Required rate of return on a debt security.
r* = Real risk-free rate.
IP = Inflation premium.
DRP = Default risk premium.
LP = Liquidity premium.
MRP = Maturity risk premium.
Premiums Added to r* for Different Types of Debt
ST Treasury: only IP for ST inflation
LT Treasury: IP for LT inflation, MRP
ST corporate: ST IP, DRP, LP
LT corporate: IP, DRP, MRP, LP
What is the “term structure of interest rates”? What is a “yield curve”?
Term structure: the relationship between interest rates (or yields) and maturities.
A graph of the term structure is called the yield curve.
How can you construct a hypothetical Treasury yield curve?
Estimate the inflation premium (IP) for each future year. This is the estimated average inflation over that time period.
Step 2: Estimate the maturity risk premium (MRP) for each future year.
Step 1: Find the average expected inflation rate over years 1 to n:
n
INFLt
t = 1
n
IPn = .
Assume investors expect inflation to be 5% next year, 6% the following year, and 8% per year thereafter.
IP1 = 5%/ = %.
IP10 = [5 + 6 + 8(8)]/10 = %.
IP20 = [5 + 6 + 8(18)]/20 = %.
Must earn these IPs to break even versus inflation; that is, these IPs would permit you to earn r* (before taxes).
Step 2: Find MRP based on this equation:
MRPt = %(t - 1).
MRP1 = % x 0 = %.
MRP10 = % x 9 = %.
MRP20 = % x 19 = %.
Assume the MRP is zero for Year 1 and increases by % each year.
Step 3: Add the IPs and MRPs to r*:
rRFt = r* + IPt + MRPt .
rRF = Quoted market interest
rate on treasury securities.
Assume r* = 3%:
rRF1 = 3% + 5% + % = %.
rRF10 = 3% + % + % = %.
rRF20 = 3% + % + % = %.
Hypothetical Treasury Yield Curve
0
5
10
15
1
10
20
Years to Maturity
Interest
Rate (%)
1 yr %
10 yr %
20 yr %
Real risk-free rate
Inflation premium
Maturity risk premium
What factors can explain the shape of this yield curve?
This constructed yield curve is upward sloping.
This is due to increasing expected inflation and an increasing maturity risk premium.
What kind of relationship exists between the Treasury yield curve and the yield curves for corporate issues?
Corporate yield curves are higher than that of the Treasury bond. However, corporate yield curves are not neces-sarily parallel to the Treasury curve.
The spread between a corporate yield curve and the Treasury curve widens as the corporate bond rating decreases.
Hypothetical Treasury and
Corporate Yield Curves
0
5
10
15
0
1
5
10
15
20
Years to
maturity
Interest
Rate (%)
%
%
%
Treasury
yield curve
BB-Rated
AAA-Rated
What is the Pure Expectations Hypothesis (PEH)?
Shape of the yield curve depends on the investors’ expectations about future interest rates.
If interest rates are expected to increase, L-T rates will be higher than S-T rates and vice versa. Thus, the yield curve can slope up or down.
PEH assumes that MRP = 0.
Long-term rates are an average of current and future short-term rates.
If PEH is correct, you can use the yield curve to “back out” expected future interest rates.
Observed Treasury Rates
If PEH holds, what does the market expect will be the interest rate on one-year securities, one year from now? Three-year securities, two years from now?
%
5 years
%
4 years
%
3 years
%
2 years
%
1 year
Yield
Maturity
0
1
2
5
%
3
4
x%
%
PEH tells us that one-year securities will yield %, one year from now (x%).
% =
% = + x%
% = x%.
(% + x%)
2
0
1
2
5
%
3
4
x%
%
[ 2(%) + 3(x%) ]
5
PEH tells us that three-year securities will yield %, two years from now (x%).
% =
% = % + 3(x%)
% = 3(x%)
% = x%.
Conclusions about PEH
Some argue that the PEH isn’t correct, because securities of different maturities have different risk.
General view (supported by most evidence) is that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (., MRP > 0).
What various types of risks arise
when investing overseas?
Country risk: Arises from investing or doing business in a particular country. It depends on the country’s economic, political, and social environment.
Exchange rate risk: If investment is denominated in a currency other than the dollar, the investment’s value will depend on what happens to exchange rate.
What two factors lead to exchange
rate fluctuations?
Changes in relative inflation will lead to changes in exchange rates.
An increase in country risk will also cause that country’s currency to fall.
Future value
Present value
Rates of return
Amortization
Chapter 2
Time Value of Money
Time lines show timing of cash flows.
CF0
CF1
CF3
CF2
0
1
2
3
i%
Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2.
Time line for a $100 lump sum due at the end of Year 2.
100
0
1
2 Year
i%
Time line for an ordinary annuity of $100 for 3 years.
100
100
100
0
1
2
3
i%
Time line for uneven CFs: -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3.
100
50
75
0
1
2
3
i%
-50
What’s the FV of an initial $100 after 3 years if i = 10%?
FV = ?
0
1
2
3
10%
Finding FVs (moving to the right
on a time line) is called compounding.
100
After 1 year:
FV1 = PV + INT1 = PV + PV (i)
= PV(1 + i)
= $100()
= $.
After 2 years:
FV2 = FV1(1+i) = PV(1 + i)(1+i)
= PV(1+i)2
= $100()2
= $.
After 3 years:
FV3 = FV2(1+i)=PV(1 + i)2(1+i)
= PV(1+i)3
= $100()3
= $.
In general,
FVn = PV(1 + i)n.
Solve the equation with a regular calculator.
Use a financial calculator.
Use a spreadsheet.
Three Ways to Find FVs
Adjust display contrast: hold down CLR and push + or -.
Choose algebra mode: Hold down orange key (., the shift key), hit MODES (the shifted DSP key), and select ALG.
Set number of decimal places to display: Hit DSP key, select FIX, then input desired decimal places (., 3).
Financial calculator: HP17BII
Set decimal mode: Hit DSP key, select the “.” instead of the “,”. Note: many non-US countries reverse the US use of decimals and commas when writing a number.
HP17BII (Continued)
Hit EXIT until you get the menu starting with FIN. Select FIN.
Select TVM.
Select OTHER.
Select P/YR. Input 1 (for 1 payment per year).
Select END (for cash flows occuring at the end of the year.)
HP17BII: Set Time Value Parameters
Financial calculators solve this equation:
There are 4 variables. If 3 are known, the calculator will solve for the 4th.
Financial Calculator Solution
3 10 -100 0
N I/YR PV PMT FV
Here’s the setup to find FV:
Clearing automatically sets everything to 0, but for safety enter PMT = 0.
Set: P/YR = 1, END.
INPUTS
OUTPUT
Use the FV function: see spreadsheet in Ch 02 Mini .
= FV(Rate, Nper, Pmt, PV)
= FV(, 3, 0, -100) =
Spreadsheet Solution
What’s the PV of $100 due in 3 years if i = 10%?
10%
Finding PVs is discounting, and it’s the reverse of compounding.
100
0
1
2
3
PV = ?
Solve FVn = PV(1 + i )n for PV:
PV
=
$100
1
=
$100
=
$.
3
Financial Calculator Solution
3 10 0 100
N I/YR PV PMT FV
Either PV or FV must be negative. Here
PV = . Put in $ today, take
out $100 after 3 years.
INPUTS
OUTPUT
Use the PV function: see spreadsheet.
= PV(Rate, Nper, Pmt, FV)
= PV(, 3, 0, 100) =
Spreadsheet Solution
Finding the Time to Double
20%
2
0
1
2
?
-1
FV = PV(1 + i)n
$2 = $1(1 + )n
()n = $2/$1 = 2
nLN() = LN(2)
n = LN(2)/LN()
n = = .
20 -1 0 2
N I/YR PV PMT FV
INPUTS
OUTPUT
Financial Calculator
Use the NPER function: see spreadsheet.
= NPER(Rate, Pmt, PV, FV)
= NPER(, 0, -1, 2) =
Spreadsheet Solution
Finding the Interest Rate
?%
2
0
1
2
3
-1
FV = PV(1 + i)n
$2 = $1(1 + i)3
(2)(1/3) = (1 + i)
= (1 + i)
i = = %.
3 -1 0 2
N I/YR PV PMT FV
INPUTS
OUTPUT
Financial Calculator
Use the RATE function:
= RATE(Nper, Pmt, PV, FV)
= RATE(3, 0, -1, 2) =
Spreadsheet Solution
Ordinary Annuity
PMT
PMT
PMT
0
1
2
3
i%
PMT
PMT
0
1
2
3
i%
PMT
Annuity Due
What’s the difference between an ordinary annuity and an annuity due?
PV
FV
What’s the FV of a 3-year ordinary annuity of $100 at 10%?
100
100
100
0
1
2
3
10%
110
121
FV = 331
The future value of an annuity with n periods and an interest rate of i can be found with the following formula:
FV Annuity Formula
Financial calculators solve this equation:
There are 5 variables. If 4 are known, the calculator will solve for the 5th.
Financial Calculator Formula
for Annuities
3 10 0 -100
N
I/YR
PV
PMT
FV
Financial Calculator Solution
Have payments but no lump sum PV, so enter 0 for present value.
INPUTS
OUTPUT
Use the FV function: see spreadsheet.
= FV(Rate, Nper, Pmt, Pv)
= FV(, 3, -100, 0) =
Spreadsheet Solution
What’s the PV of this ordinary annuity?
100
100
100
0
1
2
3
10%
= PV
The present value of an annuity with n periods and an interest rate of i can be found with the following formula:
PV Annuity Formula
Have payments but no lump sum FV, so enter 0 for future value.
3 10 100 0
N
I/YR
PV
PMT
FV
INPUTS
OUTPUT
Financial Calculator Solution
Use the PV function: see spreadsheet.
= PV(Rate, Nper, Pmt, Fv)
= PV(, 3, 100, 0) =
Spreadsheet Solution
Find the FV and PV if the
annuity were an annuity due.
100
100
0
1
2
3
10%
100
PV of annuity due:
= (PV of ordinary annuity) (1+i)
= () (1+ ) =
FV of annuity due:
= (FV of ordinary annuity) (1+i)
= () (1+ ) =
PV and FV of Annuity Due
vs. Ordinary Annuity
3 10 100 0
N
I/YR
PV
PMT
FV
Switch from “End” to “Begin”.
Then enter variables to find PVA3 = $.
Then enter PV = 0 and press FV to find
FV = $.
INPUTS
OUTPUT
Excel Function for Annuities Due
Change the formula to:
=PV(10%,3,-100,0,1)
The fourth term, 0, tells the function there are no other cash flows. The fifth term tells the function that it is an annuity due. A similar function gives the future value of an annuity due:
=FV(10%,3,-100,0,1)
What is the PV of this uneven cash
flow stream?
0
100
1
300
2
300
3
10%
-50
4
= PV
Input in “CFLO” register:
CF0 = 0
CF1 = 100
CF2 = 300
CF3 = 300
CF4 = -50
Enter I = 10%, then press NPV button to get NPV = . (Here NPV = PV.)
Spreadsheet Solution
Excel Formula in cell A3:
=NPV(10%,B2:E2)
A B C D E
1 0 1 2 3 4
2 100 300 300 -50
3
Nominal rate (iNom)
Stated in contracts, and quoted by banks and brokers.
Not used in calculations or shown on time lines
Periods per year (m) must be given.
Examples:
8%; Quarterly
8%, Daily interest (365 days)
Periodic rate (iPer )
iPer = iNom/m, where m is number of compounding periods per year. m = 4 for quarterly, 12 for monthly, and 360 or 365 for daily compounding.
Used in calculations, shown on time lines.
Examples:
8% quarterly: iPer = 8%/4 = 2%.
8% daily (365): iPer = 8%/365 = %.
Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated I% constant? Why?
LARGER! If compounding is more
frequent than once a year--for example, semiannually, quarterly,
or daily--interest is earned on interest
more often.
FV Formula with Different Compounding Periods (., $100 at a 12% nominal rate with semiannual compounding for 5 years)
= $100()10 = $.
FV
=
PV
1 .
+
i
m
n
Nom
mn
FV
=
$100
1
+
2
5S
2x5
FV of $100 at a 12% nominal rate for 5 years with different compounding
FV(Annual)= $100()5 = $.
FV(Semiannual)= $100()10=$.
FV(Quarterly)= $100()20 = $.
FV(Monthly)= $100()60 = $.
FV(Daily) = $100(1+(
= $.
Effective Annual Rate (EAR = EFF%)
The EAR is the annual rate which causes PV to grow to the same FV as under multi-period compounding Example: Invest $1 for one year at 12%, semiannual:
FV = PV(1 + iNom/m)m
FV = $1 ()2 = .
EFF% = %, because $1 invested for one year at 12% semiannual compounding would grow to the same value as $1 invested for one year at % annual compounding.
An investment with monthly payments is different from one with quarterly payments. Must put on EFF% basis to compare rates of return. Use EFF% only for comparisons.
Banks say “interest paid daily.” Same as compounded daily.
How do we find EFF% for a nominal rate of 12%, compounded semiannually?
EFF% = - 1
(1 + )
iNom
m
m
= -
(1 + )
2
2
= ()2 -
= = %.
Finding EFF with HP17BII
Go to menu starting TVM.
Select ICNV (for conversion).
Select PER (for periodic compounding).
Enter nominal rate and select NOM%.
Enter number of periods per year and select P.
Select EFF%, which returns effective rate.
EAR (or EFF%) for a Nominal Rate of of 12%
EARAnnual = 12%.
EARQ = (1 + - 1 = %.
EARM = (1 + - 1 = %.
EARD(365) = (1 + - 1 = %.
Can the effective rate ever be equal to the nominal rate?
Yes, but only if annual compounding is used, ., if m = 1.
If m > 1, EFF% will always be greater than the nominal rate.
When is each rate used?
iNom:
Written into contracts, quoted by banks and brokers. Not used in calculations or shown
on time lines.
iPer:
Used in calculations, shown on time lines.
If iNom has annual compounding,
then iPer = iNom/1 = iNom.
(Used for calculations if and only if
dealing with annuities where payments don’t match interest compounding periods.)
EAR = EFF%:
Used to compare returns on investments with different payments per year.
Amortization
Construct an amortization schedule
for a $1,000, 10% annual rate loan
with 3 equal payments.
Step 1: Find the required payments.
PMT
PMT
PMT
0
1
2
3
10%
-1,000
3 10 -1000 0
INPUTS
OUTPUT
N
I/YR
PV
FV
PMT
Step 2: Find interest charge for Year 1.
INTt = Beg balt (i)
INT1 = $1,000() = $100.
Step 3: Find repayment of principal in
Year 1.
Repmt = PMT - INT
= $ - $100
= $.
Step 4: Find ending balance after
Year 1.
End bal = Beg bal - Repmt
= $1,000 - $ = $.
Repeat these steps for Years 2 and 3
to complete the amortization table.
Interest declines. Tax implications.
BEG PRIN END
YR BAL PMT INT PMT BAL
1 $1,000 $402 $100 $302 $698
2 698 402 70 332 366
3 366 402 37 366 0
TOT 1, 1,000
$
0
1
2
3
Interest
Level payments. Interest declines because outstanding balance declines. Lender earns
10% on loan outstanding, which is falling.
Principal Payments
Amortization tables are widely used--for home mortgages, auto loans, business loans, retirement plans, and so on. They are very important!
Financial calculators (and spreadsheets) are great for setting up amortization tables.
On January 1 you deposit $100 in an account that pays a nominal interest rate of %, with daily compounding (365 days).
How much will you have on October 1, or after 9 months (273 days)? (Days given.)
iPer = %/365
= % per day.
FV=?
0
1
2
273
%
-100
Note: % in calculator, decimal in equation.
(
)
(
)
FV
=
$100
=
$100
=
$.
273
273
273 -100 0
INPUTS
OUTPUT
N
I/YR
PV
FV
PMT
iPer = iNom/m
=
= % per day.
Enter i in one step.
Leave data in calculator.
What’s the value at the end of Year 3 of the following CF stream if the quoted interest rate is 10%, compounded semiannually?
0
1
100
2
3
5%
4
5
6 6-mos.
periods
100
100
Payments occur annually, but compounding occurs each 6 months.
So we can’t use normal annuity valuation techniques.
1st Method: Compound Each CF
0
1
100
2
3
5%
4
5
6
100
FVA3 = $100()4 + $100()2 + $100
= $.
Could you find the FV with a
financial calculator?
Yes, by following these steps:
a. Find the EAR for the quoted rate:
2nd Method: Treat as an Annuity
EAR = (1 + ) - 1 = %.
2
2
3 0 -100
INPUTS
OUTPUT
N
I/YR
PV
FV
PMT
b. Use EAR = % as the annual rate in your calculator:
What’s the PV of this stream?
0
100
1
5%
2
3
100
100
You are offered a note which pays $1,000 in 15 months (or 456 days) for $850. You have $850 in a bank which pays a % nominal rate, with 365 daily compounding, which is a daily rate of % and an EAR of %. You plan to leave the money in the bank if you don’t buy the note. The note is riskless.
Should you buy it?
3 Ways to Solve:
1. Greatest future wealth: FV
2. Greatest wealth today: PV
3. Highest rate of return: Highest EFF%
iPer = % per day.
1,000
0
365
456 days
-850
1. Greatest Future Wealth
Find FV of $850 left in bank for
15 months and compare with
note’s FV = $1,000.
FVBank = $850()456
= $ in bank.
Buy the note: $1,000 > $.
456 -850 0
INPUTS
OUTPUT
N
I/YR
PV
FV
PMT
Calculator Solution to FV:
iPer = iNom/m
= %/365
= % per day.
Enter iPer in one step.
2. Greatest Present Wealth
Find PV of note, and compare
with its $850 cost:
PV = $1,000/()456
= $.
456 .018538 0 1000
INPUTS
OUTPUT
N
I/YR
PV
FV
PMT
=
PV of note is greater than its $850 cost, so buy the note. Raises your wealth.
Find the EFF% on note and compare with % bank pays, which is your opportunity cost of capital:
FVn = PV(1 + i)n
$1,000 = $850(1 + i)456
Now we must solve for i.
3. Rate of Return
456 -850 0 1000
%
per day
INPUTS
OUTPUT
N
I/YR
PV
FV
PMT
Convert % to decimal:
Decimal = = .
EAR = EFF% = ()365 - 1
= %.
Using interest conversion:
P/YR = 365
NOM% = (365) =
EFF% =
Since % > % opportunity cost,
buy the note.
Basic return concepts
Basic risk concepts
Stand-alone risk
Portfolio (market) risk
Risk and return: CAPM/SML
CHAPTER 3 Risk and Return
What are investment returns?
Investment returns measure the financial results of an investment.
Returns may be historical or prospective (anticipated).
Returns can be expressed in:
Dollar terms.
Percentage terms.
What is the return on an investment that costs $1,000 and is sold
after 1 year for $1,100?
Dollar return:
Percentage return:
$ Received - $ Invested
$1,100 - $1,000 = $100.
$ Return/$ Invested
$100/$1,000 = = 10%.
What is investment risk?
Typically, investment returns are not known with certainty.
Investment risk pertains to the probability of earning a return less than that expected.
The greater the chance of a return far below the expected return, the greater the risk.
Probability distribution
Rate of
return (%)
50
15
0
-20
Stock X
Stock Y
Which stock is riskier? Why?
Assume the Following
Investment Alternatives
Boom
Above avg.
Average
Below avg.
%
%
%
%
%
Recession
MP
USR
Coll
HT
T-Bill
Prob.
Economy
What is unique about
the T-bill return?
The T-bill will return 8% regardless of the state of the economy.
Is the T-bill riskless? Explain.
Do the returns of HT and Collections move with or counter to the economy?
HT moves with the economy, so it is positively correlated with the economy. This is the typical situation.
Collections moves counter to the economy. Such negative correlation is unusual.
Calculate the expected rate of return on each alternative.
r = expected rate of return.
rHT = (-22%) + (-2%)
+ (20%) + (35%)
+ (50%) = %.
^
^
HT has the highest rate of return.
Does that make it best?
r
Collections
T-bill
USR
Market
%
HT
^
What is the standard deviation
of returns for each alternative?
T-bills = %.
HT = %.
Coll = %.
USR = %.
M = %.
HT:
= ((-22 - ) + (-2 - )
+ (20 - ) + (35 - )
+ (50 - ))1/2 = %.
Prob.
Rate of Return (%)
T-bill
USR
HT
0
8
Standard deviation measures the stand-alone risk of an investment.
The larger the standard deviation, the higher the probability that returns will be far below the expected return.
