Outline of today’s lecture
1. Value of a firm to investors and creditors
2. Analysis of profitability: ROA
3. Analysis of profitability: ROCE
4. Analysis of profitability: EPS
The value of a firm to equity investors
V = D1/(1+r) + D2/(1+r)2 + D3/(1+r)3 …….
profitability
risk
The value of a firm to creditors
V = I1/(1+r) + I2/(1+r)2 + I3/(1+r)3 + P/(1+r)3
Ii: interest revenues in period i
P: return of principal
profitability
risk
Financial Statement Analysis
the relation between the expected return and
risk of investment alternatives, and the role of analysis
in providing risk and return information.
2. Understand the usefulness of the rate of return on assets
(ROA) as a measure of a firm’s operating profitability.
3. Understand the usefulness of the rate of return on
common shareholders’ equity (ROCE) as a measure of
profitability.
4. Understand the strengths and weaknesses of earnings
per common share as a measure of profitability.
What to compare?
1. The planned ratio for the period
2. The corresponding ratio from a prior period
(time-series analysis)
3. The corresponding ratio for another firm in
the same industry (cross-section analysis)
4. The average ratio for other firms in the same
industry (cross-section analysis)
Analysis of Profitability
a. Return on assets (ROA): return to the firm
as a whole
b. Return on common equity (ROCE): return
to common shareholders only
c. Earnings per common share
Analysis of Profitability
ROA: return to the firm
ROCE: return to
common
Shareholders only
Return on Assets (ROA)
ROA presents profitability independent of the source
of financing
– Does not consider leverage
– Measure of how well the firm uses its assets to
generate income
– As if the firm is financed by equity alone
Horrigan Corporation
Year 4
Sales Revenue $ 475
Less expense:
COGS 280
Selling 53
Administrative 22
Depreciation 18
Interest 16
Total 389
Next income before tax 86
Income tax expense 26
Next Income 60
Horrigan Corporation-assuming no debts
Year 4
Sales Revenue $ 475
Less expense:
COGS 280
Selling 53
Administrative 22
Depreciation 18
Interest 16 - 16
Total 389 - 16 = 373
Next income before tax 86 + 16 = 102
Less Income tax expense 26 + =
Next Income 60 + 16 – =
Horrigan Corporation ROA
Average total assets of this company in year 4
(520+650)/2 = 585,
Then ROA = = %
Why add back interest income net of income tax savings in
the numerator?
1) If all equity, the firm won’t pay $16 interest expense,
which increase net income by $16;
2) at 30% tax rate, government will collect an additional
amount of $ (16*30%) as tax, then the actual increase
of net income is (16 – ).
Disaggregating ROA
ROA = Profit Margin ratio * Asset turnover ratio
ATO measures the firm’s
Ability to generate sales
At a given level of
Investment in assets
PM measures the
Firm’s ability to
Control cost and
Expenses at a given
Level of sales
Activity.
How to increase ROA?
1. At the current asset base, increase sales?
2. But increased sales increases ATO while
decreases PM
3. A dilemma!
4. So one has to increase sales and at the same time
hold down costs and expenses, ., hold PM at
certain level.
How to increase ROA?-2
The evolution of ROA in the .
the graphs in the next few slides are from Penman and Nissim Review of
Accounting Studies, 2001
RNOA: Return on net operating assets
Regression to the mean （回归到平均值）
Profit margin
Asset turnover
Revenue growth
Disaggregate PM
PM = (sales – COGS – SGA – depreciation ….)/Sales
COGS-to-Sales ratio
Selling, General and administrative (SGA) expense-to-
sales ratio
Etc.
By observing the time series and cross-section of each
expense-to-sales ration, one can identify abnormal ratios
and investigate the reasons, in order to control costs and
expenses to increase PM
Disaggregate ATO
ATO = Sales/average total assets
Average total assets = (average account receivables
+ average inventory + average fixed assets +
average other assets)
Accounts receivable turnover
• Measures how quickly a firm collects cash.
• If . turn over twice a year, then they average one half of a year in
collection.
• Less time is preferred to more.
• A high turnover is preferred to a low one.
• The days of outstanding for account receivables: 365 days/accounts
receivable turnover
Inventory turnover
• Indicates how fast firms sell merchandise.
• If inventory turn over twice a year, then they average one
half of a year in inventory.
• Holding inventory is costly because the funds invested in
inventory could be used elsewhere.
• A high turnover is preferred to a low one.
• Day of inventory in warehouse: 365/Inventory turnover
Fixed asset turnover
• Measures the relation between investment in long-term or
fixed assets (such as property, plant, equipment) and sales.
• Efficient use of fixed assets would be associated with high
sales.
• If fixed assets turn over every four years, then each dollar
invested in fixed assets is generating a quarter of a dollar in
sales per year.
• A high turnover is preferred to a low one.
Return on Common Equity (ROCE)
• The numerator measures return as net income reduced by
any payments to preferred shareholders as these dividends
are not available to the common shareholder and have not
been deducted from net income.
• The denominator is the average amount contributed by
common shareholders which includes
– Common stock at par,
– Additional paid in capital, and
– Retained earnings.
Relation between ROA and ROCE
• ROCE is the residual return which goes to the
common shareholders. Since it may be low in
poor years but high in good years, it has a risk,
that is, the residual return is not known.
• Debt is characterized by a definite schedule of
payments, so there is little risk to the debt holders.
• Preferred stock is like debt, the dividends are
specified. However, debtors must be paid before
preferred shareholders and if the money runs out,
then they aren't paid.
Relation between ROA and ROCE
• ROA can be divided into
– Return to creditors or debtors
– Return to preferred shareholders, and
– Return to common shareholders (ROCE)
• Because the return to debtors and preferred
shareholders are fixed, in good years when the firm
has high returns, there is a lot of profit left over for the
common shareholders; in poor years when returns are
low, there is little or maybe no profit left over.
Relation between ROA and ROCE
• Thus, if ROCE and ROA were both linear, then ROCE
would have a greater slope than ROA, that is, it is more
highly levered.
• A prudent firm will borrow funds only when the return
on those marginal funds exceed the cost of borrowing
giving a net positive return to the common shareholder.
• ROCE can be disaggregated into three related ratios
1. Profit margin ratio
2. Total assets turnover
3. Leverage ratio
Relation between ROA and ROCE
• The first two have been previously defined.
• Leverage ratio indicates the relative proportion of capital
provided by common shareholders as distinct from that
provided by creditors (debtors) or preferred shareholders.
Relation between ROA and ROCE
• A high leverage ratio means that the firm has a lot
of assets at its command, but that the shareholders
have less of their own investments at risk.
• This is good in good years because the common
shareholders capture all profits over what is
needed to service the debt.
• This is bad in poor years because the debt has to
be serviced whether or not the common
shareholders make a profit.
• Therefore, borrowing is only beneficial when
ROA is greater than the cost to borrow money
The evolution of ROCE and net borrowing cost
(NBC) in the .
Debit-to-Equity ratio (leverage) in the .
Earnings per Share (EPS) of Common Stock
• This ratio is the profit that goes to each share of common stock.
• It would be simply the net income less preferred dividends
divided by the number of common shares.
• However, the number of common shares is complicated by certain
securities that may become (convert to ) a common share. How
to account for these is a complex issue.
• For example, if there are 100 common shares but 50 preferred
shares that could convert to 50 common shares, do you divide
earnings by 100 or 150? The answer depends on how likely it is
that the convertible securities will convert.
Earnings per Share (EPS) of Common Stock
• EPS does not consider the amount of assets or capital
required to generate earnings.
• EPS is of limited use in comparing two firms.
• For investment purposes, the price to earnings ratio is
sometimes used (P/E ratio).
• This is the return to the purchaser of a share.
– P/E = (market price of a share of stock)/(EPS)
– A low P/E is preferred to a high P/E, same earnings at a
lower price.
Northwest Airlines 2001