Coefficient of variation is an alternative measure of stand-alone risk.
Expected Return versus Risk
Collections
T-bills
USR
Market
%
%
HT
Risk,
return
Security
Expected
Coefficient of Variation:
CV = standard deviation/Expected return.
CVT-BILLS = %/% = .
CVHIGH TECH = %/% = .
CVCOLLECTIONS = %/% = .
. RUBBER = %/% = .
CVM = %/% = .
Expected Return versus Coefficient of Variation
CV
Risk:
Collections
T-bills
USR
Market
HT
Security
%
return
Expected
%
Risk:
Return vs. Risk (Std. Dev.):
Which investment is best?
Portfolio Risk and Return
Assume a two-stock portfolio with $50,000 in HT and $50,000 in Collections.
Calculate rp and p.
^
Portfolio Return, rp
rp is a weighted average:
rp = (%) + (%) = %.
rp is between rHT and rColl.
^
^
^
^
^
^
^
^
rp = wiri
n
i = 1
Alternative Method
rp = (%) + (%) + (%)
+ (%) + (%) = %.
^
Estimated Return
(More...)
Boom
Above avg.
Average
Below avg.
%
%
%
Recession
Port.
Coll.
HT
Prob.
Economy
p = (( - ) + ( - ) + ( - ) + ( - ) + ( - ))1/2 = %.
p is much lower than:
either stock (20% and %).
average of HT and Coll (%).
The portfolio provides average return but much lower risk. The key here is negative correlation.
Two-Stock Portfolios
Two stocks can be combined to form a riskless portfolio if r = .
Risk is not reduced at all if the two stocks have r = +.
In general, stocks have r , so risk is lowered but not eliminated.
Investors typically hold many stocks.
What happens when r = 0?
What would happen to the
risk of an average 1-stock
portfolio as more randomly
selected stocks were added?
p would decrease because the added stocks would not be perfectly correlated, but rp would remain relatively constant.
^
Large
0
15
Prob.
2
1
1 35% ; Large 20%.
Return
# Stocks in Portfolio
10 20 30 40 2,000+
Company Specific (Diversifiable) Risk
Market Risk
20
0
Stand-Alone Risk, p
p (%)
35
Stand-alone Market Diversifiable
Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.
Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.
risk risk risk
= + .
Conclusions
As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.
p falls very slowly after about 40 stocks are included. The lower limit for p is about 20% = M .
By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.
No. Rational investors will minimize risk by holding portfolios.
They bear only market risk, so prices and returns reflect this lower risk.
The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk.
Can an investor holding one stock earn a return commensurate with its risk?
Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio.
It is measured by a stock’s beta coefficient. For stock i, its beta is:
bi = (riM si) / sM
How is market risk measured for individual securities?
How are betas calculated?
In addition to measuring a stock’s contribution of risk to a portfolio, beta also which measures the stock’s volatility relative to the market.
Using a Regression to Estimate Beta
Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.
The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.
Use the historical stock returns to calculate the beta for KWE.
%
%
10
%
%
9
%
%
8
%
%
7
%
%
6
%
%
5
%
%
4
%
%
3
%
%
2
%
%
1
KWE
Market
Year
Calculating Beta for KWE
r
KWE
=
M
+
R
2
=
-40%
-20%
0%
20%
40%
-40%
-20%
0%
20%
40%
r
M
r
KWE
What is beta for KWE?
The regression line, and hence beta, can be found using a calculator with a regression function or a spreadsheet program. In this example, b = .
Calculating Beta in Practice
Many analysts use the S&P 500 to find the market return.
Analysts typically use four or five years’ of monthly returns to establish the regression line.
Some analysts use 52 weeks of weekly returns.
How is beta interpreted?
If b = , stock has average risk.
If b > , stock is riskier than average.
If b < , stock is less risky than average.
Most stocks have betas in the range of to .
Can a stock have a negative beta?
Finding Beta Estimates on the Web
Go to
Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell.
When the quote comes up, look in the section on Fundamentals.
Expected Return versus Market Risk
Which of the alternatives is best?
Collections
T-bills
USR
Market
%
HT
Risk, b
return
Security
Expected
Use the SML to calculate each
alternative’s required return.
The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM).
SML: ri = rRF + (RPM)bi .
Assume rRF = 8%; rM = rM = 15%.
RPM = (rM - rRF) = 15% - 8% = 7%.
^
Required Rates of Return
rHT = % + (7%)()
= % + % = %.
rM = % + (7%)() = %.
rUSR = % + (7%)() = %.
rT-bill = % + (7%)() = %.
rColl = % + (7%)() = %.
Expected versus Required Returns
^
Overvalued
Coll
Fairly valued
T-bills
Undervalued
USR
Fairly valued
Market
Undervalued
%
%
HT
r
r
.
.
Coll.
.
HT
T-bills
.
USR
rM = 15
rRF = 8
-1 0 1 2
.
SML: ri = rRF + (RPM) bi
ri = 8% + (7%) bi
ri (%)
Risk, bi
SML and Investment Alternatives
Market
Calculate beta for a portfolio with 50% HT and 50% Collections
bp = Weighted average
= (bHT) + (bColl)
= () + ()
= .
What is the required rate of return
on the HT/Collections portfolio?
rp = Weighted average r
= (17%) + (2%) = %.
Or use SML:
rp = rRF + (RPM) bp
= % + 7%() = %.
SML1
Original situation
Required Rate
of Return r (%)
SML2
0
18
15
11
8
New SML
I = 3%
Impact of Inflation Change on SML
rM = 18%
rM = 15%
SML1
Original situation
Required Rate of Return (%)
SML2
After increase
in risk aversion
Risk, bi
18
15
8
RPM = 3%
Impact of Risk Aversion Change
Has the CAPM been completely confirmed or refuted through empirical tests?
No. The statistical tests have problems that make empirical verification or rejection virtually impossible.
Investors’ required returns are based on future risk, but betas are calculated with historical data.
Investors may be concerned about both stand-alone and market risk.
CHAPTER 4
Bonds and Their Valuation
Key features of bonds
Bond valuation
Measuring yield
Assessing risk
Key Features of a Bond
1. Par value: Face amount; paid at maturity. Assume $1,000.
2. Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest.
Generally fixed.
(More…)
3. Maturity: Years until bond
must be repaid. Declines.
4. Issue date: Date when bond
was issued.
5. Default risk: Risk that issuer will not make interest or principal payments.
How does adding a call provision affect a bond?
Issuer can refund if rates decline. That helps the issuer but hurts the investor.
Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.
Most bonds have a deferred call and a declining call premium.
What’s a sinking fund?
Provision to pay off a loan over its life rather than all at maturity.
Similar to amortization on a term loan.
Reduces risk to investor, shortens average maturity.
But not good for investors if rates decline after issuance.
1. Call x% at par per year for sinking fund purposes.
2. Buy bonds on open market.
Company would call if rd is below the coupon rate and bond sells at a premium. Use open market purchase if rd is above coupon rate and bond sells at a discount.
Sinking funds are generally handled in 2 ways
Financial Asset Valuation
PV
=
CF
1
+
r
.
.
.
+
CF
1
+
r
1
n
1
2
2
1
CF
r
n
.
0
1
2
n
r
CF1
CFn
CF2
Value
...
+
+
+
The discount rate (ri) is the opportunity cost of capital, ., the rate that could be earned on alternative investments of equal risk.
ri = r* + IP + LP + MRP + DRP
for debt securities.
What’s the value of a 10-year, 10% coupon bond if rd = 10%?
V
r
B
d
$100
$1
,
000
1
1
10
10
.
.
.
+
$100
1
+
r
d
100
100
0
1
2
10
10%
100 + 1,000
V = ?
...
= $ + . . . + $ + $
= $1,000.
+
+
+
1
r
+
d
10 10 100 1000
N I/YR PV PMT FV
-1,000
The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:
$
$1,
PV annuity
PV maturity value
Value of bond
=
=
=
INPUTS
OUTPUT
10 13 100 1000
N I/YR PV PMT FV
When kd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.
What would happen if expected inflation rose by 3%, causing r = 13%?
INPUTS
OUTPUT
What would happen if inflation fell, and rd declined to 7%?
10 7 100 1000
N I/YR PV PMT FV
-1,
If coupon rate > rd, price rises above par, and bond sells at a premium.
INPUTS
OUTPUT
Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?
M
Bond Value ($)
Years remaining to Maturity
1,372
1,211
1,000
837
775
30 25 20 15 10 5 0
rd = 7%.
rd = 13%.
rd = 10%.
At maturity, the value of any bond must equal its par value.
The value of a premium bond would decrease to $1,000.
The value of a discount bond would increase to $1,000.
A par bond stays at $1,000 if rd remains constant.
What’s “yield to maturity”?
YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”
What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887?
90
90
90
0
1
9
10
rd=?
1,000
PV1
.
.
.
PV10
PVM
887
Find rd that “works”!
...
10 -887 90 1000
N I/YR PV PMT FV
V
INT
r
M
r
B
d
N
d
N
1
1
1
...
+
INT
1
+
r
d
887
90
1
1
000
1
1
10
10
r
r
d
d
+
90
1
+
r
d
,
Find rd
+
+
+
+
+
+
+
+
INPUTS
OUTPUT
...
If coupon rate < rd, bond sells at a discount.
If coupon rate = rd, bond sells at its par value.
If coupon rate > rd, bond sells at a premium.
If rd rises, price falls.
Price = par at maturity.
Find YTM if price were $1,.
10 90 1000
N I/YR PV PMT FV
Sells at a premium. Because coupon = 9% > rd = %, bond’s value > par.
INPUTS
OUTPUT
Definitions
Current yield =
Capital gains yield =
= YTM = +
Annual coupon pmt
Current price
Change in price
Beginning price
Exp total
return
Exp
Curr yld
Exp cap
gains yld
Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = %.
Current yield =
= = %.
$90
$887
YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= % - %
= %.
Could also find values in Years 1 and 2,
get difference, and divide by value in
Year 1. Same answer.
What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?
rd
1-year
Change
10-year
Change
5%
$1,048
$1,386
10%
1,000
%
1,000
%
15%
956
%
749
%
Interest rate risk: Rising rd causes bond’s price to fall.
0
500
1,000
1,500
0%
5%
10%
15%
1-year
10-year
rd
Value
What is reinvestment rate risk?
The risk that CFs will have to be reinvested in the future at lower rates, reducing income.
Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.
Year 1 income = $50,000. At year-end get back $500,000 to reinvest.
If rates fall to 3%, income will drop from $50,000 to $15,000. Had you bought 30-year bonds, income would have remained constant.
Long-term bonds: High interest rate risk, low reinvestment rate risk.
Short-term bonds: Low interest rate risk, high reinvestment rate risk.
Nothing is riskless!
True or False: “All 10-year bonds have the same price and reinvestment rate risk.”
False! Low coupon bonds have less
reinvestment rate risk but more price risk than high coupon bonds.
Semiannual Bonds
1. Multiply years by 2 to get periods = 2n.
2. Divide nominal rate by 2 to get periodic rate = rd/2.
3. Divide annual INT by 2 to get PMT = INT/2.
2n rd/2 OK INT/2 OK
N I/YR PV PMT FV
INPUTS
OUTPUT
2(10) 13/2 100/2
20 50 1000
N I/YR PV PMT FV
Find the value of 10-year, 10% coupon,
semiannual bond if rd = 13%.
INPUTS
OUTPUT
Spreadsheet Functions
for Bond Valuation
See Ch 04 Mini for details.
PRICE
YIELD
You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10-year semiannual bond. Which would you prefer?
The semiannual bond’s EFF% is:
% > 10% EFF% on annual bond, so buy semiannual bond.
.
If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond?
Semiannual bond has rNom = 10%, with EFF% = %. Should earn same EFF% on annual payment bond, so:
INPUTS
OUTPUT
10 100 1000
N I/YR PV PMT FV
At a price of $, the annual and semiannual bonds would be in equilibrium, because investors would earn EFF% = % on either bond.
A 10-year, 10% semiannual coupon,
$1,000 par value bond is selling for
$1, with an 8% yield to maturity.
It can be called after 5 years at $1,050.
What’s the bond’s nominal yield to
call (YTC)?
10 50 1050
N I/YR PV PMT FV
x 2 = %
INPUTS
OUTPUT
rNom = % is the rate brokers would quote. Could also calculate EFF% to call:
EFF% = ()2 - 1 = %.
This rate could be compared to monthly mortgages, and so on.
If you bought bonds, would you be more likely to earn YTM or YTC?
Coupon rate = 10% vs. YTC = rd = %. Could raise money by selling new bonds which pay %.
Could thus replace bonds which pay $100/year with bonds that pay only $
Investors should expect a call, hence YTC = %, not YTM = 8%.
In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is likely.
So, expect to earn:
YTC on premium bonds.
YTM on par & discount bonds.
Disney recently issued 100-year bonds with a YTM of %--this represents the promised return. The expected return was less than % when the bonds were issued.
If issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return.
Bond Ratings Provide One Measure
of Default Risk
Investment Grade
Junk Bonds
Moody’s
Aaa
Aa
A
Baa
Ba
B
Caa
C
S&P
AAA
AA
A
BBB
BB
B
CCC
D
What factors affect default risk and bond ratings?
Financial performance
Debt ratio
Coverage ratios, such as interest coverage ratio or EBITDA coverage ratio
Current ratios
(More…)
Provisions in the bond contract
Secured versus unsecured debt
Senior versus subordinated debt
Guarantee provisions
Sinking fund provisions
Debt maturity
(More…)
Other factors
Earnings stability
Regulatory environment
Potential product liability
Accounting policies
Top Ten Largest . Corporate
Bond Financings, as of July 1999
Issuer
Ford Motor Co.
AT&T
RJR Holdings
WorldCom
Sprint
Date
July 1999
Mar 1999
May 1989
Aug 1998
Nov 1998
Amount
$ billion
$ billion
$ billion
$ billion
$ billion
Bankruptcy
Two main chapters of Federal Bankruptcy Act:
Chapter 11, Reorganization
Chapter 7, Liquidation
Typically, company wants Chapter 11, creditors may prefer Chapter 7.
If company can’t meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business.
Company has 120 days to file a reorganization plan.
Court appoints a “trustee” to supervise reorganization.
Management usually stays in control.
Company must demonstrate in its reorganization plan that it is “worth more alive than dead.”
Otherwise, judge will order liquidation under Chapter 7.
If the company is liquidated, here’s the payment priority:
1. Secured creditors from sales of secured assets.
2. Trustee’s costs
3. Wages, subject to limits
4. Taxes
5. Unfunded pension liabilities
6. Unsecured creditors
7. Preferred stock
8. Common stock
In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.
Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.
CHAPTER 5
Stocks and Their Valuation
Features of common stock
Determining common stock values
Efficient markets
Preferred stock
Common Stock: Owners, Directors, and Managers
Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Since managers are “agents” of shareholders, their goal should be: Maximize stock price.
What’s classified stock? How might classified stock be used?
Classified stock has special provisions.
Could classify existing stock as founders’ shares, with voting rights but dividend restrictions.
New shares might be called “Class A” shares, with voting restrictions but full dividend rights.
What is tracking stock?
The dividends of tracking stock are tied to a particular division, rather than the company as a whole.
Investors can separately value the divisions.
Its easier to compensate division managers with the tracking stock.
But tracking stock usually has no voting rights, and the financial disclosure for the division is not as regulated as for the company.
When is a stock sale an initial public offering (IPO)?
A firm “goes public” through an IPO when the stock is first offered to the public.
Prior to an IPO, shares are typically owned by the firm’s managers, key employees, and, in many situations, venture capital providers.
What is a seasoned equity offering (SEO)?
A seasoned equity offering occurs when a company with public stock issues additional shares.
After an IPO or SEO, the stock trades in the secondary market, such as the NYSE or Nasdaq.
Different Approaches for Valuing Common Stock
Dividend growth model
Using the multiples of comparable firms
Free cash flow method (covered in Chapter 12)
One whose dividends are expected to
grow forever at a constant rate, g.
Stock Value = PV of Dividends
What is a constant growth stock?
For a constant growth stock,
If g is constant, then:
$
Years (t)
0
What happens if g > rs?
If rs< g, get negative stock price, which is nonsense.
We can’t use model unless (1) g rs and (2) g is expected to be constant forever. Because g must be a long-term growth rate, it cannot be rs.
Assume beta = , kRF = 7%, and RPM = 5%. What is the required rate of return on the firm’s stock?
ks = kRF + (RPM)bFirm
= 7% + (5%) ()
= 13%.
Use the SML to calculate ks:
D0 was $ and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. rs = 13%.
0
1
2
3
g=6%
4
D0=
13%
What’s the stock’s market value?
D0 = , rs = 13%, g = 6%.
Constant growth model:
= = $.
-
$
$
What is the stock’s market value one year from now, P1?
D1 will have been paid, so expected dividends are D2, D3, D4 and so on. Thus,
^
Find the expected dividend yield and capital gains yield during the first year.
Dividend yield = = = %.
$
$
D1
P0
CG Yield = =
P1 - P0
^
P0
$ - $
$
= %.
Find the total return during the
first year.
Total return = Dividend yield + Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = g.
Rearrange model to rate of return form:
Then, rs = $ +
= + = 13%.
^
What would P0 be if g = 0?
The dividend stream would be a perpetuity.
0
1
2
3
rs=13%
P0 = = = $.
PMT
r
$
^
If we have supernormal growth of
30% for 3 years, then a long-run constant g = 6%, what is P0? r is
still 13%.
Can no longer use constant growth model.
However, growth becomes constant after 3 years.
^
Nonconstant growth followed by constant
growth:
0
1
2
3
4
rs=13%
= P0
g = 30%
g = 30%
g = 30%
g = 6%
D0 =
^
What is the expected dividend yield and capital gains yield at t = 0? At t = 4?
Dividend yield = = = %.
$
$
D1
P0
CG Yield = % - % = %.
At t = 0:
(More…)
During nonconstant growth, dividend yield and capital gains yield are not constant.
If current growth is greater than g, current capital gains yield is greater than g.
After t = 3, g = constant = 6%, so the t t = 4 capital gains gains yield = 6%.
Because rs = 13%, the t = 4 dividend yield = 13% - 6% = 7%.
Is the stock price based on
short-term growth?
The current stock price is $.
The PV of dividends beyond year 3 is $ (P3 discounted back to t = 0).
The percentage of stock price due to “long-term” dividends is:
^
= %.
$
$
If most of a stock’s value is due to long-term cash flows, why do so many managers focus on quarterly earnings?
Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This would affect the current stock price.
Sometimes managers have bonuses tied to quarterly earnings.
Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P0?
0
1
2
3
4
rs=13%
g = 0%
g = 0%
g = 0%
g = 6%
.
P
3
0
07
^
...
What is dividend yield and capital gains yield at t = 0 and at t = 3?
t = 0:
D1
P0
CGY = % - % = %.
$
%.
t = 3: Now have constant growth with g = capital gains yield = 6% and dividend yield = 7%.
If g = -6%, would anyone buy the stock? If so, at what price?
Firm still has earnings and still pays
dividends, so P0 > 0:
^
= = = $.
$()
- ()
$
What are the annual dividend
and capital gains yield?
Capital gains yield = g = %.
Dividend yield = % - (%)
= %.
Both yields are constant over time, with the high dividend yield (19%) offsetting the negative capital gains yield.
Using the Stock Price Multiples to Estimate Stock Price
Analysts often use the P/E multiple (the price per share divided by the earnings per share) or the P/CF multiple (price per share divided by cash flow per share, which is the earnings per share plus the dividends per share) to value stocks.
Example:
Estimate the average P/E ratio of comparable firms. This is the P/E multiple.
Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price.
Using Entity Multiples
The entity value (V) is:
the market value of equity (# shares of stock multiplied by the price per share)
plus the value of debt.
Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, etc.
Calculate the average entity ratio for a sample of comparable firms. For example,
V/EBITDA
V/Customers
Using Entity Multiples (Continued)
Find the entity value of the firm in question. For example,
Multiply the firm’s sales by the V/Sales multiple.
Multiply the firm’s # of customers by the V/Customers ratio
The result is the total value of the firm.
Subtract the firm’s debt to get the total value of equity.
Divide by the number of shares to get the price per share.
Problems with Market Multiple Methods
It is often hard to find comparable firms.
The average ratio for the sample of comparable firms often has a wide range.
For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?
Why are stock prices volatile?
rs = rRF + (RPM)bi could change.
Inflation expectations
Risk aversion
Company risk
g could change.
^
Stock value vs. changes in rs and g
D1 = $2, rs = 10%, and g = 5%:
P0 = D1 / (rs-g) = $2 / ( - ) = $40.
What if rs or g change?
g g g
rs 4% 5% 6%
9%
10%
11%
Are volatile stock prices consistent with rational pricing?
Small changes in expected g and rs cause large changes in stock prices.
As new information arrives, investors continually update their estimates of g and rs.
If stock prices aren’t volatile, then this means there isn’t a good flow of information.
What is market equilibrium?
^
In equilibrium, stock prices are stable.
There is no general tendency for
people to buy versus to sell.
The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price.
(More…)
In equilibrium, expected returns must
equal required returns:
rs = D1/P0 + g = rs = rRF + (rM - rRF)b.
^
How is equilibrium established?
If rs = + g > rs, then P0 is “too low.”
If the price is lower than the fundamental value, then the stock is a “bargain.”
Buy orders will exceed sell orders, the price will be bid up, and D1/P0 falls until
D1/P0 + g = rs = rs.
^
^
D1
P0
^
Why do stock prices change?
ri = rRF + (rM - rRF )bi could change.
Inflation expectations
Risk aversion
Company risk
g could change.
^
What’s the Efficient Market
Hypothesis (EMH)?
Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information.
(More…)
1. Weak-form EMH:
Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future. Evidence supports weak-form EMH, but “technical analysis” is still used.
2. Semistrong-form EMH:
All publicly available information is reflected in stock prices, so it doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true.
3. Strong-form EMH:
All information, even inside information, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.
Markets are generally efficient because:
1. 100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential.
2. These analysts have similar access to data and megabucks to invest.
3. Thus, news is reflected in P0 almost instantaneously.
Preferred Stock
Hybrid security.
Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock.
However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy.
What’s the expected return on preferred stock with Vps = $50 and annual dividend = $5?
CHAPTER 6
The Cost of Capital
Cost of Capital Components
Debt
Preferred
Common Equity
WACC
What types of long-term capital do firms use?
Long-term debt
Preferred stock
Common equity
Capital components are sources of funding that come from investors.
Accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the cost of capital.
We do adjust for these items when calculating the cash flows of a project, but not when calculating the cost of capital.
Should we focus on before-tax or
after-tax capital costs?
Tax effects associated with financing can be incorporated either in capital budgeting cash flows or in cost of capital.
Most firms incorporate tax effects in the cost of capital. Therefore, focus on after-tax costs.
Only cost of debt is affected.
Should we focus on historical (embedded) costs or new (marginal) costs?
The cost of capital is used primarily to make decisions which involve raising and investing new capital. So, we should focus on marginal costs.
Cost of Debt
Method 1: Ask an investment banker what the coupon rate would be on new debt.
Method 2: Find the bond rating for the company and use the yield on other bonds with a similar rating.
Method 3: Find the yield on the company’s debt, if it has any.
A 15-year, 12% semiannual bond sells for $1,. What’s rd?
60
60 + 1,000
60
0
1
2
30
i = ?
30 60 1000
% x 2 = rd = 10%
N
I/YR
PV
FV
PMT
-1,
...
INPUTS
OUTPUT
Component Cost of Debt
Interest is tax deductible, so the after tax (AT) cost of debt is:
rd AT = rd BT(1 - T)
= 10%(1 - ) = 6%.
Use nominal rate.
Flotation costs small, so ignore.
What’s the cost of preferred stock?
PP = $; 10%Q; Par = $100; F = $2.
Use this formula:
Picture of Preferred
0
1
2
rps = ?
...
Note:
Flotation costs for preferred are significant, so are reflected. Use net price.
Preferred dividends are not deductible, so no tax adjustment. Just rps.
Nominal rps is used.
Is preferred stock more or less risky to investors than debt?
More risky; company not required to pay preferred dividend.
However, firms want to pay preferred dividend. Otherwise, (1) cannot pay common dividend, (2) difficult to raise additional funds, and (3) preferred stockholders may gain control of firm.
Why is yield on preferred lower than rd?
Corporations own most preferred stock, because 70% of preferred dividends are nontaxable to corporations.
Therefore, preferred often has a lower B-T yield than the B-T yield on debt.
The A-T yield to investors and A-T cost to the issuer are higher on preferred than on debt, which is consistent with the higher risk of preferred.
Example:
rps = 9% rd = 10% T = 40%
rps, AT = rps - rps (1 - )(T)
= 9% - 9%()() = %
rd, AT = 10% - 10%() = %
A-T Risk Premium on Preferred = %
What are the two ways that companies can raise common equity?
Directly, by issuing new shares of common stock.
Indirectly, by reinvesting earnings that are not paid out as dividends (., retaining earnings).
Why is there a cost for reinvested earnings?
Earnings can be reinvested or paid out as dividends.
Investors could buy other securities, earn a return.
Thus, there is an opportunity cost if earnings are reinvested.
Opportunity cost: The return stockholders could earn on alternative investments of equal risk.
They could buy similar stocks and earn rs, or company could repurchase its own stock and earn rs. So, rs, is the cost of reinvested earnings and it is the cost of equity.
Three ways to determine the
cost of equity, rs:
1. CAPM: rs = rRF + (rM - rRF)b
= rRF + (RPM)b.
2. DCF: rs = D1/P0 + g.
3. Own-Bond-Yield-Plus-Risk Premium:
rs = rd + RP.
What’s the cost of equity
based on the CAPM?
rRF = 7%, RPM = 6%, b = .
rs = rRF + (rM - rRF )b.
= % + (%) = %.
Issues in Using CAPM
Most analysts use the rate on a long-term (10 to 20 years) government bond as an estimate of rRF. For a current estimate, go to, select “. Treasuries” from the section on the left under the heading “Market.”
More…
Issues in Using CAPM (Continued)
Most analysts use a rate of 5% to % for the market risk premium (RPM)
Estimates of beta vary, and estimates are “noisy” (they have a wide confidence interval). For an estimate of beta, go to and enter the ticker symbol for STOCK QUOTES.
What’s the DCF cost of equity, rs?
Given: D0 = $;P0 = $50; g = 5%.
Estimating the Growth Rate
Use the historical growth rate if you believe the future will be like the past.
Obtain analysts’ estimates: Value Line, Zack’s, Yahoo!.Finance.
Use the earnings retention model, illustrated on next slide.
Suppose the company has been earning 15% on equity (ROE = 15%) and retaining 35% (dividend payout = 65%), and this situation is expected to continue.
What’s the expected future g?
Retention growth rate:
g = ROE(Retention rate)
g = (15%) = %.
This is close to g = 5% given earlier. Think of bank account paying 15% with retention ratio = 0. What is g of account balance? If retention ratio is 100%, what is g?
Could DCF methodology be applied
if g is not constant?
YES, nonconstant g stocks are expected to have constant g at some point, generally in 5 to 10 years.
But calculations get complicated. See “Ch 6 Tool ”.
Find rs using the own-bond-yield-
plus-risk-premium method.
(rd = 10%, RP = 4%.)
This RP CAPM RPM.
Produces ballpark estimate of rs. Useful check.
rs = rd + RP
= % + % = %
What’s a reasonable final estimate
of rs?
Method Estimate
CAPM %
DCF %
rd + RP %
Average %
Determining the Weights for the WACC
The weights are the percentages of the firm that will be financed by each component.
If possible, always use the target weights for the percentages of the firm that will be financed with the various types of capital.
Estimating Weights for the
Capital Structure
If you don’t know the targets, it is better to estimate the weights using current market values than current book values.
If you don’t know the market value of debt, then it is usually reasonable to use the book values of debt, especially if the debt is short-term.
(More...)
Estimating Weights (Continued)
Suppose the stock price is $50, there are 3 million shares of stock, the firm has $25 million of preferred stock, and $75 million of debt.
(More...)
Vce = $50 (3 million) = $150 million.
Vps = $25 million.
Vd = $75 million.
Total value = $150 + $25 + $75 = $250 million.
wce = $150/$250 =
wps = $25/$250 =
wd = $75/$250 =
What’s the WACC?
WACC = wdrd(1 - T) + wpsrps + wcers
= (10%)() + (9%) + (14%)
= % + % + % = %.
WACC Estimates for Some Large
U. S. Corporations
Company WACC
General Electric (GE)
Coca-Cola (KO)
Intel (INTC)
Motorola (MOT)
Wal-Mart (WMT)
Walt Disney (DIS)
AT&T (T)
Exxon Mobil (XOM)
. Heinz (HNZ)
BellSouth (BLS)
What factors influence a company’s WACC?
Market conditions, especially interest rates and tax rates.
The firm’s capital structure and dividend policy.
The firm’s investment policy. Firms with riskier projects generally have a higher WACC.
Should the company use the composite WACC as the hurdle rate for each of its divisions?
NO! The composite WACC reflects the risk of an average project undertaken by the firm.
Different divisions may have different risks. The division’s WACC should be adjusted to reflect the division’s risk and capital structure.
What procedures are used to determine the risk-adjusted cost of capital for a particular division?
Estimate the cost of capital that the division would have if it were a stand-alone firm.
This requires estimating the division’s beta, cost of debt, and capital structure.
Methods for Estimating Beta for a Division or a Project
1. Pure play. Find several publicly traded companies exclusively in project’s business.
Use average of their betas as proxy for project’s beta.
Hard to find such companies.
2. Accounting beta. Run regression between project’s ROA and S&P index ROA.
Accounting betas are correlated ( – ) with market betas.
But normally can’t get data on new projects’ ROAs before the capital budgeting decision has been made.
Find the division’s market risk and cost of capital based on the CAPM, given these inputs:
Target debt ratio = 10%.
rd = 12%.
rRF = 7%.
Tax rate = 40%.
betaDivision = .
Market risk premium = 6%.
Beta = , so division has more market risk than average.
Division’s required return on equity:
rs = rRF + (rM – rRF)bDiv.
= 7% + (6%) = %.
WACCDiv. = wdrd(1 – T) + wcrs
= (12%)() + (%)
= %.
How does the division’s WACC compare with the firm’s overall WACC?
Division WACC = % versus company WACC = %.
“Typical” projects within this division would be accepted if their returns are above %.
Divisional Risk and the Cost of Capital
What are the three types of project risk?
Stand-alone risk
Corporate risk
Market risk
How is each type of risk used?
Stand-alone risk is easiest to calculate.
Market risk is theoretically best in most situations.
However, creditors, customers, suppliers, and employees are more affected by corporate risk.
Therefore, corporate risk is also relevant.
A Project-Specific, Risk-Adjusted
Cost of Capital
Start by calculating a divisional cost of capital.
Estimate the risk of the project using the techniques in Chapter 8.
Use judgment to scale up or down the cost of capital for an individual project relative to the divisional cost of capital.
Why is the cost of internal equity from reinvested earnings cheaper than the cost of issuing new common stock?
1. When a company issues new common stock they also have to pay flotation costs to the underwriter.
2. Issuing new common stock may send a negative signal to the capital markets, which may depress stock price.
Estimate the cost of new common equity: P0=$50, D0=$, g=5%, and F=15%.
Estimate the cost of new 30-year debt: Par=$1,000, Coupon=10%paid annually, and F=2%.
Using a financial calculator:
N = 30
PV = 1000() = 980
PMT = -(.10)(1000)() = -60
FV = -1000
Solving for I: %
Comments about flotation costs:
Flotation costs depend on the risk of the firm and the type of capital being raised.
The flotation costs are highest for common equity. However, since most firms issue equity infrequently, the per-project cost is fairly small.
We will frequently ignore flotation costs when calculating the WACC.
Four Mistakes to Avoid
1. When estimating the cost of debt, don’t use the coupon rate on existing debt. Use the current interest rate on new debt.
2. When estimating the risk premium for the CAPM approach, don’t subtract the current long-term T-bond rate from the historical average return on common stocks.
(More ...)
For example, if the historical rM has been about % and inflation drives the current rRF up to 10%, the current market risk premium is not % - 10% = %!
(More ...)
Don’t use book weights to estimate the weights for the capital structure.
Use the target capital structure to determine the weights.
If you don’t know the target weights, then use the current market value of equity, and never the book value of equity.
If you don’t know the market value of debt, then the book value of debt often is a reasonable approximation, especially for short-term debt.
(More...)
4. Always remember that capital components are sources of funding that come from investors.
Accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the WACC.
We do adjust for these items when calculating the cash flows of the project, but not when calculating the WACC.
Chapter 7: The Basics of Capital Budgeting: Evaluating Cash Flows
Overview and “vocabulary”
Methods
Payback, discounted payback
NPV
IRR, MIRR
Profitability Index
Unequal lives
Economic life
What is capital budgeting?
Analysis of potential projects.
Long-term decisions; involve large expenditures.
Very important to firm’s future.
Steps in Capital Budgeting
Estimate cash flows (inflows & outflows).
Assess risk of cash flows.
Determine r = WACC for project.
Evaluate cash flows.
What is the difference between independent and mutually exclusive projects?
Projects are:
independent, if the cash flows of one are unaffected by the acceptance of the other.
mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.
What is the payback period?
The number of years required to recover a project’s cost,
or how long does it take to get the business’s money back?
Payback for Project L
(Long: Most CFs in out years)
10
80
60
0
1
2
3
-100
=
CFt
Cumulative
-100
-90
-30
50
PaybackL
2 + 30/80 = years
0
100
Project S (Short: CFs come quickly)
70
20
50
0
1
2
3
-100
CFt
Cumulative
-100
-30
20
40
PaybackS
1 + 30/50 = years
100
0
=
Strengths of Payback:
1. Provides an indication of a project’s risk and liquidity.
2. Easy to calculate and understand.
Weaknesses of Payback:
1. Ignores the TVM.
2. Ignores CFs occurring after the payback period.
10
80
60
0
1
2
3
CFt
Cumulative
-100
Discounted
payback
2 + = yrs
Discounted Payback: Uses discounted
rather than raw CFs.
PVCFt
-100
-100
10%
=
Recover invest. + cap. costs in yrs.
NPV: Sum of the PVs of inflows and outflows.
Cost often is CF0 and is negative.
What’s Project L’s NPV?
10
80
60
0
1
2
3
10%
Project L:
= NPVL
NPVS = $.
Calculator Solution
Enter in CFLO for L:
-100
10
60
80
10
CF0
CF1
NPV
CF2
CF3
I
= = NPVL
Rationale for the NPV Method
NPV = PV inflows - Cost
= Net gain in wealth.
Accept project if NPV > 0.
Choose between mutually
exclusive projects on basis of
higher NPV. Adds most value.
Using NPV method, which project(s) should be accepted?
If Projects S and L are mutually exclusive, accept S because NPVs > NPVL .
If S & L are independent, accept both; NPV > 0.
Internal Rate of Return: IRR
0
1
2
3
CF0
CF1
CF2
CF3
Cost
Inflows
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
NPV: Enter r, solve for NPV.
IRR: Enter NPV = 0, solve for IRR.
What’s Project L’s IRR?
10
80
60
0
1
2
3
IRR = ?
PV3
PV2
PV1
0 = NPV
Enter CFs in CFLO, then press IRR:
IRRL = %.
IRRS = %.
40
40
40
0
1
2
3
IRR = ?
Find IRR if CFs are constant:
-100
Or, with CFLO, enter CFs and press
IRR = %.
3 -100 40 0
%
N
I/YR
PV
PMT
FV
INPUTS
OUTPUT
Rationale for the IRR Method
If IRR > WACC, then the project’s rate of return is greater than its cost-- some return is left over to boost stockholders’ returns.
Example: WACC = 10%, IRR = 15%.
Profitable.
Decisions on Projects S and L per IRR
If S and L are independent, accept both. IRRs > r = 10%.
If S and L are mutually exclusive, accept S because IRRS > IRRL .
Construct NPV Profiles
Enter CFs in CFLO and find NPVL and
NPVS at different discount rates:
r
0
5
10
15
20
NPVL
50
33
19
7
NPVS
40
29
20
12
5
(4)
NPV ($)
Discount Rate (%)
IRRL = %
IRRS = %
Crossover
Point = %
r
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
S
L
NPV and IRR always lead to the same accept/reject decision for independent projects:
r > IRR
and NPV < 0.
Reject.
NPV ($)
r (%)
IRR
IRR > r
and NPV > 0
Accept.
Mutually Exclusive Projects
r r
NPV
%
IRRS
IRRL
L
S
r < : NPVL> NPVS , IRRS > IRRL
CONFLICT
r > : NPVS> NPVL , IRRS > IRRL
NO CONFLICT
To Find the Crossover Rate
1. Find cash flow differences between the projects. See data at beginning of the case.
2. Enter these differences in CFLO register, then press IRR. Crossover rate = %, rounded to %.
3. Can subtract S from L or vice versa, but better to have first CF negative.
4. If profiles don’t cross, one project dominates the other.
Two Reasons NPV Profiles Cross
1. Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high r favors small projects.
2. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPVS > NPVL.
Reinvestment Rate Assumptions
NPV assumes reinvest at r (opportunity cost of capital).
IRR assumes reinvest at IRR.
Reinvest at opportunity cost, r, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.
Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR?
Yes, MIRR is the discount rate which
causes the PV of a project’s terminal
value (TV) to equal the PV of costs.
TV is found by compounding inflows
at WACC.
Thus, MIRR assumes cash inflows are reinvested at WACC.
MIRR = %
0
1
2
3
10%
MIRR for Project L (r = 10%)
10%
10%
TV inflows
PV outflows
MIRRL = %
$100 =
$
(1+MIRRL)3
To find TV with 10B, enter in CFLO:
I = 10
NPV = = PV of inflows.
Enter PV = , N = 3, I = 10, PMT = 0.
Press FV = = FV of inflows.
Enter FV = , PV = -100, PMT = 0, N = 3.
Press I = % = MIRR.
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
Why use MIRR versus IRR?
MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs.
Managers like rate of return comparisons, and MIRR is better for this than IRR.
Normal Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.
Most common: Cost (negative
CF), then string of positive CFs,
then cost to close project.
Nuclear power plant, strip mine.
Inflow (+) or Outflow (-) in Year
0
1
2
3
4
5
N
NN
-
+
+
+
+
+
N
-
+
+
+
+
-
NN
-
-
-
+
+
+
N
+
+
+
-
-
-
N
-
+
+
-
+
-
NN
Pavilion Project: NPV and IRR?
5,000
-5,000
0
1
2
r = 10%
-800
Enter CFs in CFLO, enter I = 10.
NPV =
IRR = ERROR. Why?
We got IRR = ERROR because there
are 2 IRRs. Nonnormal CFs--two sign
changes. Here’s a picture:
NPV Profile
450
-800
0
400
100
IRR2 = 400%
IRR1 = 25%
r
NPV
Logic of Multiple IRRs
1. At very low discount rates, the PV of CF2 is large & negative, so NPV < 0.
2. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0.
3. In between, the discount rate hits CF2 harder than CF1, so NPV > 0.
4. Result: 2 IRRs.
Could find IRR with calculator:
1. Enter CFs as before.
2. Enter a “guess” as to IRR by storing the guess. Try 10%:
10 STO
IRR = 25% = lower IRR
Now guess large IRR, say, 200:
200 STO
IRR = 400% = upper IRR
When there are nonnormal CFs and more than one IRR, use MIRR:
0
1
2
-800,000
5,000,000
-5,000,000
PV outflows @ 10% = -4,932,.
TV inflows @ 10% = 5,500,.
MIRR = %
Accept Project P?
NO. Reject because MIRR = % < r = 10%.
Also, if MIRR < r, NPV will be negative: NPV = -$386,777.
S and L are mutually exclusive and will be repeated. r = 10%. Which is better? (000s)
0
1
2
3
4
Project S:
(100)
Project L:
(100)
60
60
S L
CF0 -100,000 -100,000
CF1 60,000 33,500
Nj 2 4
I 10 10
NPV 4,132 6,190
NPVL > NPVS. But is L better?
Can’t say yet. Need to perform common life analysis.
Note that Project S could be repeated after 2 years to generate additional profits.
Can use either replacement chain or equivalent annual annuity analysis to make decision.
Project S with Replication:
NPV = $7,547.
Replacement Chain Approach (000s)
0
1
2
3
4
Project S:
(100)
(100)
60
60
60
(100)
(40)
60
60
60
60
Compare to Project L NPV = $6,190.
Or, use NPVs:
0
1
2
3
4
4,132
3,415
7,547
4,132
10%
If the cost to repeat S in two years rises to $105,000, which is best? (000s)
NPVS = $3,415 < NPVL = $6,190.
Now choose L.
0
1
2
3
4
Project S:
(100)
60
60
(105)
(45)
60
60
Year
0
1
2
3
CF
($5,000)
2,100
2,000
1,750
Salvage Value
$5,000
3,100
2,000
0
Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value.
1. No termination
2. Terminate 2 years
3. Terminate 1 year
(5)
(5)
(5)
2
4
0
1
2
3
CFs Under Each Alternative (000s)
NPV(no) = -$123.
NPV(2) = $215.
NPV(1) = -$273.
Assuming a 10% cost of capital, what is the project’s optimal, or economic life?
The project is acceptable only if operated for 2 years.
A project’s engineering life does not always equal its economic life.
Conclusions
Choosing the Optimal Capital Budget
Finance theory says to accept all positive NPV projects.
Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects:
An increasing marginal cost of capital.
Capital rationing
Increasing Marginal Cost of Capital
Externally raised capital can have large flotation costs, which increase the cost of capital.
Investors often perceive large capital budgets as being risky, which drives up the cost of capital.
(More...)
If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.
Capital Rationing
Capital rationing occurs when a company chooses not to fund all positive NPV projects.
The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.
(More...)
Reason: Companies want to avoid the direct costs (., flotation costs) and the indirect costs of issuing new capital.
Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital.
(More...)
Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects.
Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing.
(More...)
Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted.
Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project.
Estimating cash flows:
Relevant cash flows
Working capital treatment
Inflation
Risk Analysis: Sensitivity Analysis, Scenario Analysis, and Simulation Analysis
CHAPTER 8
Cash Flow Estimation and Risk Analysis
Cost: $200,000 + $10,000 shipping + $30,000 installation.
Depreciable cost $240,000.
Economic life = 4 years.
Salvage value = $25,000.
MACRS 3-year class.
Proposed Project
Annual unit sales = 1,250.
Unit sales price = $200.
Unit costs = $100.
Net operating working capital (NOWC) = 12% of sales.
Tax rate = 40%.
Project cost of capital = 10%.
Incremental Cash Flow for a Project
Project’s incremental cash flow is:
Corporate cash flow with the project
Minus
Corporate cash flow without the project.
NO. We discount project cash flows with a cost of capital that is the rate of return required by all investors (not just debtholders or stockholders), and so we should discount the total amount of cash flow available to all investors.
They are part of the costs of capital. If we subtracted them from cash flows, we would be double counting capital costs.
Should you subtract interest expense or dividends when calculating CF?
NO. This is a sunk cost. Focus on incremental investment and operating cash flows.
Suppose $100,000 had been spent last year to improve the production line site. Should this cost be included in the analysis?
Yes. Accepting the project means we will not receive the $25,000. This is an opportunity cost and it should be charged to the project.
. opportunity cost = $25,000 (1 - T) = $15,000 annual cost.
Suppose the plant space could be leased out for $25,000 a year. Would this affect the analysis?
Yes. The effects on the other projects’ CFs are “externalities”.
Net CF loss per year on other lines would be a cost to this project.
Externalities will be positive if new projects are complements to existing assets, negative if substitutes.
If the new product line would decrease sales of the firm’s other products by $50,000 per year, would this affect the analysis?
Basis = Cost
+ Shipping
+ Installation
$240,000
What is the depreciation basis?
Year
1
2
3
4
%
Depr.
$
x Basis =
Annual Depreciation Expense (000s)
$240
Annual Sales and Costs
Year 1 Year 2 Year 3 Year 4
Units 1250 1250 1250 1250
Unit price $200 $206 $ $
Unit cost $100 $103 $ $
Sales $250,000 $257,500 $265,225 $273,188
Costs $125,000 $128,750 $132,613 $136,588
Why is it important to include inflation when estimating cash flows?
Nominal r > real r. The cost of capital, r, includes a premium for inflation.
Nominal CF > real CF. This is because nominal cash flows incorporate inflation.
If you discount real CF with the higher nominal r, then your NPV estimate is too low.
Continued…
Inflation (Continued)
Nominal CF should be discounted with nominal r, and real CF should be discounted with real r.
It is more realistic to find the nominal CF (., increase cash flow estimates with inflation) than it is to reduce the nominal r to a real r.
Operating Cash Flows (Years 1 and 2)
Year 1 Year 2
Sales $250,000 $257,500
Costs $125,000 $128,750
Depr. $79,200 $108,000
EBIT $45,800 $20,750
Taxes (40%) $18,320 $8,300
NOPAT $27,480 $12,450
+ Depr. $79,200 $108,000
Net Op. CF $106,680 $120,450
Operating Cash Flows (Years 3 and 4)
Year 3 Year 4
Sales $265,225 $273,188
Costs $132,613 $136,588
Depr. $36,000 $16,800
EBIT $96,612 $119,800
Taxes (40%) $38,645 $47,920
NOPAT $57,967 $71,880
+ Depr. $36,000 $16,800
Net Op. CF $93,967 $88,680
Cash Flows due to Investments in Net Operating Working Capital (NOWC)
NOWC
Sales (% of sales) CF
Year 0 $30,000 -$30,000
Year 1 $250,000 $30,900 -$900
Year 2 $257,500 $31,827 -$927
Year 3 $265,225 $32,783 -$956
Year 4 $273,188 $32,783
Salvage Cash Flow at t = 4 (000s)
Salvage value
Tax on SV
Net terminal CF
$25
(10)
$35
What if you terminate a project before the asset is fully depreciated?
Cash flow from sale = Sale proceeds
- taxes paid.
Taxes are based on difference between sales price and tax basis, where:
Basis = Original basis - Accum. deprec.
Original basis = $240.
After 3 years = $ remaining.
Sales price = $25.
Tax on sale = ($25-$) = $.
Cash flow = $25-$=$.
Example: If Sold After 3 Years (000s)
Net Cash Flows for Years 1-3
Year 0 Year 1 Year 2
Init. Cost -$240,000 0 0
Op. CF 0 $106,680 $120,450
NOWC CF -$30,000 -$900 -$927
Salvage CF 0 0 0
Net CF -$270,000 $105,780 $119,523
Net Cash Flows for Years 4-5
Year 3 Year 4
Init. Cost 0 0
Op CF $93,967 $88,680
NOWC CF -$956 $32,783
Salvage CF 0 $15,000
Net CF $93,011 $136,463
Project Net CFs on a Time Line
Enter CFs in CFLO register and I = 10.
NPV = $88,030.
IRR = %.
0
1
2
3
4
(270,000)
105,780
119,523
93,011
136,463
What is the project’s MIRR? (000s)
(270,000)
MIRR = ?
0
1
2
3
4
(270,000)
105,780
119,523
93,011
136,463
102,312
144,623
140,793
524,191
1. Enter positive CFs in CFLO: I = 10; Solve for NPV = $358,.
2. Use TVM keys: PV = -358,, N = 4, I = 10; PMT = 0; Solve for FV = 524,191. (TV of inflows)
Use TVM keys: N = 4; FV = 524,191; PV = -270,000; PMT= 0; Solve for I = .
MIRR = %.
Calculator Solution
What is the project’s payback? (000s)
Cumulative:
Payback = 2 + 44/93 = years.
0
1
2
3
4
(270)*
(270)
106
(164)
120
(44)
93
49
136
185
What does “risk” mean in
capital budgeting?
Uncertainty about a project’s future profitability.
Measured by NPV, IRR, beta.
Will taking on the project increase the firm’s and stockholders’ risk?
Is risk analysis based on historical data or subjective judgment?
Can sometimes use historical data, but generally cannot.
So risk analysis in capital budgeting is usually based on subjective judgments.
What three types of risk are relevant in capital budgeting?
Stand-alone risk
Corporate risk
Market (or beta) risk
How is each type of risk measured, and how do they relate to one another?
1. Stand-Alone Risk:
The project’s risk if it were the firm’s only asset and there were no shareholders.
Ignores both firm and shareholder diversification.
Measured by the or CV of NPV, IRR, or MIRR.
0 E(NPV)
Probability Density
Flatter distribution,
larger , larger
stand-alone risk.
Such graphics are increasingly used
by corporations.
NPV
2. Corporate Risk:
Reflects the project’s effect on corporate earnings stability.
Considers firm’s other assets (diversification within firm).
Depends on:
project’s , and
its correlation, r, with returns on firm’s other assets.
Measured by the project’s corporate beta.
Profitability
0
Years
Project X
Total Firm
Rest of Firm
1. Project X is negatively correlated to firm’s other assets.
2. If r < , some diversification benefits.
3. If r = , no diversification effects.
3. Market Risk:
Reflects the project’s effect on a well-diversified stock portfolio.
Takes account of stockholders’ other assets.
Depends on project’s and correlation with the stock market.
Measured by the project’s market beta.
How is each type of risk used?
Market risk is theoretically best in most situations.
However, creditors, customers, suppliers, and employees are more affected by corporate risk.
Therefore, corporate risk is also relevant.
Continued…
Stand-alone risk is easiest to measure, more intuitive.
Core projects are highly correlated with other assets, so stand-alone risk generally reflects corporate risk.
If the project is highly correlated with the economy, stand-alone risk also reflects market risk.
What is sensitivity analysis?
Shows how changes in a variable such as unit sales affect NPV or IRR.
Each variable is fixed except one. Change this one variable to see the effect on NPV or IRR.
Answers “what if” questions, . “What if sales decline by 30%?”
Sensitivity Analysis
-30% $113 $17 $85
-15% $100 $52 $86
0% $88 $88 $88
15% $76 $124 $90
30% $65 $159 $91
Change from Resulting NPV (000s)
Base Level r Unit Sales Salvage
-30 -20 -10 Base 10 20 30
Value (%)
88
NPV
(000s)
Unit Sales
Salvage
r
Results of Sensitivity Analysis
Steeper sensitivity lines show greater risk. Small changes result in large declines in NPV.
Unit sales line is steeper than salvage value or r, so for this project, should worry most about accuracy of sales forecast.
What are the weaknesses of
sensitivity analysis?
Does not reflect diversification.
Says nothing about the likelihood of change in a variable, . a steep sales line is not a problem if sales won’t fall.
Ignores relationships among variables.
Why is sensitivity analysis useful?
Gives some idea of stand-alone risk.
Identifies dangerous variables.
Gives some breakeven information.
What is scenario analysis?
Examines several possible situations, usually worst case, most likely case, and best case.
Provides a range of possible outcomes.
Best scenario: 1,600 units @ $240
Worst scenario: 900 units @ $160
Scenario Probability NPV(000)
Best $ 279
Base 88
Worst -49
E(NPV) = $
(NPV) =
CV(NPV) = (NPV)/E(NPV) =
Are there any problems with scenario analysis?
Only considers a few possible out-comes.
Assumes that inputs are perfectly correlated--all “bad” values occur together and all “good” values occur together.
Focuses on stand-alone risk, although subjective adjustments can be made.
What is a simulation analysis?
A computerized version of scenario analysis which uses continuous probability distributions.
Computer selects values for each variable based on given probability distributions.
(More...)
NPV and IRR are calculated.
Process is repeated many times (1,000 or more).
End result: Probability distribution of NPV and IRR based on sample of simulated values.
Generally shown graphically.
Simulation Example
Assume a:
Normal distribution for unit sales:
Mean = 1,250
Standard deviation = 200
Triangular distribution for unit price:
Lower bound = $160
Most likely = $200
Upper bound = $250
Simulation Process
Pick a random variable for unit sales and sale price.
Substitute these values in the spreadsheet and calculate NPV.
Repeat the process many times, saving the input variables (units and price) and the output (NPV).
Simulation Results (1000 trials)
(See Ch 08 Min Case )
Units Price NPV
Mean 1260 $202 $95,914
St. Dev. 201 $18 $59,875
CV
Max 1883 $248 $353,238
Min 685 $163 ($45,713)
Prob NPV>0 97%
Interpreting the Results
Inputs are consistent with specificied distributions.
Units: Mean = 1260, St. Dev. = 201.
Price: Min = $163, Mean = $202, Max = $248.
Mean NPV = $95,914. Low probability of negative NPV (100% - 97% = 3%).
Histogram of Results
What are the advantages of simulation analysis?
Reflects the probability distributions of each input.
Shows range of NPVs, the expected NPV, NPV, and CVNPV.
Gives an intuitive graph of the risk situation.
What are the disadvantages of simulation?
Difficult to specify probability distributions and correlations.
If inputs are bad, output will be bad: “Garbage in, garbage out.”
(More...)
Sensitivity, scenario, and simulation analyses do not provide a decision rule. They do not indicate whether a project’s expected return is sufficient to compensate for its risk.
Sensitivity, scenario, and simulation analyses all ignore diversification. Thus they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting.
If the firm’s average project has a CV of to , is this a high-risk project? What type of risk is being measured?
CV from scenarios = , CV from simulation = . Both are > , this project has high risk.
CV measures a project’s stand-alone risk.
High stand-alone risk usually indicates high corporate and market risks.
With a 3% risk adjustment, should
our project be accepted?
Project r = 10% + 3% = 13%.
That’s 30% above base r.
NPV = $65,371.
Project remains acceptable after accounting for differential (higher) risk.
Should subjective risk factors be considered?
Yes. A numerical analysis may not capture all of the risk factors inherent in the project.
For example, if the project has the potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate.
Balance sheet
Income statement
Statement of cash flows
Accounting income versus cash flow
MVA and EVA
Personal taxes
Corporate taxes
CHAPTER 9
Financial Statements, Cash Flow, and Taxes
Income Statement
2001 2002
Sales 3,432,000 5,834,400
COGS 2,864,000 4,980,000
Other expenses 340,000 720,000
Deprec. 18,900 116,960
Tot. op. costs 3,222,900 5,816,960
EBIT 209,100 17,440
Int. expense 62,500 176,000
EBT 146,600 (158,560)
Taxes (40%) 58,640 (63,424)
Net income 87,960 (95,136)
What happened to sales and net income?
Sales increased by over $ million.
Costs shot up by more than sales.
Net income was negative.
However, the firm received a tax refund since it paid taxes of more than $63,424 during the past two years.
Balance Sheet: Assets
2001 2002
Cash 9,000 7,282
S-T invest. 48,600 20,000
AR 351,200 632,160
Inventories 715,200 1,287,360
Total CA 1,124,000 1,946,802
Gross FA 491,000 1,202,950
Less: Depr. 146,200 263,160
Net FA 344,800 939,790
Total assets 1,468,800 2,886,592
What effect did the expansion have on the asset section of the balance sheet?
Net fixed assets almost tripled in size.
AR and inventory almost doubled.
Cash and short-term investments fell.
Statement of Retained Earnings: 2002
Balance of ret. earnings,
12/31/2001 203,768
Add: Net income, 2002 (95,136)
Less: Dividends paid, 2002 (11,000)
Balance of ret. earnings,
12/31/2002 97,632
Balance Sheet: Liabilities & Equity
2001 2002
Accts. payable 145,600 324,000
Notes payable 200,000 720,000
Accruals 136,000 284,960
Total CL 481,600 1,328,960
Long-term debt 323,432 1,000,000
Common stock 460,000 460,000
Ret. earnings 203,768 97,632
Total equity 663,768 557,632
Total L&E 1,468,800 2,886,592
What effect did the expansion have on liabilities & equity?
CL increased as creditors and suppliers “financed” part of the expansion.
Long-term debt increased to help finance the expansion.
The company didn’t issue any stock.
Retained earnings fell, due to the year’s negative net income and dividend payment.
Statement of Cash Flows: 2002
Operating Activities
Net Income (95,136)
Adjustments:
Depreciation 116,960
Change in AR (280,960)
Change in inventories (572,160)
Change in AP 178,400
Change in accruals 148,960
Net cash provided by ops. (503,936)
Long-Term Investing Activities
Cash used to acquire FA (711,950)
Financing Activities
Change in S-T invest. 28,600
Change in notes payable 520,000
Change in long-term debt 676,568
Payment of cash dividends (11,000)
Net cash provided by fin. act. 1,214,168
Summary of Statement of CF
Net cash provided by ops. (503,936)
Net cash to acquire FA (711,950)
Net cash provided by fin. act. 1,214,168
Net change in cash (1,718)
Cash at beginning of year 9,000
Cash at end of year 7,282
What can you conclude from the statement of cash flows?
Net CF from operations = -$503,936, because of negative net income and increases in working capital.
The firm spent $711,950 on FA.
The firm borrowed heavily and sold some short-term investments to meet its cash requirements.
Even after borrowing, the cash account fell by $1,718.
What is free cash flow (FCF)?
Why is it important?
FCF is the amount of cash available from operations for distribution to all investors (including stockholders and debtholders) after making the necessary investments to support operations.
A company’s value depends upon the amount of FCF it can generate.
What are the five uses of FCF?
1. Pay interest on debt.
2. Pay back principal on debt.
3. Pay dividends.
4. Buy back stock.
5. Buy nonoperating assets (., marketable securities, investments in other companies, etc.)
What are operating current assets?
Operating current assets are the CA needed to support operations.
Op CA include: cash, inventory, receivables.
Op CA exclude: short-term investments, because these are not a part of operations.
What are operating current liabilities?
Operating current liabilities are the CL resulting as a normal part of operations.
Op CL include: accounts payable and accruals.
Op CA exclude: notes payable, because this is a source of financing, not a part of operations.
What effect did the expansion have on net operating working capital (NOWC)?
NOWC02 = ($7,282 + $632,160 + $1,287,360)
- ($324,000 + $284,960)
= $1,317,842.
NOWC01 = $793,800.
= -
Operating CA
Operating CL
NOWC
What effect did the expansion have on total operating capital?
= NOWC + Net fixed assets.
= $1,317,842 + $939,790
= $2,257,632.
= $1,138,600.
Operating
capital02
Operating
capital01
Operating
capital
Did the expansion create additional net operating profit after taxes (NOPAT)?
NOPAT = EBIT(1 - Tax rate)
NOPAT02 = $17,440(1 - )
= $10,464.
NOPAT01 = $125,460.
What was the free cash flow (FCF)
for 2002?
FCF = NOPAT - Net investment in capital
= $10,464 - ($2,257,632 - $1,138,600)
= $10,464 - $1,119,032
= -$1,108,568.
How do you suppose investors reacted?
Return on Invested Capital (ROIC)
ROIC = NOPAT / Total operating capital
ROIC02 = $10,464 / $2,257,632 = %.
ROIC01 = %.
The firm’s cost of capital is 10%. Did the growth add value?
No. The ROIC of % is less than the WACC of 10%. Investors did not get the return they require.
Note: High growth usually causes negative FCF (due to investment in capital), but that’s ok if ROIC > WACC. For example, Home Depot has high growth, negative FCF, but a high ROIC.
Calculate EVA. Assume the cost of capital (WACC) was 10% for both years.
EVA = NOPAT- (WACC)(Capital)
EVA02 = $10,464 - ()($2,257,632)
= $10,464 - $225,763
= -$215,299.
EVA01 = $125,460 - ()($1,138,600)
= $125,460 - $113,860
= $11,600.
Stock Price and Other Data
2001 2002
Stock price $ $
# of shares 100,000 100,000
EPS $ -$
DPS $ $
What is MVA (Market Value Added)?
MVA = Market Value of the Firm - Book Value of the Firm
Market Value = (# shares of stock)(price per share) + Value of debt
Book Value = Total common equity + Value of debt
(More…)
MVA (Continued)
If the market value of debt is close to the book value of debt, then MVA is:
MVA = Market value of equity – book value of equity
Find 2002 MVA. (Assume market value of debt = book value of debt.)
Market Value of Equity 2002:
(100,000)($) = $600,000.
Book Value of Equity 2002:
$557,632.
MVA02 = $600,000 - $557,632 = $42,368.
MVA01 = $850,000 - $663,768 = $186,232.
Key Features of the Tax Code
Corporate Taxes
Individual Taxes
2001 Corporate Tax Rates
Taxable Income
Tax on Base
Rate*
0 - 50,000
0
15%
50,000 - 75,000
7,500
25%
75,000 - 100,000
13,750
34%
100,000 - 335,000
22,250
39%
Over
35%
*Plus this percentage on the amount over the bracket base.
... ... ...
Features of Corporate Taxation
Progressive rate up until $ million taxable income.
Below $ million, the marginal rate is not equal to the average rate.
Above $ million, the marginal rate and the average rate are 35%.
Features of Corporate Taxes (Cont.)
A corporation can:
deduct its interest expenses but not its dividend payments;
carry-back losses for two years, carry-forward losses for 20 years.
exclude 70% of dividend income if it owns less than 20% of the company’s stock
Assume a corporation has $100,000 of taxable income from operations, $5,000 of interest income, and $10,000 of dividend income.
What is its tax liability?
Operating income
$100,000
Interest income
5,000
Taxable dividend
income
3,000*
Taxable income
$108,000
Tax = $22,250 + ($8,000)
= $25,370.
*Dividends - Exclusion
= $10,000 - ($10,000) = $3,000.
Key Features of Individual Taxation
Individuals face progressive tax rates, from 15% to %. (The Tax Relief Act of 2001 will reduce these rates.)
The rate on long-term (., more than one year) capital gains is 20%. But capital gains are only taxed if you sell the asset.
Interest on municipal (., state and local government) bonds is not subject to Federal taxation.
Individual Rates for 2001
Taxable Income Tax on Base Rate*
0 - 27,050 0 %
27,050 - 65,550 4, %
65,550 - 136,750 14, %
136,750 - 297,350 36, %
297,350 - 93, %
*Plus this percentage on the amount over the bracket base.
Assume your salary is $45,000, and you received $3,000 in dividends.
You are single, so your personal exemption is $2,900 and your itemized deductions are $7,100.
On the basis of the information above and the 2001 tax year tax rate schedule, what is your tax liability?
Calculation of Taxable Income
Salary
$45,000
Dividends
3,000
Personal exemptions
(2,900)
Deductions
(7,100)
Taxable Income
$38,000
Tax Liability:
TL = $4, + ($38,000-$27,050)
= $7,.
Marginal Tax Rate = %.
Average Tax Rate:
Tax rate = $7, = %.
Or
Tax rate = $7, = %.
State and local government bonds (municipals, or “munis”) are generally exempt from federal taxes.
Taxable versus Tax Exempt Bonds
Exxon bonds at 10% versus California muni bonds at 7%.
T = Tax rate = %.
After-tax interest income:
Exxon = ($5,000)- ($5,000)()
= ($5,000)() = $.
CAL = ($5,000) - 0 = $350.
Solve for T in this equation:
Muni yield = Corp Yield(1-T)
% = %(1-T)
T = %.
At what tax rate would you be indifferent between the muni and the corporate bonds?
If T > 30%, buy tax exempt munis.
If T < 30%, buy corporate bonds.
Only high income, and hence high tax bracket, individuals should buy munis.
Implications
Ratio analysis
Du Pont system
Effects of improving ratios
Limitations of ratio analysis
Qualitative factors
CHAPTER 10 Analysis of Financial Statements
Income Statement
2002 2003E
Sales 5,834,400 7,035,600
COGS 4,980,000 5,800,000
Other expenses 720,000 612,960
Deprec. 116,960 120,000
Tot. op. costs 5,816,960 6,532,960
EBIT 17,440 502,640
Int. expense 176,000 80,000
EBT (158,560) 422,640
Taxes (40%) (63,424) 169,056
Net income (95,136) 253,584
Balance Sheets: Assets
2002 2003E
Cash 7,282 14,000
S-T invest. 20,000 71,632
AR 632,160 878,000
Inventories 1,287,360 1,716,480
Total CA 1,946,802 2,680,112
Net FA 939,790 836,840
Total assets 2,886,592 3,516,952
Balance Sheets: Liabilities & Equity
2002 2003E
Accts. payable 324,000 359,800
Notes payable 720,000 300,000
Accruals 284,960 380,000
Total CL 1,328,960 1,039,800
Long-term debt 1,000,000 500,000
Common stock 460,000 1,680,936
Ret. earnings 97,632 296,216
Total equity 557,632 1,977,152
Total L&E 2,886,592 3,516,952
Other Data
2002 2003E
Stock price $ $
# of shares 100,000 250,000
EPS -$ $
DPS $ $
Book val. per share $ $
Lease payments 40,000 40,000
Tax rate
Why are ratios useful?
Standardize numbers; facilitate comparisons
Used to highlight weaknesses and strengths
What are the five major categories of ratios, and what questions do they answer?
Liquidity: Can we make required payments as they fall due?
Asset management: Do we have the right amount of assets for the level of sales?
(More…)
Debt management: Do we have the right mix of debt and equity?
Profitability: Do sales prices exceed unit costs, and are sales high enough as reflected in PM, ROE, and ROA?
Market value: Do investors like what they see as reflected in P/E and M/B ratios?
Calculate the firm’s forecasted current and quick ratios for 2003.
CR03 = = = .
QR03 =
= = .
CA
CL
$2,680
$1,040
$2,680 - $1,716
$1,040
CA - Inv.
CL
Comments on CR and QR
Expected to improve but still below the industry average.
Liquidity position is weak.
2003E 2002 2001 Ind.
CR
QR
What is the inventory turnover ratio as compared to the industry average?
Inv. turnover =
= = .
Sales
Inventories
$7,036
$1,716
2003E 2002 2001 Ind.
Inv. T.
Comments on Inventory Turnover
Inventory turnover is below industry average.
Firm might have old inventory, or its control might be poor.
No improvement is currently forecasted.
Receivables
Average sales per day
DSO is the average number of days after making a sale before receiving cash.
DSO =
= =
= days.
Receivables
Sales/365
$878
$7,036/365
Appraisal of DSO
Firm collects too slowly, and situation is getting worse.
Poor credit policy.
2003 2002 2001 Ind.
DSO
Fixed Assets and Total Assets
Turnover Ratios
Fixed assets
turnover
Sales
Net fixed assets
=
= = .
$7,036
$837
Total assets
turnover
Sales
Total assets
=
= = .
$7,036
$3,517
(More…)
FA turnover is expected to exceed industry average. Good.
TA turnover not up to industry average. Caused by excessive current assets (A/R and inventory).
2003E 2002 2001 Ind.
FA TO
TA TO
Total liabilities
Total assets
Debt ratio =
= = %.
$1,040 + $500
$3,517
EBIT
Int. expense
TIE =
= = .
$
$80
Calculate the debt, TIE, and EBITDA coverage ratios.
(More…)
All three ratios reflect use of debt, but focus on different aspects.
EBITDA
coverage
= EC
= = .
EBIT + Depr. & Amort. + Lease payments
Interest Lease
expense pmt.
+ + Loan pmt.
$ + $120 + $40
$80 + $40 + $0
Recapitalization improved situation, but lease payments drag down EC.
How do the debt management ratios compare with industry averages?
2003E 20012 2001 Ind.
D/A % % % %
TIE
EC
Profit Margin (PM)
Very bad in 2002, but projected to
meet industry average in 2003. Looking good.
2003E 2002 2001 Ind.
PM % % % %
PM = = = %.
NI
Sales
$
$7,036
BEP =
= = %.
Basic Earning Power (BEP)
EBIT
Total assets
$
$3,517
(More…)
BEP removes effect of taxes and financial leverage. Useful for comparison.
Projected to be below average.
Room for improvement.
2003E 2002 2001 Ind.
BEP % % % %
ROA =
= = %.
Return on Assets (ROA)
and Return on Equity (ROE)
Net income
Total assets
$
$3,517
(More…)
ROE =
= = %.
Net income
Common equity
$
$1,977
2003E 2002 2001 Ind.
ROA % % % %
ROE % % % %
Both below average but improving.
ROA is lowered by debt--interest expense lowers net income, which also lowers ROA.
However, the use of debt lowers equity, and if equity is lowered more than net income, ROE would increase.
Effects of Debt on ROA and ROE
Calculate and appraise the
P/E, P/CF, and M/B ratios.
Price = $.
EPS = = = $.
P/E = = = 12x.
NI
Shares out.
$
250
Price per share
EPS
$
$
Industry P/E Ratios
Industry Ticker* P/E
Banking STI
Software MSFT
Drug PFE
Electric Utilities DUK
Semiconductors INTC
Steel NUE
Tobacco MO
Water Utilities CFT
S&P 500
*Ticker is for typical firm in industry, but P/E ratio is for the industry, not the individual firm.
NI + Depr.
Shares out.
CF per share =
= = $.
$ + $
250
Price per share
Cash flow per share
P/CF =
= = .
$
$
Com. equity
Shares out.
BVPS =
= = $.
$1,977
250
Mkt. price per share
Book value per share
M/B =
= = .
$
$
P/E: How much investors will pay for $1 of earnings. High is good.
M/B: How much paid for $1 of book value. Higher is good.
P/E and M/B are high if ROE is high, risk is low.
2003E 2002 2001 Ind.
P/E
P/CF
M/B
Common Size Balance Sheets:
Divide all items by Total Assets
Assets 2001 2002 2003E Ind.
Cash % % % %
ST Invest. % % % %
AR % % % %
Invent. % % % %
Total CA % % % %
Net FA % % % %
TA % % % %
Divide all items by
Total Liabilities & Equity
2001 2002 2003E Ind.
AP % % % %
Notes pay. % % % %
Accruals % % % %
Total CL % % % %
LT Debt % % % %
Total eq. % % % %
Total L&E % % % %
Analysis of Common Size Balance Sheets
Computron has higher proportion of inventory and current assets than Industry.
Computron now has more equity (which means LESS debt) than Industry.
Computron has more short-term debt than industry, but less long-term debt than industry.
Common Size Income Statement:
Divide all items by Sales
2001 2002 2003E Ind.
Sales % % % %
COGS % % % %
Other exp. % % % %
Depr. % % % %
EBIT % % % %
Int. Exp. % % % %
EBT % % % %
Taxes % % % %
NI % % % %
Analysis of Common Size Income Statements
Computron has lower COGS () than industry (), but higher other expenses. Result is that Computron has similar EBIT () as industry.
Percentage Change Analysis: Find Percentage Change from First Year (2001)
Income St. 2001 2002 2003E
Sales % % %
COGS % % %
Other exp. % % %
Depr. % % %
EBIT % % %
Int. Exp. % % %
EBT % % %
Taxes % % %
NI % % %
Analysis of Percent Change Income Statement
We see that 2003 sales grew 105% from 2001, and that NI grew 188% from 2001.
So Computron has become more profitable.
Percentage Change Balance Sheets
Assets 2001 2002 2003E
Cash % % %
ST Invest. % % %
AR % % %
Invent. % % %
Total CA % % %
Net FA % % %
TA % % %
Liab. & Eq. 2001 2002 2003E
AP % % %
Notes pay. % % %
Accruals % % %
Total CL % % %
LT Debt % % %
Total eq. % % %
Total L&E % % %
Analysis of Percent Change Balance Sheets
We see that total assets grew at a rate of 139%, while sales grew at a rate of only 105%. So asset utilization remains a problem.
Explain the Du Pont System
The Du Pont system focuses on:
Expense control (PM)
Asset utilization (TATO)
Debt utilization (EM)
It shows how these factors combine to determine the ROE.
( )( )( ) = ROE
Profit
margin
TA
turnover
Equity
multiplier
NI
Sales
Sales
TA
TA
CE
2001 % x x = %
2002 % x x = %
2003 % x x = %
Ind. % x x = %
The Du Pont System
x
x
= ROE.
What are some potential problems and limitations of financial ratio analysis?
Comparison with industry averages is difficult if the firm operates many different divisions.
“Average” performance is not necessarily good.
Seasonal factors can distort ratios.
(More…)
Window dressing techniques can make statements and ratios look better.
Different accounting and operating practices can distort comparisons.
Sometimes it is difficult to tell if a ratio value is “good” or “bad.”
Often, different ratios give different signals, so it is difficult to tell, on balance, whether a company is in a strong or weak financial condition.
What are some qualitative factors analysts should consider when evaluating a company’s likely future financial performance?
Are the company’s revenues tied to a single customer?
To what extent are the company’s revenues tied to a single product?
To what extent does the company rely on a single supplier?
(More…)
What percentage of the company’s business is generated overseas?
What is the competitive situation?
What does the future have in store?
What is the company’s legal and regulatory environment?
CHAPTER 11
Financial Planning and Forecasting Financial Statements
Financial planning
Additional Funds Needed (AFN) formula
Pro forma financial statements
Sales forecasts
Percent of sales method
Financial Planning and
Pro Forma Statements
Three important uses:
Forecast the amount of external financing that will be required
Evaluate the impact that changes in the operating plan have on the value of the firm
Set appropriate targets for compensation plans
Steps in Financial Forecasting
Forecast sales
Project the assets needed to support sales
Project internally generated funds
Project outside funds needed
Decide how to raise funds
See effects of plan on ratios and stock price
2002 Balance Sheet
(Millions of $)
Cash & sec.
$ 20
Accts. pay. &
accruals
$ 100
Accounts rec.
240
Notes payable
100
Inventories
240
Total CL
$ 200
Total CA
$ 500
L-T debt
100
Common stk
500
Net fixed
assets
Retained
earnings
200
Total assets
$1,000
Total claims
$1,000
500
2002 Income Statement
(Millions of $)
Sales
$2,
Less: COGS (60%)
1,
SGA costs
EBIT
$
Interest
EBT
$
Taxes (40%)
Net income
$
Dividends (40%)
$
Add’n to RE
$
AFN (Additional Funds Needed):
Key Assumptions
Operating at full capacity in 2002.
Each type of asset grows proportionally with sales.
Payables and accruals grow proportionally with sales.
2002 profit margin ($54/$2,000 = %) and payout (40%) will be maintained.
Sales are expected to increase by $500 million.
Definitions of Variables in AFN
A*/S0: assets required to support sales; called capital intensity ratio.
S: increase in sales.
L*/S0: spontaneous liabilities ratio
M: profit margin (Net income/sales)
RR: retention ratio; percent of net income not paid as dividend.
Assets
Sales
0
1,000
2,000
1,250
2,500
A*/S0 = $1,000/$2,000 =
= $1,250/$2,500.
Assets =
(A*/S0)Sales
= ($500)
= $250.
Assets = sales
Assets must increase by $250 million. What is the AFN, based on the AFN equation?
AFN = (A*/S0)S - (L*/S0)S - M(S1)(RR)
= ($1,000/$2,000)($500)
- ($100/$2,000)($500)
- ($2,500)(1 - )
= $ million.
How would increases in these items affect the AFN?
Higher sales:
Increases asset requirements, increases AFN.
Higher dividend payout ratio:
Reduces funds available internally, increases AFN.
(More…)
Higher profit margin:
Increases funds available internally, decreases AFN.
Higher capital intensity ratio, A*/S0:
Increases asset requirements, increases AFN.
Pay suppliers sooner:
Decreases spontaneous liabilities, increases AFN.
Projecting Pro Forma Statements with the Percent of Sales Method
Project sales based on forecasted growth rate in sales
Forecast some items as a percent of the forecasted sales
Costs
Cash
Accounts receivable
(More...)
Items as percent of sales (Continued...)
Inventories
Net fixed assets
Accounts payable and accruals
Choose other items
Debt
Dividend policy (which determines retained earnings)
Common stock
Sources of Financing Needed to Support Asset Requirements
Given the previous assumptions and choices, we can estimate:
Required assets to support sales
Specified sources of financing
Additional funds needed (AFN) is:
Required assets minus specified sources of financing
Implications of AFN
If AFN is positive, then you must secure additional financing.
If AFN is negative, then you have more financing than is needed.
Pay off debt.
Buy back stock.
Buy short-term investments.
How to Forecast Interest Expense
Interest expense is actually based on the daily balance of debt during the year.
There are three ways to approximate interest expense. Base it on:
Debt at end of year
Debt at beginning of year
Average of beginning and ending debt
More…
Basing Interest Expense
on Debt at End of Year
Will over-estimate interest expense if debt is added throughout the year instead of all on January 1.
Causes circularity called financial feedback: more debt causes more interest, which reduces net income, which reduces retained earnings, which causes more debt, etc.
More…
Basing Interest Expense
on Debt at Beginning of Year
Will under-estimate interest expense if debt is added throughout the year instead of all on December 31.
But doesn’t cause problem of circularity.
More…
Basing Interest Expense on Average of Beginning and Ending Debt
Will accurately estimate the interest payments if debt is added smoothly throughout the year.
But has problem of circularity.
More…
A Solution that Balances Accuracy and Complexity
Base interest expense on beginning debt, but use a slightly higher interest rate.
Easy to implement
Reasonably accurate
See Ch 11 Mini Case for an example basing interest expense on average debt.
Percent of Sales: Inputs
COGS/Sales 60% 60%
SGA/Sales 35% 35%
Cash/Sales 1% 1%
Acct. rec./Sales 12% 12%
Inv./Sales 12% 12%
Net FA/Sales 25% 25%
AP & accr./Sales 5% 5%
2002 2003
Actual Proj.
Other Inputs
Percent growth in sales 25%
Growth factor in sales (g)
Interest rate on debt 10%
Tax rate 40%
Dividend payout rate 40%
2003 Forecasted Income Statement
2002
Factor
2003
1st Pass
Sales
$2,000
g=
$2,
Less: COGS
Pct=60%
1,
SGA
Pct=35%
EBIT
$
Interest
(Debt02)
EBT
$
Taxes (40%)
Net. income
$
Div. (40%)
$
Add. to RE
$
2003 Balance Sheet (Assets)
Forecasted assets are a percent of forecasted sales.
Factor
2003
Cash
Pct= 1%
$
Accts. rec.
Pct=12%
Pct=12%
Total CA
$
Net FA
Pct=25%
Total assets
$1,
2003 Sales = $2,500
Inventories
2003 Preliminary Balance Sheet (Claims)
*From forecasted income statement.
2002
Factor
Without AFN
AP/accruals
Pct=5%
$
Notes payable
100
Total CL
$
L-T debt
100
Common stk.
500
Ret. earnings
200
+*
Total claims
$1,
2003
2003 Sales = $2,500
What are the additional funds
needed (AFN)?
Required assets = $1,
Specified sources of fin. = $1,
Forecast AFN = $
NWC must have the assets to make forecasted sales, and so it needs an equal amount of financing. So, we must secure another $ of financing.
Assumptions about How AFN Will
Be Raised
No new common stock will be issued.
Any external funds needed will be raised as debt, 50% notes payable, and 50% L-T debt.
How will the AFN be financed?
Additional notes payable =
($) = $.
Additional L-T debt =
($) = $.
2003 Balance Sheet (Claims)
w/o AFN AFN With AFN
AP/accruals $ $
Notes payable +
Total CL $ $
L-T debt +
Common stk.
Ret. earnings
Total claims $1, $1,
Equation method assumes a constant profit margin.
Pro forma method is more flexible. More important, it allows different items to grow at different rates.
Equation AFN = $ vs. Pro Forma AFN = $. Why are they different?
Forecasted Ratios
2002 2003(E) Industry
Profit Margin % % %
ROE % % %
DSO (days)
Inv. turnover
FA turnover
Debt ratio % % %
TIE
Current ratio
What are the forecasted
free cash flow and ROIC?
2002 2003(E)
Net operating WC $400 $500
(CA - AP & accruals)
Total operating capital $900 $1,125
(Net op. WC + net FA)
NOPAT (EBITx(1-T)) $60 $75
Less Inv. in op. capital $225
Free cash flow -$150
ROIC (NOPAT/Capital) %
Proposed Improvements
DSO (days)
Accts. rec./Sales % %
Inventory turnover
Inventory/Sales % %
SGA/Sales % %
Before After
Impact of Improvements
(see Ch 11 Mini for details)
AFN $ $
Free cash flow -$ $
ROIC (NOPAT/Capital) % %
ROE % %
Before After
Suppose in 2002 fixed assets had been operated at only 75% of capacity.
With the existing fixed assets, sales could be $2,667. Since sales are forecasted at only $2,500, no new fixed assets are needed.
Capacity sales =
Actual sales
% of capacity
= = $2,667.
$2,000
How would the excess capacity situation affect the 2003 AFN?
The previously projected increase in fixed assets was $125.
Since no new fixed assets will be needed, AFN will fall by $125, to
$ - $125 = $.
Assets
Sales
0
1,100
1,000
2,000
2,500
Declining A/S Ratio
$1,000/$2,000 = ; $1,100/$2,500 = . Declining ratio shows economies of scale. Going from S = $0 to S = $2,000 requires $1,000 of assets. Next $500 of sales requires only $100 of assets.
Base
Stock
Economies of Scale
Assets
Sales
1,000
2,000
500
A/S changes if assets are lumpy. Generally will have excess capacity, but eventually a small S leads to a large A.
500
1,000
1,500
Lumpy Assets
Summary: How different factors affect the AFN forecast.
Excess capacity: lowers AFN.
Economies of scale: leads to less-than-proportional asset increases.
Lumpy assets: leads to large periodic AFN requirements, recurring excess capacity.
CHAPTER 12
Corporate Valuation and Value-Based Management
Corporate Valuation
Value-Based Management
Corporate Governance
Corporate Valuation:
List the two types of assets that a company owns.
Assets-in-place
Financial, or nonoperating, assets
Assets-in-Place
Assets-in-place are tangible, such as buildings, machines, inventory.
Usually they are expected to grow.
They generate free cash flows.
The PV of their expected future free cash flows, discounted at the WACC, is the value of operations.
Value of Operations
Nonoperating Assets
Marketable securities
Ownership of non-controlling interest in another company
Value of nonoperating assets usually is very close to figure that is reported on balance sheets.
Total Corporate Value
Total corporate value is sum of:
Value of operations
Value of nonoperating assets
Claims on Corporate Value
Debtholders have first claim.
Preferred stockholders have the next claim.
Any remaining value belongs to stockholders.
Applying the Corporate Valuation Model
Forecast the financial statements, as shown in Chapter 11.
Calculate the projected free cash flows.
Model can be applied to a company that does not pay dividends, a privately held company, or a division of a company, since FCF can be calculated for each of these situations.
Data for Valuation
FCF0 = $20 million
WACC = 10%
g = 5%
Marketable securities = $100 million
Debt = $200 million
Preferred stock = $50 million
Book value of equity = $210 million
Value of Operations:
Constant Growth
Suppose FCF grows at constant rate g.
Constant Growth Formula
Notice that the term in parentheses is less than one and gets smaller as t gets larger. As t gets very large, term approaches zero.
Constant Growth Formula (Cont.)
The summation can be replaced by a single formula:
Find Value of Operations
Value of Equity
Sources of Corporate Value
Value of operations = $420
Value of non-operating assets = $100
Claims on Corporate Value
Value of Debt = $200
Value of Preferred Stock = $50
Value of Equity = ?
Value of Equity
Total corporate value = VOp + Mkt. Sec.
= $420 + $100
= $520 million
Value of equity = Total - Debt - Pref.
= $520 - $200 - $50
= $270 million
Market Value Added (MVA)
MVA = Total corporate value of firm minus total book value of firm
Total book value of firm = book value of equity + book value of debt + book value of preferred stock
MVA = $520 - ($210 + $200 + $50)
= $60 million
Breakdown of Corporate Value
Expansion Plan: Nonconstant Growth
Finance expansion by borrowing $40 million and halting dividends.
Projected free cash flows (FCF):
Year 1 FCF = -$5 million.
Year 2 FCF = $10 million.
Year 3 FCF = $20 million
FCF grows at constant rate of 6% after year 3.
(More…)
The weighted average cost of capital, rc, is 10%.
The company has 10 million shares of stock.
Horizon Value
Free cash flows are forecast for three years in this example, so the forecast horizon is three years.
Growth in free cash flows is not constant during the forecast,so we can’t use the constant growth formula to find the value of operations at time 0.
Horizon Value (Cont.)
Growth is constant after the horizon (3 years), so we can modify the constant growth formula to find the value of all free cash flows beyond the horizon, discounted back to the horizon.
Horizon Value Formula
Horizon value is also called terminal value, or continuing value.
Vop at 3
Find the value of operations by discounting the free cash flows at the cost of capital.
0
1
2
3
4
rc=10%
= Vop
g = 6%
FCF=
$
.
.
$530.
10
0
06
0
Find the price per share of common stock.
Value of equity = Value of operations
- Value of debt
= $ - $40
= $ million.
Price per share = $ /10 = $.
Value-Based Management (VBM)
VBM is the systematic application of the corporate valuation model to all corporate decisions and strategic initiatives.
The objective of VBM is to increase Market Value Added (MVA)
MVA and the Four Value Drivers
MVA is determined by four drivers:
Sales growth
Operating profitability (OP=NOPAT/Sales)
Capital requirements (CR=Operating capital / Sales)
Weighted average cost of capital
MVA for a Constant Growth Firm
Insights from the Constant Growth Model
The first bracket is the MVA of a firm that gets to keep all of its sales revenues (., its operating profit margin is 100%) and that never has to make additional investments in operating capital.
Insights (Cont.)
The second bracket is the operating profit (as a %) the firm gets to keep, less the return that investors require for having tied up their capital in the firm.
Improvements in MVA due to the Value Drivers
MVA will improve if:
WACC is reduced
operating profitability (OP) increases
the capital requirement (CR) decreases
The Impact of Growth
The second term in brackets can be either positive or negative, depending on the relative size of profitability, capital requirements, and required return by investors.
The Impact of Growth (Cont.)
If the second term in brackets is negative, then growth decreases MVA. In other words, profits are not enough to offset the return on capital required by investors.
If the second term in brackets is positive, then growth increases MVA.
Expected Return on Invested Capital (EROIC)
The expected return on invested capital is the NOPAT expected next period divided by the amount of capital that is currently invested:
MVA in Terms of Expected ROIC
If the spread between the expected return, EROICt, and the required return, WACC, is positive, then MVA is positive and growth makes MVA larger. The opposite is true if the spread is negative.
The Impact of Growth on MVA
A company has two divisions. Both have current sales of $1,000, current expected growth of 5%, and a WACC of 10%.
Division A has high profitability (OP=6%) but high capital requirements (CR=78%).
Division B has low profitability (OP=4%) but low capital requirements (CR=27%).
What is the impact on MVA if growth goes from 5% to 6%?
Division A Division B
OP 6% 6% 4% 4%
CR 78% 78% 27% 27%
Growth 5% 6% 5% 6%
MVA () ()
Note: MVA is calculated using the formula on slide 12-27.
Expected ROIC and MVA
Division A Division B
Capital0 $780 $780 $270 $270
Growth 5% 6% 5% 6%
Sales1 $1,050 $1,060 $1,050 $1,060
NOPAT1 $63 $ $42 $
EROIC0 % % % %
MVA () ()
Analysis of Growth Strategies
The expected ROIC of Division A is less than the WACC, so the division should postpone growth efforts until it improves EROIC by reducing capital requirements (., reducing inventory) and/or improving profitability.
The expected ROIC of Division B is greater than the WACC, so the division should continue with its growth plans.
Two Primary Mechanisms of Corporate Governance
“Stick”
Provisions in the charter that affect takeovers.
Composition of the board of directors.
“Carrot: Compensation plans.
Entrenched Management
Occurs when there is little chance that poorly performing managers will be replaced.
Two causes:
Anti-takeover provisions in the charter
Weak board of directors
How are entrenched managers harmful to shareholders?
Management consumes perks:
Lavish offices and corporate jets
Excessively large staffs
Memberships at country clubs
Management accepts projects (or acquisitions) to make firm larger, even if MVA goes down.
Anti-Takeover Provisions
Targeted share repurchases (., greenmail)
Shareholder rights provisions (., poison pills)
Restricted voting rights plans
Board of Directors
Weak boards have many insiders (., those who also have another position in the company) compared with outsiders.
Interlocking boards are weaker (CEO of company A sits on board of company B, CEO of B sits on board of A).
Stock Options in Compensation Plans
Gives owner of option the right to buy a share of the company’s stock at a specified price (called the exercise price) even if the actual stock price is higher.
Usually can’t exercise the option for several years (called the vesting period).
Stock Options (Cont.)
Can’t exercise the option after a certain number of years (called the expiration, or maturity, date).
Chapter 13: Capital Structure Decisions
Overview and preview of capital structure effects
Business versus financial risk
The impact of debt on returns
Capital structure theory
Example: Choosing the optimal structure
Setting the capital structure in practice
Basic Definitions
V = value of firm
FCF = free cash flow
WACC = weighted average cost of capital
rs and rd are costs of stock and debt
re and wd are percentages of the firm that are financed with stock and debt.
How can capital structure affect value?
(Continued…)
WACC = wd (1-T) rd + we rs
A Preview of Capital Structure Effects
The impact of capital structure on value depends upon the effect of debt on:
WACC
FCF
(Continued…)
The Effect of Additional Debt on WACC
Debtholders have a prior claim on cash flows relative to stockholders.
Debtholders’ “fixed” claim increases risk of stockholders’ “residual” claim.
Cost of stock, rs, goes up.
Firm’s can deduct interest expenses.
Reduces the taxes paid
Frees up more cash for payments to investors
Reduces after-tax cost of debt
(Continued…)
The Effect on WACC (Continued)
Debt increases risk of bankruptcy
Causes pre-tax cost of debt, rd, to increase
Adding debt increase percent of firm financed with low-cost debt (wd) and decreases percent financed with high-cost equity (we)
Net effect on WACC = uncertain.
(Continued…)
The Effect of Additional Debt on FCF
Additional debt increases the probability of bankruptcy.
Direct costs: Legal fees, “fire” sales, etc.
Indirect costs: Lost customers, reduction in productivity of managers and line workers, reduction in credit (., accounts payable) offered by suppliers
(Continued…)
Impact of indirect costs
NOPAT goes down due to lost customers and drop in productivity
Investment in capital goes up due to increase in net operating working capital (accounts payable goes up as suppliers tighten credit).
(Continued…)
Additional debt can affect the behavior of managers.
Reductions in agency costs: debt “pre-commits,” or “bonds,” free cash flow for use in making interest payments. Thus, managers are less likely to waste FCF on perquisites or non-value adding acquisitions.
Increases in agency costs: debt can make managers too risk-averse, causing “underinvestment” in risky but positive NPV projects.
(Continued…)
Asymmetric Information and Signaling
Managers know the firm’s future prospects better than investors.
Managers would not issue additional equity if they thought the current stock price was less than the true value of the stock (given their inside information).
Hence, investors often perceive an additional issuance of stock as a negative signal, and the stock price falls.
What is business risk?
Uncertainty about future pre-tax operating income (EBIT).
Note that business risk focuses on operating income, so it ignores financing effects.
Probability
EBIT
E(EBIT)
0
Low risk
High risk
Factors That Influence Business Risk
Uncertainty about demand (unit sales).
Uncertainty about output prices.
Uncertainty about input costs.
Product and other types of liability.
Degree of operating leverage (DOL).
What is operating leverage, and how does it affect a firm’s business risk?
Operating leverage is the change in EBIT caused by a change in quantity sold.
The higher the proportion of fixed costs within a firm’s overall cost structure, the greater the operating leverage.
(More...)
Higher operating leverage leads to more business risk, because a small sales decline causes a larger EBIT decline.
(More...)
Sales
$
Rev.
TC
F
QBE
Sales
$
Rev.
TC
F
QBE
EBIT
}
Operating Breakeven
Q is quantity sold, F is fixed cost, V is variable cost, TC is total cost, and P is price per unit.
Operating breakeven = QBE
QBE = F / (P – V)
Example: F=$200, P=$15, and V=$10:
QBE = $200 / ($15 – $10) = 40.
(More...)
Probability
EBITL
Low operating leverage
High operating leverage
EBITH
In the typical situation, higher operating leverage leads to higher expected EBIT, but also increases risk.
Business Risk versus Financial Risk
Business risk:
Uncertainty in future EBIT.
Depends on business factors such as competition, operating leverage, etc.
Financial risk:
Additional business risk concentrated on common stockholders when financial leverage is used.
Depends on the amount of debt and preferred stock financing.
Firm U Firm L
No debt $10,000 of 12% debt
$20,000 in assets $20,000 in assets
40% tax rate 40% tax rate
Consider Two Hypothetical Firms
Both firms have same operating leverage, business risk, and EBIT of $3,000. They differ only with respect to use of debt.
Impact of Leverage on Returns
EBIT $3,000 $3,000
Interest 0 1,200
EBT $3,000 $1,800
Taxes (40%) 1 ,200 720
NI $1,800 $1,080
ROE % %
Firm U Firm L
Why does leveraging increase return?
More EBIT goes to investors in Firm L.
Total dollars paid to investors:
U: NI = $1,800.
L: NI + Int = $1,080 + $1,200 = $2,280.
Taxes paid:
U: $1,200; L: $720.
Equity $ proportionally lower than NI.
Now consider the fact that EBIT is not known with certainty. What is the impact of uncertainty on stockholder profitability and risk for Firm U and Firm L?
Continued…
Firm U: Unleveraged
Prob.
EBIT $2,000 $3,000 $4,000
Interest 0 0 0
EBT $2,000 $3,000 $4,000
Taxes (40%) 800 1,200 1,600
NI $1,200 $1,800 $2,400
Economy
Bad Avg. Good
Firm L: Leveraged
Prob.*
EBIT* $2,000 $3,000 $4,000
Interest 1,200 1,200 1,200
EBT $ 800 $1,800 $2,800
Taxes (40%) 320 720 1,120
NI $ 480 $1,080 $1,680
*Same as for Firm U.
Economy
Bad Avg. Good
Firm U Bad Avg. Good
BEP % % %
ROIC % % %
ROE % % %
TIE . . .
Firm L Bad Avg. Good
BEP % % %
ROIC % % %
ROE % % %
TIE
Profitability Measures:
E(BEP) % %
E(ROIC) % %
E(ROE) % %
Risk Measures:
ROIC % %
ROE % %
U L
Conclusions
Basic earning power (EBIT/TA) and ROIC (NOPAT/Capital = EBIT(1-T)/TA) are unaffected by financial leverage.
L has higher expected ROE: tax savings and smaller equity base.
L has much wider ROE swings because of fixed interest charges. Higher expected return is accompanied by higher risk.
(More...)
In a stand-alone risk sense, Firm L’s stockholders see much more risk than Firm U’s.
U and L: ROIC = %.
U: ROE = %.
L: ROE = %.
L’s financial risk is ROE - ROIC = % - % = %. (U’s is zero.)
(More...)
For leverage to be positive (increase expected ROE), BEP must be > rd.
If rd > BEP, the cost of leveraging will be higher than the inherent profitability of the assets, so the use of financial leverage will depress net income and ROE.
In the example, E(BEP) = 15% while interest rate = 12%, so leveraging “works.”
Capital Structure Theory
MM theory
Zero taxes
Corporate taxes
Corporate and personal taxes
Trade-off theory
Signaling theory
Debt financing as a managerial constraint
MM Theory: Zero Taxes
MM prove, under a very restrictive set of assumptions, that a firm’s value is unaffected by its financing mix:
VL = VU.
Therefore, capital structure is irrelevant.
Any increase in ROE resulting from financial leverage is exactly offset by the increase in risk (., ks), so WACC is constant.
MM Theory: Corporate Taxes
Corporate tax laws favor debt financing over equity financing.
With corporate taxes, the benefits of financial leverage exceed the risks: More EBIT goes to investors and less to taxes when leverage is used.
MM show that: VL = VU + TD.
If T=40%, then every dollar of debt adds 40 cents of extra value to firm.
Value of Firm, V
0
Debt
VL
VU
MM relationship between value and debt when corporate taxes are considered.
Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.
TD
Cost of Capital (%)
0 20 40 60 80 100
Debt/Value Ratio (%)
MM relationship between capital costs and leverage when corporate taxes are considered.
ks
WACC
kd(1 - T)
Miller’s Theory: Corporate and
Personal Taxes
Personal taxes lessen the advantage of corporate debt:
Corporate taxes favor debt financing since corporations can deduct interest expenses.
Personal taxes favor equity financing, since no gain is reported until stock is sold, and long-term gains are taxed at a lower rate.
Miller’s Model with Corporate and Personal Taxes
VL = VU + [1 - ]D.
Tc = corporate tax rate.
Td = personal tax rate on debt income.
Ts = personal tax rate on stock income.
(1 - Tc)(1 - Ts)
(1 - Td)
Tc = 40%, Td = 30%, and Ts = 12%.
VL = VU + [1 - ]D
= VU + (1 - )D
= VU + .
Value rises with debt; each $1 increase in debt raises L’s value by $.
(1 - )(1 - )
(1 - )
Conclusions with Personal Taxes
Use of debt financing remains advantageous, but benefits are less than under only corporate taxes.
Firms should still use 100% debt.
Note: However, Miller argued that in equilibrium, the tax rates of marginal investors would adjust until there was no advantage to debt.
Trade-off Theory
MM theory ignores bankruptcy (financial distress) costs, which increase as more leverage is used.
At low leverage levels, tax benefits outweigh bankruptcy costs.
At high levels, bankruptcy costs outweigh tax benefits.
An optimal capital structure exists that balances these costs and benefits.
Signaling Theory
MM assumed that investors and managers have the same information.
But, managers often have better information. Thus, they would:
Sell stock if stock is overvalued.
Sell bonds if stock is undervalued.
Investors understand this, so view new stock sales as a negative signal.
Implications for managers?
Debt Financing and Agency Costs
One agency problem is that managers can use corporate funds for non-value maximizing purposes.
The use of financial leverage:
Bonds “free cash flow.”
Forces discipline on managers to avoid perks and non-value adding acquisitions.
(More...)
A second agency problem is the potential for “underinvestment”.
Debt increases risk of financial distress.
Therefore, managers may avoid risky projects even if they have positive NPVs.
Choosing the Optimal Capital Structure: Example
Currently is all-equity financed.
Expected EBIT = $500,000.
Firm expects zero growth.
100,000 shares outstanding; rs = 12%;
P0 = $25; T = 40%; b = ; rRF = 6%;
RPM = 6%.
Estimates of Cost of Debt
Percent financed
with debt, wd rd
0% -
20% %
30% %
40% %
50% %
If company recapitalizes, debt would be issued to repurchase stock.
The Cost of Equity at Different Levels of Debt: Hamada’s Equation
MM theory implies that beta changes with leverage.
bU is the beta of a firm when it has no debt (the unlevered beta)
bL = bU [1 + (1 - T)(D/S)]
The Cost of Equity for wd = 20%
Use Hamada’s equation to find beta:
bL = bU [1 + (1 - T)(D/S)]
= [1 + () (20% / 80%) ]
=
Use CAPM to find the cost of equity:
rs = rRF + bL (RPM)
= 6% + (6%) = %
Cost of Equity vs. Leverage
wd D/S bL rs
0% %
20% %
30% %
40% %
50% %
The WACC for wd = 20%
WACC = wd (1-T) rd + we rs
WACC = (1 – ) (8%) + (%)
WACC = %
Repeat this for all capital structures under consideration.
WACC vs. Leverage
wd rd rs WACC
0% % % %
20% % % %
30% % % %
40% % % %
50% % % %
Corporate Value for wd = 20%
V = FCF / (WACC-g)
g=0, so investment in capital is zero; so FCF = NOPAT = EBIT (1-T).
NOPAT = ($500,000)() = $300,000.
V = $300,000 / = $2,659,574.
Corporate Value vs. Leverage
wd WACC Corp. Value
0% % $2,500,000
20% % $2,659,574
30% % $2,724,796
40% % $2,717,391
50% % $2,631,579
Debt and Equity for wd = 20%
The dollar value of debt is:
D = wd V = ($2,659,574) = $531,915.
S = V – D
S = $2,659,574 - $531,915 = $2,127,659.
Debt and Stock Value vs. Leverage
wd Debt, D Stock Value, S
0% $0 $2,500,000
20% $531,915 $2,127,660
30% $817,439 $1,907,357
40% $1,086,957 $1,630,435
50% $1,315,789 $1,315,789
Note: these are rounded; see Ch 13 Mini for full calculations.
Wealth of Shareholders
Value of the equity declines as more debt is issued, because debt is used to repurchase stock.
But total wealth of shareholders is value of stock after the recap plus the cash received in repurchase, and this total goes up (It is equal to Corporate Value on earlier slide).
Stock Price for wd = 20%
The firm issues debt, which changes its WACC, which changes value.
The firm then uses debt proceeds to repurchase stock.
Stock price changes after debt is issued, but does not change during actual repurchase (or arbitrage is possible).
(More…)
Stock Price for wd = 20% (Continued)
The stock price after debt is issued but before stock is repurchased reflects shareholder wealth:
S, value of stock
Cash paid in repurchase.
(More…)
Stock Price for wd = 20% (Continued)
D0 and n0 are debt and outstanding shares before recap.
D - D0 is equal to cash that will be used to repurchase stock.
S + (D - D0) is wealth of shareholders’ after the debt is issued but immediately before the repurchase.
(More…)
Stock Price for wd = 20% (Continued)
P = S + (D – D0)
n0
P = $2,127,660 + ($531,915 – 0)
100,000
P = $ per share.
Number of Shares Repurchased
# Repurchased = (D - D0) / P
# Rep. = ($531,915 – 0) / $
= 20,000.
# Remaining = n = S / P
n = $2,127,660 / $
= 80,000.
Price per Share vs. Leverage
# shares # shares
wd P Repurch. Remaining
0% $ 0 100,000
20% $ 20,000 80,000
30% $ 30,000 70,000
40% $ 40,000 60,000
50% $ 50,000 50,000
Optimal Capital Structure
wd = 30% gives:
Highest corporate value
Lowest WACC
Highest stock price per share
But wd = 40% is close. Optimal range is pretty flat.
Debt ratios of other firms in the industry.
Pro forma coverage ratios at different capital structures under different economic scenarios.
Lender and rating agency attitudes (impact on bond ratings).
What other factors would managers consider when setting the target capital structure?
Reserve borrowing capacity.
Effects on control.
Type of assets: Are they tangible, and hence suitable as collateral?
Tax rates.
CHAPTER 14
Distributions to Shareholders:
Dividends and Repurchases
Theories of investor preferences
Signaling effects
Residual model
Dividend reinvestment plans
Stock dividends and stock splits
Stock repurchases
What is “dividend policy”?
It’s the decision to pay out earnings versus retaining and reinvesting them. Includes these elements:
1. High or low payout?
2. Stable or irregular dividends?
3. How frequent?
4. Do we announce the policy?
Dividend Payout Ratios for Selected Industries
Industry Payout ratio
Banking
Computer Software Services
Drug
Electric Utilities (Eastern U. S.)
Internet n/a
Semiconductors
Steel
Tobacco
Water utilities
*None of the internet companies included in the Value Line Investment Survey paid a dividend.
Do investors prefer high or low payouts? There are three theories:
Dividends are irrelevant: Investors don’t care about payout.
Bird-in-the-hand: Investors prefer a high payout.
Tax preference: Investors prefer a low payout, hence growth.
Dividend Irrelevance Theory
Investors are indifferent between dividends and retention-generated capital gains. If they want cash, they can sell stock. If they don’t want cash, they can use dividends to buy stock.
Modigliani-Miller support irrelevance.
Theory is based on unrealistic assumptions (no taxes or brokerage costs), hence may not be true. Need empirical test.
Bird-in-the-Hand Theory
Investors think dividends are less risky than potential future capital gains, hence they like dividends.
If so, investors would value high payout firms more highly, ., a high payout would result in a high P0.
Tax Preference Theory
Retained earnings lead to capital gains, which are taxed at lower rates than dividends: 28% maximum vs. up to %. Capital gains taxes are also deferred.
This could cause investors to prefer firms with low payouts, ., a high payout results in a low P0.
Implications of 3 Theories for Managers
Theory
Implication
Irrelevance
Any payout OK
Bird-in-the-hand
Set high payout
Tax preference
Set low payout
But which, if any, is correct???
Which theory is most correct?
Empirical testing has not been able to determine which theory, if any, is correct.
Thus, managers use judgment when setting policy.
Analysis is used, but it must be applied with judgment.
What’s the “information content,” or “signaling,” hypothesis?
Managers hate to cut dividends, so won’t raise dividends unless they think raise is sustainable. So, investors view dividend increases as signals of management’s view of the future.
Therefore, a stock price increase at time of a dividend increase could reflect higher expectations for future EPS, not a desire for dividends.
What’s the “clientele effect”?
Different groups of investors, or clienteles, prefer different dividend policies.
Firm’s past dividend policy determines its current clientele of investors.
Clientele effects impede changing dividend policy. Taxes & brokerage costs hurt investors who have to switch companies.
What’s the “residual dividend model”?
Find the retained earnings needed for the capital budget.
Pay out any leftover earnings (the residual) as dividends.
This policy minimizes flotation and equity signaling costs, hence minimizes the WACC.
Using the Residual Model to Calculate Dividends Paid
Dividends = – .
Net
income
Target
equity
ratio
Total
capital
budget
[
]
)
)
(
(
Data for SSC
Capital budget: $800,000. Given.
Target capital structure: 40% debt, 60% equity. Want to maintain.
Forecasted net income: $600,000.
How much of the $600,000 should we pay out as dividends?
Of the $800,000 capital budget, ($800,000) = $480,000 must be equity to keep at target capital structure. [($800,000) = $320,000 will be debt.]
With $600,000 of net income, the residual is $600,000 - $480,000 = $120,000 = dividends paid.
Payout ratio = $120,000/$600,000 = = 20%.
How would a drop in NI to $400,000 affect the dividend? A rise to $800,000?
NI = $400,000: Need $480,000 of equity, so should retain the whole $400,000. Dividends = 0.
NI = $800,000: Dividends = $800,000 - $480,000 = $320,000. Payout = $320,000/$800,000 = 40%.
How would a change in investment opportunities affect dividend under the residual policy?
Fewer good investments would lead to smaller capital budget, hence to a higher dividend payout.
More good investments would lead to a lower dividend payout.
Advantages and Disadvantages of the Residual Dividend Policy
Advantages: Minimizes new stock issues and flotation costs.
Disadvantages: Results in variable dividends, sends conflicting signals, increases risk, and doesn’t appeal to any specific clientele.
Conclusion: Consider residual policy when setting target payout, but don’t follow it rigidly.
Setting Dividend Policy
Forecast capital needs over a planning horizon, often 5 years.
Set a target capital structure.
Estimate annual equity needs.
Set target payout based on the residual model.
Generally, some dividend growth rate emerges. Maintain target growth rate if possible, varying capital structure somewhat if necessary.
Stock Repurchases
Reasons for repurchases:
As an alternative to distributing cash as dividends.
To dispose of one-time cash from an asset sale.
To make a large capital structure change.
Repurchases: Buying own stock back from stockholders.
Advantages of Repurchases
Stockholders can tender or not.
Helps avoid setting a high dividend that cannot be maintained.
Repurchased stock can be used in takeovers or resold to raise cash as needed.
Income received is capital gains rather than higher-taxed dividends.
Stockholders may take as a positive signal--management thinks stock is undervalued.
Disadvantages of Repurchases
May be viewed as a negative signal (firm has poor investment opportunities).
IRS could impose penalties if repurchases were primarily to avoid taxes on dividends.
Selling stockholders may not be well informed, hence be treated unfairly.
Firm may have to bid up price to complete purchase, thus paying too much for its own stock.
What’s a “dividend reinvestment
plan (DRIP)”?
Shareholders can automatically reinvest their dividends in shares of the company’s common stock. Get more stock than cash.
There are two types of plans:
Open market
New stock
Open Market Purchase Plan
Dollars to be reinvested are turned over to trustee, who buys shares on the open market.
Brokerage costs are reduced by volume purchases.
Convenient, easy way to invest, thus useful for investors.
New Stock Plan
Firm issues new stock to DRIP enrollees, keeps money and uses it to buy assets.
No fees are charged, plus sells stock at discount of 5% from market price, which is about equal to flotation costs of underwritten stock offering.
Optional investments sometimes possible, up to $150,000 or so.
Firms that need new equity capital use new stock plans.
Firms with no need for new equity capital use open market purchase plans.
Most NYSE listed companies have a DRIP. Useful for investors.
Stock Dividends vs. Stock Splits
Stock dividend: Firm issues new shares in lieu of paying a cash dividend. If 10%, get 10 shares for each 100 shares owned.
Stock split: Firm increases the number of shares outstanding, say 2:1. Sends shareholders more shares.
Both stock dividends and stock splits increase the number of shares outstanding, so “the pie is divided into smaller pieces.”
Unless the stock dividend or split conveys information, or is accompanied by another event like higher dividends, the stock price falls so as to keep each investor’s wealth unchanged.
But splits/stock dividends may get us to an “optimal price range.”
When should a firm consider splitting its stock?
There’s a widespread belief that the optimal price range for stocks is $20 to $80.
Stock splits can be used to keep the price in the optimal range.
Stock splits generally occur when management is confident, so are interpreted as positive signals.
CHAPTER 15
Multinational Financial Management
Factors that make multinational financial management different
Exchange rates and trading
International monetary system
International financial markets
Specific features of multinational financial management
A multinational corporation is one that operates in two or more countries.
At one time, most multinationals produced and sold in just a few countries.
Today, many multinationals have world-wide production and sales.
What is a multinational corporation?
To seek new markets.
To seek new supplies of raw materials.
To gain new technologies.
To gain production efficiencies.
To avoid political and regulatory obstacles.
To reduce risk by diversification.
Why do firms expand into other countries?
Currency differences
Economic and legal differences
Language differences
Cultural differences
Government roles
Political risk
What are the major factors that distinguish multinational from domestic financial management?
Are these currency prices direct or indirect quotations?
Since they are prices of foreign currencies expressed in . dollars, they are direct quotations (dollars per currency).
Consider the following exchange rates:
. $ to buy
1 Unit
Euro
Swedish krona
An indirect quotation gives the amount of a foreign currency required to buy one . dollar (currency per dollar).
Note than an indirect quotation is the reciprocal of a direct quotation.
What is an indirect quotation?
Calculate the indirect quotations
for euros and kronas.
# of Units of Foreign
Currency per . $
Euro
Swedish krona
Euro: 1 / = .
Krona: 1 / = .
A cross rate is the exchange rate between any two currencies not involving . dollars.
In practice, cross rates are usually calculated from direct or indirect rates. That is, on the basis of . dollar exchange rates.
What is a cross rate?
Cross rate = x
= x = euros/krona.
Cross rate = x
= x = kronas/euro.
Calculate the two cross rates
between euros and kronas.
Euros Dollars Dollar Krona
Kronas Dollars Dollar Euros
The two cross rates are reciprocals of one another.
They can be calculated by dividing either the direct or indirect quotations.
Note:
Target price = ($)()=$
Spanish price = ($)( euros/$)
= € .
Assume the firm can produce a liter of
orange juice in the . and ship it to Spain for $. If the firm wants a 50% markup on the product, what should the juice sell for in Spain?
euros ( kronas/euro) = 16 kronas.
20 - 16 = kronas profit.
Dollar profit = kronas( dollars per krona) = $.
Now the firm begins producing the
orange juice in Spain. The product
costs euros to produce and
ship to Sweden, where it can be sold
for 20 kronas. What is the dollar
profit on the sale?
Exchange rate risk is the risk that the value of a cash flow in one currency translated from another currency will decline due to a change in exchange rates.
For example, in the last slide, a weakening krona (strengthening dollar) would lower the dollar profit.
What is exchange rate risk?
The current system is a floating rate system.
Prior to 1971, a fixed exchange rate system was in effect.
The . dollar was tied to gold.
Other currencies were tied to the dollar.
Describe the current and former
international monetary systems.
The European Monetary Union
In 2002, the full implementation of the “euro” is expected to be complete. The national currencies of the 11 participating countries will be phased out in favor of the “euro.” The newly formed European Central Bank will control the monetary policy of the EMU.
The 12 Member Nations of the
European Monetary Union
Austria
Belgium
Finland
France
Germany
Ireland
Italy
Luxembourg
Netherlands
Portugal
Spain
Greece
European Union countries not in the EMU: Britain Sweden Denmark
A currency is convertible when the issuing country promises to redeem the currency at current market rates.
Convertible currencies are traded in world currency markets.
What is a convertible currency?
It becomes very difficult for multi-national companies to conduct business because there is no easy way to take profits out of the country.
Often, firms will barter for goods to export to their home countries.
What problems arise when a firm
operates in a country whose
currency is not convertible?
A spot rate is the rate applied to buy currency for immediate delivery.
A forward rate is the rate applied to buy currency at some agreed-upon future date.
What is the difference between
spot rates and forward rates?
When is the forward rate at a premium to the spot rate?
If the . dollar buys fewer units of a foreign currency in the forward than in the spot market, the foreign currency is selling at a premium.
In the opposite situation, the foreign currency is selling at a discount.
The primary determinant of the spot/forward rate relationship is relative interest rates.
What is interest rate parity?
Interest rate parity implies that investors should expect to earn the same return on similar-risk securities in all countries:
Forward and spot rates are direct quotations.
rh = periodic interest rate in the home country.
rf = periodic interest rate in the foreign country.
Forward rate
Spot rate
=
1 + rh
1 + rf
.
Assume 1 euro = $ in the
180-day forward market and and 180-day risk-free rate is 6% in the . and 4% in Spain.
Does interest rate parity hold?
Spot rate = $.
rh = 6%/2 = 3%.
rf = 4%/2 = 2%.
(More...)
Forward rate
If interest rate parity holds, the implied forward rate, , would equal the observed forward rate, ; so parity doesn’t hold.
Forward rate
Spot rate
=
1 + rh
1 + rf
=
Forward rate = .
Which 180-day security (. or Spanish) offers the higher return?
A . investor could directly invest in the . security and earn an annualized rate of 6%.
Alternatively, the . investor could convert dollars to euros, invest in the Spanish security, and then convert profit back into dollars. If the return on this strategy is higher than 6%, then the Spanish security has the higher rate.
What is the return to a . investor in the Spanish security?
Buy $1,000 worth of euros in the spot market:
$1,000( euros/$) = 1,250 euros.
Spanish investment return (in euros):
1,250()= 1,275 euros.
(More...)
Buy contract today to exchange 1,275 euros in 180 days at forward rate of dollars/euro.
At end of 180 days, convert euro investment to dollars:
€1,275 ( $/€) = $1,.
Calculate the rate of return:
$ = % per 180 days
= % per year.
(More...)
The Spanish security has the highest return, even though it has a lower interest rate.
. rate is 6%, so Spanish securities at % offer a higher rate of return to . investors.
But could such a situation exist for very long?
Arbitrage
Traders could borrow at the . rate, convert to pesetas at the spot rate, and simultaneously lock in the forward rate and invest in Spanish securities.
This would produce arbitrage: a positive cash flow, with no risk and none of the traders own money invested.
Impact of Arbitrage Activities
Traders would recognize the arbitrage opportunity and make huge investments.
Their actions would tend to move interest rates, forward rates, and spot rates to parity.
What is purchasing power parity?
Purchasing power parity implies that the level of exchange rates adjusts so that identical goods cost the same amount in different countries.
Ph = Pf(Spot rate),
or
Spot rate = Ph/Pf.
If grapefruit juice costs $ in the . and purchasing power parity holds, what is price in Spain?
Spot rate = Ph/Pf.
$ = $
Pf = $
= euros.
Do interest rate and purchasing power parity hold exactly at any point in time?
Lower inflation leads to lower interest rates, so borrowing in low-interest countries may appear attractive to multinational firms.
However, currencies in low-inflation countries tend to appreciate against those in high-inflation rate countries, so the true interest cost increases over the life of the loan.
What impact does relative
inflation have on interest rates
and exchange rates?
Eurodollar markets
Dollars held outside the .
Mostly Europe, but also elsewhere
International bonds
Foreign bonds: Sold by foreign borrower, but denominated in the currency of the country of issue.
Eurobonds: Sold in country other than the one in whose currency it is denominated.
Describe the international money and capital markets.
To what extent do capital structures vary across different countries?
Early studies suggested that average capital structures varied widely among the large industrial countries.
However, a recent study, which controlled for differences in accounting practices, suggests that capital structures are more similar across different countries than previously thought.
Distances are greater.
Access to more markets for loans and for temporary investments.
Cash is often denominated in different currencies.
What is the impact of multinational
operations on each of the
following topics?
Cash Management
Foreign operations are taxed locally, and then funds repatriated may be subject to . taxes.
Foreign projects are subject to political risk.
Funds repatriated must be converted to . dollars, so exchange rate risk must be taken into account.
Capital Budgeting Decisions
Credit is more important, because commerce to lesser-developed countries often relies on credit.
Credit for future payment may be subject to exchange rate risk.
Credit Management
Inventory decisions can be more complex, especially when inventory can be stored in locations in different countries.
Some factors to consider are shipping times, carrying costs, taxes, import duties, and exchange rates.
Inventory Management
CHAPTER 16
Working Capital Management
Alternative working capital policies
Cash, inventory, and A/R management
Accounts payable management
Short-term financing policies
Bank debt and commercial paper
Basic Definitions
Gross working capital:
Total current assets.
Net working capital:
Current assets - Current liabilities.
Net operating working capital (NOWC):
Operating CA – Operating CL =
(Cash + Inv. + A/R) – (Accruals + A/P)
(More…)
Working capital management:
Includes both establishing working capital policy and then the day-to-day control of cash, inventories, receivables, accruals, and accounts payable.
Working capital policy:
The level of each current asset.
How current assets are financed.
Selected Ratios for SKI
SKI Industry
Current
Quick
Debt/Assets % %
Turnover of cash
DSO (365-day basis)
Inv. turnover
F. A. turnover
T. A. turnover
Profit margin % %
ROE % %
Payables deferral
How does SKI’s working capital policy compare with the industry?
Working capital policy is reflected in a firm’s current ratio, quick ratio, turnover of cash and securities, inventory turnover, and DSO.
These ratios indicate SKI has large amounts of working capital relative to its level of sales. Thus, SKI is following a relaxed policy.
Is SKI inefficient or just conservative?
A relaxed policy may be appropriate if it reduces risk more than profitability.
However, SKI is much less profitable than the average firm in the industry. This suggests that the company probably has excessive working capital.
Cash Conversion Cycle
The cash conversion cycle focuses on the time between payments made for materials and labor and payments received from sales:
Cash Inventory Receivables Payables
conversion = conversion + collection - deferral .
cycle period period period
Cash Conversion Cycle (Cont.)
CCC = + –
CCC = + – 30
CCC = + – 30
CCC = days.
Days per year
Inv. turnover
Payables
deferral
period
Days sales
outstanding
365
Cash Management:
Cash doesn’t earn interest,
so why hold it?
Transactions: Must have some cash to pay current bills.
Precaution: “Safety stock.” But lessened by credit line and marketable securities.
Compensating balances: For loans and/or services provided.
Speculation: To take advantage of bargains, to take discounts, and so on. Reduced by credit line, marketable securities.
What’s the goal of cash management?
To have sufficient cash on hand to meet the needs listed on the previous slide.
However, since cash is a non-earning asset, to have not one dollar more.
Ways to Minimize Cash Holdings
Use lockboxes.
Insist on wire transfers from customers.
Synchronize inflows and outflows.
Use a remote disbursement account.
(More…)
Increase forecast accuracy to reduce the need for a cash “safety stock.”
Hold marketable securities instead of a cash “safety stock.”
Negotiate a line of credit (also reduces need for a “safety stock”).
Cash Budget: The Primary Cash Management Tool
Purpose: Uses forecasts of cash inflows, outflows, and ending cash balances to predict loan needs and funds available for temporary investment.
Timing: Daily, weekly, or monthly, depending upon budget’s purpose. Monthly for annual planning, daily for actual cash management.
Data Required for Cash Budget
1. Sales forecast.
2. Information on collections delay.
3. Forecast of purchases and payment terms.
4. Forecast of cash expenses: wages, taxes, utilities, and so on.
5. Initial cash on hand.
6. Target cash balance.
SKI’s Cash Budget for January and February
Net Cash Inflows
January February
Collections $67, $62,
Purchases 44, 36,
Wages 6, 5,
Rent 2, 2,
Total payments $53, $44,
Net CF $13, $18,
Cash Budget (Continued)
January February
Cash at start if no borrowing $ 3, $16,
Net CF (slide 13) 13, 18,
Cumulative cash $16, $35,
Less: target cash 1, 1,
Surplus $15, $33,
Should depreciation be explicitly included in the cash budget?
No. Depreciation is a noncash charge. Only cash payments and receipts appear on cash budget.
However, depreciation does affect taxes, which do appear in the cash budget.
What are some other potential cash inflows besides collections?
Proceeds from fixed asset sales.
Proceeds from stock and bond sales.
Interest earned.
Court settlements.
How can interest earned or paid on short-term securities or loans be incorporated in the cash budget?
Interest earned: Add line in the collections section.
Interest paid: Add line in the payments section.
Found as interest rate x surplus/loan line of cash budget for preceding month.
Note: Interest on any other debt would need to be incorporated as well.
How could bad debts be worked into the cash budget?
Collections would be reduced by the amount of bad debt losses.
For example, if the firm had 3% bad debt losses, collections would total only 97% of sales.
Lower collections would lead to lower surpluses and higher borrowing requirements.
SKI’s forecasted cash budget
indicates that the company’s cash holdings will exceed the targeted
cash balance every month, except for October and November.
Cash budget indicates the company probably is holding too much cash.
SKI could improve its EVA by either investing its excess cash in more productive assets or by paying it out to the firm’s shareholders.
What reasons might SKI have for maintaining a relatively
high amount of cash?
If sales turn out to be considerably less than expected, SKI could face a cash shortfall.
A company may choose to hold large amounts of cash if it does not have much faith in its sales forecast, or if it is very conservative.
The cash may be there, in part, to fund a planned fixed asset acquisition.
Inventory Management:
Categories of Inventory Costs
Carrying Costs: Storage and handling costs, insurance, property taxes, depreciation, and obsolescence.
Ordering Costs: Cost of placing orders, shipping, and handling costs.
Costs of Running Short: Loss of sales, loss of customer goodwill, and the disruption of production schedules.
Is SKI holding too much inventory?
SKI’s inventory turnover () is considerably lower than the industry average (). The firm is carrying a lot of inventory per dollar of sales.
By holding excessive inventory, the firm is increasing its operating costs which reduces its NOPAT. Moreover, the excess inventory must be financed, so EVA is further lowered.
If SKI reduces its inventory, without adversely affecting sales, what effect will this have on its cash position?
Short run: Cash will increase as inventory purchases decline.
Long run: Company is likely to then take steps to reduce its cash holdings.
Accounts Receivable Management:
Do SKI’s customers pay more or less promptly than those of its competitors?
SKI’s days’ sales outstanding (DSO) of days is well above the industry average (32 days).
SKI’s customers are paying less promptly.
SKI should consider tightening its credit policy to reduce its DSO.
Elements of Credit Policy
Cash Discounts: Lowers price. Attracts new customers and reduces DSO.
Credit Period: How long to pay? Shorter period reduces DSO and average A/R, but it may discourage sales.
(More…)
Credit Standards: Tighter standards reduce bad debt losses, but may reduce sales. Fewer bad debts reduces DSO.
Collection Policy: Tougher policy will reduce DSO, but may damage customer relationships.
Does SKI face any risk if it tightens its credit policy?
YES! A tighter credit policy may
discourage sales. Some customers
may choose to go elsewhere if they
are pressured to pay their bills
sooner.
If SKI succeeds in reducing DSO without adversely affecting sales, what effect would this have on its cash position?
Short run: If customers pay sooner, this increases cash holdings.
Long run: Over time, the company would hopefully invest the cash in more productive assets, or pay it out to shareholders. Both of these actions would increase EVA.
Is there a cost to accruals? Do firms have much control over amount of accruals?
Accruals are free in that no explicit interest is charged.
Firms have little control over the level of accruals. Levels are influenced more by industry custom, economic factors, and tax laws.
What is trade credit?
Trade credit is credit furnished by a firm’s suppliers.
Trade credit is often the largest source of short-term credit, especially for small firms.
Spontaneous, easy to get, but cost can be high.
SKI buys $506,985 net, on terms of 1/10, net 30, and pays on Day 40. How much free and costly trade credit, and what’s the cost of costly trade credit?
Net daily purchases = $506,985/365
= $1,389.
Annual gross purch. = $506,985/()
=$512,106
Gross/Net Breakdown
Company buys goods worth $506,985. That’s the cash price.
They must pay $5,121 more if they don’t take discounts.
Think of the extra $5,121 as a financing cost similar to the interest on a loan.
Want to compare that cost with the cost of a bank loan.
Payables level if take discount:
Payables = $1,389(10) = $13,890.
Payables level if don’t take discount:
Payables = $1,389(40) = $55,560.
Credit Breakdown:
Total trade credit = $55,560
Free trade credit = 13,890
Costly trade credit = $41,670
Nominal Cost of Costly Trade Credit
But the $5,121 is paid all during the year, not at year-end, so EAR rate is higher.
Firm loses ($512,106) = $5,121 of discounts to obtain $41,670 in
extra trade credit, so
kNom = = = %.
$5,121
$41,670
Nominal Cost Formula, 1/10, net 40
Pays % times per year.
Effective Annual Rate, 1/10, net 40
Periodic rate = = %.
Periods/year = 365/(40 – 10) = .
EAR = (1 + Periodic rate)n –
= () – = %.
Working Capital Financing Policies
Moderate: Match the maturity of the assets with the maturity of the financing.
Aggressive: Use short-term financing to finance permanent assets.
Conservative: Use permanent capital for permanent assets and temporary assets.
Moderate Financing Policy
Years
$
Perm NOWC
Fixed Assets
Temp. NOWC
Lower dashed line, more aggressive.
}
S-T
Loans
L-T Fin:
Stock &
Bonds,
Conservative Financing Policy
Fixed Assets
Years
$
Perm NOWC
L-T Fin:
Stock &
Bonds
Marketable Securities
Zero S-T
debt
What are the advantages of short-term debt vs. long-term debt?
Low cost-- yield curve usually slopes upward.
Can get funds relatively quickly.
Can repay without penalty.
What are the disadvantages of short-term debt vs. long-term debt?
Higher risk. The required repayment comes quicker, and the company may have trouble rolling over loans.
Commercial Paper (CP)
Short term notes issued by large, strong companies. SKI couldn’t issue CP--it’s too small.
CP trades in the market at rates just above T-bill rate.
CP is bought with surplus cash by banks and other companies, then held as a marketable security for liquidity purposes.
CHAPTER 17
Option Pricing with Applications to Real Options
Financial options
Black-Scholes Option Pricing Model
Real options
Decision trees
Application of financial options to real options
What is a real option?
Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions.
Alert managers always look for real options in projects.
Smarter managers try to create real options.
An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time.
What is a financial option?
It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.
What is the single most important
characteristic of an option?
Call option: An option to buy a specified number of shares of a security within some future period.
Put option: An option to sell a specified number of shares of a security within some future period.
Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold.
Option Terminology
Option price: The market price of the option contract.
Expiration date: The date the option matures.
Exercise value: The value of a call option if it were exercised today = Current stock price - Strike price.
Note: The exercise value is zero if the stock price is less than the strike price.
Covered option: A call option written against stock held in an investor’s portfolio.
Naked (uncovered) option: An option sold without the stock to back it up.
In-the-money call: A call whose exercise price is less than the current price of the underlying stock.
Out-of-the-money call: A call option whose exercise price exceeds the current stock price.
LEAPs: Long-term Equity AnticiPation securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years.
Exercise price = $25.
Stock Price Call Option Price
$25 $
30
35
40
45
50
Consider the following data:
Price of Strike Exercise Value
Stock (a) Price (b) of Option (a) - (b)
$ $ $
Create a table which shows (a) stock
price, (b) strike price, (c) exercise
value, (d) option price, and (e) premium
of option price over the exercise value.
Exercise Value Mkt. Price Premium
of Option (c) of Option (d) (d) - (c)
$ $ $
Table (Continued)
Call Premium Diagram
5 10 15 20 25 30 35 40 45 50
Stock Price
Option value
30
25
20
15
10
5
Market price
Exercise value
The premium of the option price over the exercise value declines as the stock price increases.
This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.
What happens to the premium of the
option price over the exercise
value as the stock price rises?
The stock underlying the call option provides no dividends during the call option’s life.
There are no transactions costs for the sale/purchase of either the stock or the option.
RRF is known and constant during the option’s life.
What are the assumptions of the
Black-Scholes Option Pricing Model?
(More...)
Security buyers may borrow any fraction of the purchase price at the short-term risk-free rate.
No penalty for short selling and sellers receive immediately full cash proceeds at today’s price.
Call option can be exercised only on its expiration date.
Security trading takes place in continuous time, and stock prices move randomly in continuous time.
V = P[N(d1)] - Xe -rRFt[N(d2)].
d1 = .
t
d2 = d1 - t.
What are the three equations that
make up the OPM?
ln(P/X) + [rRF + (2/2)]t
V = $27[N(d1)] - $25e-()()[N(d2)].
ln($27/$25) + [( +
()()
= .
d2 = d1 - ()() = d1 -
= - = .
What is the value of the following
call option according to the OPM? Assume: P = $27; X = $25; rRF = 6%; t = years: 2 =
d1 =
N(d1) = N() = +
= .
N(d2) = N() = +
= .
Note: Values obtained from Excel using NORMSDIST function.
V = $27() - $()
= $ - $25()()
= $.
Current stock price: Call option value increases as the current stock price increases.
Exercise price: As the exercise price increases, a call option’s value decreases.
What impact do the following para-
meters have on a call option’s value?
Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.)
Risk-free rate: Call option’s value tends to increase as rRF increases (reduces the PV of the exercise price).
Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).
How are real options different from financial options?
Financial options have an underlying asset that is traded--usually a security like a stock.
A real option has an underlying asset that is not a security--for example a project or a growth opportunity, and it isn’t traded.
(More...)
How are real options different from financial options?
The payoffs for financial options are specified in the contract.
Real options are “found” or created inside of projects. Their payoffs can be varied.
What are some types of
real options?
Investment timing options
Growth options
Expansion of existing product line
New products
New geographic markets
Types of real options (Continued)
Abandonment options
Contraction
Temporary suspension
Flexibility options
Five Procedures for Valuing
Real Options
1. DCF analysis of expected cash flows, ignoring the option.
2. Qualitative assessment of the real option’s value.
3. Decision tree analysis.
4. Standard model for a corresponding financial option.
5. Financial engineering techniques.
Analysis of a Real Option: Basic Project
Initial cost = $70 million, Cost of Capital = 10%, risk-free rate = 6%, cash flows occur for 3 years. Annual
Demand Probability Cash Flow
High 30% $45
Average 40% $30
Low 30% $15
Approach 1: DCF Analysis
E(CF) =.3($45)+.4($30)+.3($15)
= $30.
PV of expected CFs = ($30/) + ($30/) + ($30/1/13) = $ million.
Expected NPV = $ - $70
= $ million
Investment Timing Option
If we immediately proceed with the project, its expected NPV is $ million.
However, the project is very risky:
If demand is high, NPV = $ million.*
If demand is low, NPV = -$ million.*
_______________________________________
* See Ch 17 Mini for calculations.
Investment Timing (Continued)
If we wait one year, we will gain additional information regarding demand.
If demand is low, we won’t implement project.
If we wait, the up-front cost and cash flows will stay the same, except they will be shifted ahead by a year.
Procedure 2: Qualitative Assessment
The value of any real option increases if:
the underlying project is very risky
there is a long time before you must exercise the option
This project is risky and has one year before we must decide, so the option to wait is probably valuable.
Procedure 3: Decision Tree Analysis
(Implement only if demand is not low.)
Discount the cost of the project at the risk-free rate, since the cost is known. Discount the operating cash flows at the cost of capital. Example: $ = -$70/ + $45/ + $45/ + $45/.
See Ch 17 Mini for calculations.
Use these scenarios, with their given probabilities, to find the project’s expected NPV if we wait.
E(NPV) = [($)]+[($)]
+ [ ($0)]
E(NPV) = $.
Decision Tree with Option to Wait vs. Original DCF Analysis
Decision tree NPV is higher ($ million vs. $).
In other words, the option to wait is worth $ million. If we implement project today, we gain $ million but lose the option worth $ million.
Therefore, we should wait and decide next year whether to implement project, based on demand.
The Option to Wait Changes Risk
The cash flows are less risky under the option to wait, since we can avoid the low cash flows. Also, the cost to implement may not be risk-free.
Given the change in risk, perhaps we should use different rates to discount the cash flows.
But finance theory doesn’t tell us how to estimate the right discount rates, so we normally do sensitivity analysis using a range of different rates.
Procedure 4: Use the existing model
of a financial option.
The option to wait resembles a financial call option-- we get to “buy” the project for $70 million in one year if value of project in one year is greater than $70 million.
This is like a call option with an exercise price of $70 million and an expiration date of one year.
Inputs to Black-Scholes Model for Option to Wait
X = exercise price = cost to implement project = $70 million.
rRF = risk-free rate = 6%.
t = time to maturity = 1 year.
P = current stock price = Estimated on following slides.
2 = variance of stock return = Estimated on following slides.
Estimate of P
For a financial option:
P = current price of stock = PV of all of stock’s expected future cash flows.
Current price is unaffected by the exercise cost of the option.
For a real option:
P = PV of all of project’s future expected cash flows.
P does not include the project’s cost.
Step 1: Find the PV of future CFs at option’s exercise year.
PV at
2002
Prob.
2003
2004
2005
2006
2003
$45
$45
$45
$
30%
40%
$30
$30
$30
$
30%
$15
$15
$15
$
Future Cash Flows
Example: $ = $45/ + $45/ + $45/.
See Ch 17 Mini for calculations.
Step 2: Find the expected PV at the current date, 2002.
PV2002=PV of Exp. PV2003 = [(* $) +(*$) +(*$)]/ = $.
See Ch 17 Mini for calculations.
PV
2002
PV
2003
$
High
$
Average
$
Low
$
The Input for P in the Black-Scholes Model
The input for price is the present value of the project’s expected future cash flows.
Based on the previous slides,
P = $.
Estimating s2 for the Black-Scholes Model
For a financial option, s2 is the variance of the stock’s rate of return.
For a real option, s2 is the variance of the project’s rate of return.
Three Ways to Estimate s2
Judgment.
The direct approach, using the results from the scenarios.
The indirect approach, using the expected distribution of the project’s value.
Estimating s2 with Judgment
The typical stock has s2 of about 12%.
A project should be riskier than the firm as a whole, since the firm is a portfolio of projects.
The company in this example has s2 = 10%, so we might expect the project to have s2 between 12% and 19%.
Estimating s2 with the Direct Approach
Use the previous scenario analysis to estimate the return from the present until the option must be exercised. Do this for each scenario
Find the variance of these returns, given the probability of each scenario.
Find Returns from the Present until the Option Expires
Example: % = ($- $) / $.
See Ch 17 Mini for calculations.
PV
2002
PV
2003
Return
$
%
High
$
Average
$
%
Low
$
%
Use these scenarios, with their given probabilities, to find the expected return and variance of return.
E(Ret.)=()+()+()
E(Ret.)= = 10%.
2 = ()2 + ()2
+ ()2
2 = = %.
Estimating s2 with the Indirect Approach
From the scenario analysis, we know the project’s expected value and the variance of the project’s expected value at the time the option expires.
The questions is: “Given the current value of the project, how risky must its expected return be to generate the observed variance of the project’s value at the time the option expires?”
The Indirect Approach (Cont.)
From option pricing for financial options, we know the probability distribution for returns (it is lognormal).
This allows us to specify a variance of the rate of return that gives the variance of the project’s value at the time the option expires.
Indirect Estimate of 2
Here is a formula for the variance of a stock’s return, if you know the coefficient of variation of the expected stock price at some time, t, in the future:
We can apply this formula to the real option.
From earlier slides, we know the value of the project for each scenario at the expiration date.
PV
2003
$
High
Average
$
Low
$
Use these scenarios, with their given probabilities, to find the project’s expected PV and PV.
E(PV)=.3($)+.4($)+.3($)
E(PV)= $.
PV = [.3($-$)2
+ .4($-$)2
+ .3($-$)2]1/2
PV = $.
Find the project’s expected coefficient of variation, CVPV, at the time the option expires.
CVPV = $ /$ = .
Now use the formula to estimate 2.
From our previous scenario analysis, we know the project’s CV, , at the time it the option expires (t=1 year).
The Estimate of 2
Subjective estimate:
12% to 19%.
Direct estimate:
%.
Indirect estimate:
%
For this example, we chose %, but we recommend doing sensitivity analysis over a range of s2.
V = $[N(d1)] - $70e-()(1)[N(d2)].
ln($ +
() (1).05
= .
d2 = d1 - () (1).05= d1 -
= - =- .
Use the Black-Scholes Model:
P = $; X = $70; rRF = 6%; t = 1 year: 2 =
d1 =
N(d1) = N() =
N(d2) = N(- ) =
V = $() - $()
= $ - $70()()
= $.
Note: Values of N(di) obtained from Excel using NORMSDIST function. See Ch 17 Mini for details.
Step 5: Use financial engineering techniques.
Although there are many existing models for financial options, sometimes none correspond to the project’s real option.
In that case, you must use financial engineering techniques, which are covered in later finance courses.
Alternatively, you could simply use decision tree analysis.
Other Factors to Consider When Deciding When to Invest
Delaying the project means that cash flows come later rather than sooner.
It might make sense to proceed today if there are important advantages to being the first competitor to enter a market.
Waiting may allow you to take advantage of changing conditions.
A New Situation: Cost is $75 Million, No Option to Wait
Cost
NPV this
2002
Prob.
2003
2004
2005
Scenario
$45
$45
$45
$
30%
-$75
40%
$30
$30
$30
-$
30%
$15
$15
$15
-$
Future Cash Flows
Example: $ = -$75 + $45/ + $45/ + $45/.
See Ch 17 Mini for calculations.
Expected NPV of New Situation
E(NPV) = [($)]+[(-$)]
+ [ (-$)]
E(NPV) = -$.
The project now looks like a loser.
Growth Option: You can replicate the original project after it ends in 3 years.
NPV = NPV Original + NPV Replication
= -$ + -$
= -$ + -$ = -$.
Still a loser, but you would implement Replication only if demand is high.
Note: the NPV would be even lower if we separately discounted the $75 million cost of Replication at the risk-free rate.
Decision Tree Analysis
Notes: The 2005 CF includes the cost of the project if it is optimal to replicate. The cost is discounted at the risk-free rate, other cash flows are discounted at the cost of capital. See Ch 17 Mini for all calculations.
Cost
NPV this
2002
Prob.
2003
2004
2005
2006
2007
2008
Scenario
$45
$45
-$30
$45
$45
$45
$
30%
-$75
40%
$30
$30
$30
$0
$0
$0
-$
30%
$15
$15
$15
$0
$0
$0
-$
Future Cash Flows
Expected NPV of Decision Tree
E(NPV) = [($)]+[(-$)]
+ [ (-$)]
E(NPV) = $.
The growth option has turned a losing project into a winner!
Financial Option Analysis: Inputs
X = exercise price = cost of implement project = $75 million.
rRF = risk-free rate = 6%.
t = time to maturity = 3 years.
Estimating P: First, find the value of future CFs at exercise year.
Example: $ = $45/ + $45/ + $45/.
See Ch 17 Mini for calculations.
Cost
PV at
Prob.
2002
Prob.
2003
2004
2005
2006
2007
2008
2005
x NPV
$45
$45
$45
$
$
30%
40%
$30
$30
$30
$
$
30%
$15
$15
$15
$
$
Future Cash Flows
Now find the expected PV at the current date, 2002.
PV2002=PV of Exp. PV2005 = [(* $) +(*$) +(*$)]/ = $.
See Ch 17 Mini for calculations.
PV
2002
2003
2004
PV
2005
$
High
$
Average
$
Low
$
The Input for P in the Black-Scholes Model
The input for price is the present value of the project’s expected future cash flows.
Based on the previous slides,
P = $.
Estimating s2: Find Returns from the Present until the Option Expires
Example: % = ($ - 1.
See Ch 17 Mini for calculations.
Annual
PV
2002
2003
2004
PV
2005
Return
$
%
High
$
Average
$
%
Low
$
%
Use these scenarios, with their given probabilities, to find the expected return and variance of return.
E(Ret.)=()+()+()
E(Ret.)= = %.
2 = ()2 + ()2
+ ()2
2 = = %.
Why is s2 so much lower than in the investment timing example?
s2 has fallen, because the dispersion of cash flows for replication is the same as for the original project, even though it begins three years later. This means the rate of return for the replication is less volatile.
We will do sensitivity analysis later.
Estimating s2 with the Indirect Method
From earlier slides, we know the value of the project for each scenario at the expiration date.
PV
2005
$
High
Average
$
Low
$
Use these scenarios, with their given probabilities, to find the project’s expected PV and PV.
E(PV)=.3($)+.4($)+.3($)
E(PV)= $.
PV = [.3($-$)2
+ .4($-$)2
+ .3($-$)2]1/2
PV = $.
Now use the indirect formula to estimate 2.
CVPV = $ /$ = .
The option expires in 3 years, t=3.
V = $[N(d1)] - $75e-()(3)[N(d2)].
ln($ +
() (3).05
= .
d2 = d1 - () (3).05= d1 -
= - =- .
Use the Black-Scholes Model:
P = $; X = $75; rRF = 6%; t = 3 years: 2 =
d1 =
N(d1) = N() =
N(d2) = N(- ) =
V = $() - $75e()(3)()
= $.
Note: Values of N(di) obtained from Excel using NORMSDIST function. See Ch 17 Mini for calculations.
Total Value of Project with Growth Opportunity
Total value = NPV of Original Project + Value of growth option
=-$ + $
= $ million.
Sensitivity Analysis on the Impact of Risk (using the Black-Scholes model)
If risk, defined by s2, goes up, then value of growth option goes up:
s2 = %, Option Value = $
s2 = %, Option Value = $
s2 = 50%, Option Value = $
Does this help explain the high value of many companies?
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50
52
53
1
6
7
8
9
11
12
13
14
15
16
17
18
14
20
21
22
23
24
25
25
26
27
28
29
30
31
32
33
34
31
1
1
2
2
4
5
6
7
8
9
11
12
15
16
17
18
19
20
21
22
23
24
25
26
27
8
16
