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第六章 边际成本及本量利分析
一、成本性态： 变动成本、固定成本及混合成本
1. The total variable cost will be changed in proportion to
output, however, the cost per unit is constant;
2. The total fixed cost will be unaffected when the output is
changing, however, the cost of per unit is changing. For
example, the cost per unit will be decrease as the output
increase. (The fixed cost usually is irrelevant to the
decision !!!)
3. Prime cost per unit of output should be considered to be a
variable cost. It including direct material, direct labour
and direct expense.
第一节 边际成本概述
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第一节 边际成本概述
And cost per unit shown as:
Units 200 300 350
£ £ £
Variable cost 70 70 70
Fixed cost 90 60
Total cost 160 130
Marginal cost is the part of the cost of one unit of product or
service which would be avoided if that unit were not
produced, or which would increase if one extra unit were
produced. It is the amount of extra cost that we incur by
producing one more unit of output. For example:
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二、相关概念
Units 299 300 301
Prime cost 20930 21000 21070
Fixed o/h 18,000 18,000 18,000
Total cost £38,930 £39,000 £39,070.
From above table, the cost of producing 1 extra unit is 39,070- 39,000 = £70
Avoidable cost emphasizes that the cost already incurred. the
depreciation and insurance are costs that cannot be avoided.
Out-of-pocket cost emphasises that to do extra activity(kilometres), cash is
needed from the pocket to pay for more it(fuel), no additional cash is
needed for depreciation and insurance.
In cost accounting the terms variable cost, out-of-pocket cost, and marginal
cost are often used interchangeably. (Not correct technically)
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三、边际成本法概述
Introduction to Marginal Costing
Contribution（边际贡献） : Sales value less variable cost of
sales. It may be expressed as total contribution, contribution per
unit or as a percentage of sales. The definition of contribution
refers to the variable cost of sales.
贡献毛利=收入-变动成本；
毛利=收入-销售产品成本，其中销售成本是制造成本（包括
了固定的制造成本）
Definition of marginal costing: The accounting system in which
variable cost are charged to cost units and fixed costs of the period
are written off in full against the aggregate contribution.
Its specially value is in recognising cost behaviour, and hence
assisting in decision making.
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三、边际成本法概述
Contrast between absorption costing and
marginal costing:
1. With absorption costing, all costs are absorbed into the
cost unit. With the marginal costing, only variable
costs are absorbed into the cost unit.
2. Under the marginal costing, the fixed cost will be
deducted from contribution and then to get profit.
Under the absorption costing, the stock will be valued
at full production cost, inclusive of fixed overheads;
however, they are only fixed production overheads.
Under marginal costing, any unsold stocks will be
valued at variable production cost only.
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三、边际成本法－－－举例
Example 1
Company X starts production on 1 January Year 1. It
makes one product and budgets to make and sell 1000
units during Year 1. The product will be sold direct to the
public from its factory premises. ( there will be no
distribution costs). A selling price of £200 per unit has
been set. The prime costs have been forecast as :
Material 40kg@£ kg £ 20
Direct labour 20 hours@£5hour £ 100
Overheads (all fixed)are budgeted @ £50,000.
Calculate the profit using two approaches: Absorption
costing approach and Marginal costing approach.
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三、边际成本法 －－－Example 1 (Solution)
1) Absorption approach:
The absorption rate can be calculated as followings:
The budgeted hours=1,000 units*20hours=2,0000hours
The absorption rate= £ 50,000/20,000hours= £ per hour
Direct Material 40kg@ £ kg £ 20
Direct labour 20 hours@ £ 5hour £ 100
Prime cost £ 120
Fixed overhead 20hours* £ per hour £ 50
Total cost £ 170
Sale £ 200
Cost of sale £ 170
Profit per unit £ 30
Total profit £ 30,000
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三、边际成本法 Example 1 (Solution)
2) Marginal costing approach £
Selling price 200
Variable cost 120
Contribution per unit 80
The aggregation contribution
1,000 units* £ 80 per unit= £ 80,000
Less fixed costs £ 50,000
Profit £ 30,000
Note: two approaches have both reported a profit of
£ 30,000. This is because 1,000 units are to be made and 1,000
units are to be sold. There is no stock at the year end.
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三、边际成本法 Example 1 (Solution)
Using the earlier example, although the firm plans to make
1,000 units in its first year, it only expects to sell 900 units.
1) Absorption costing: £
Sales 900 units* £ 200 180,000
Cost of sales:
Material 1,000* £ 20 20,000
Direct labour 1,000* £ 100 100,000
Fixed overhead 50,000
Total cost 170,000
Less stock 100units* £ 170 17,000
153,000
Profit 27,000
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三、边际成本法 Example 1 (Solution)
2)Marginal costing: £
Sales 200*900 180,000
Variable costs of sales
Material 1,000units* £ 20 20,000
Direct labour 1,000* £ 100 100,000
120,000
Less stock 100* £120 12,000
108,000
Contribution 72,000
Fixed cost 50,000
Profit 22,000
The difference of £ 5,000 in profit is because of the difference of the stock
valuations under two approaches. with absorption approach, stock per unit
value at £170, but under marginal costing , the stock per unit value at £120
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三、边际成本法 Example 1 (Solution)
Using the earlier example, although the firm plans to make
1,000 units in its first year, it expects to sell 1040 units,
provided that it has opening stock 100 units.
Reported profits will depend on whether absorption or
marginal principles are used.
Which method reports the higher profits depends upon
whether stocks are rising or falling.
If stocks rising, . produce more than sale, then
absorption costing approach report a higher profit; if
stock failing, . produce less than sale, means sale the
previous stock, then the marginal costing method report a
higher profit.
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四、边际成本法在企业决策中的应用
1. marginal costing can be used to decide between in
-house manufacture and; subcontracting（转包）
2. marginal costing can be used to assess the value
of further processing;
3. marginal costing can be used, with other
measures, to assist in setting prices for goods or
services.
4. Marginal costing is a useful technique when
considering closures. It identifies the costs and
revenue changes that result from the closure.
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四、边际成本法在企业决策中的应用
(一)、关于自制（in-house manufacture）还是转包
（subcontracting）的决策
Product (£ per unit) A B C D
Material 10 8 4 7
Other variable costs 12 28 15 17
Fixed cost 19 26 14 17
Total cost 41 62 33 41
Selling price 50 70 40 45
Profit 9 8 7 4
Annual production
and sales (units) 1,200 1,200 100 50
Question 1: should we be making and selling these products?
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四、边际成本法在企业决策中的应用
(一)关于自制（in-house manufacture） 还是转包
（subcontracting）的决策
Answer to question 1:Yes, because each product
makes a profit on an absorption basis, and each
therefore makes a contribution.
Question 2: In which case, should we let another firm
make these products for us? Suppose a firm could, and
quotes per unit;
Product A B C D
Quoted price £ £ £ £
Per unit 40 63 18 26
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四、边际成本法在企业决策中的应用
(一)关于自制（in-house manufacture） 还是转包
（subcontracting）的决策
1. Product A: total internal cost of manufacture £41. This is irrelevant,
because fixed costs will not saved if they are all general fixed costs.
Internal variable cost of manufacture £22. Therefore, it is not worth
paying £40 to save £22. So carry on with internal manufacture.
2. Product B: Total internal cost of manufacture £62. This is irrelevant,
because fixed costs will not saved if they are all general fixed costs.
Internal variable cost of manufacture £36. Therefore, it is not worth
paying £63 to save £36. So carry on with internal manufacture.
3. Product C: Total internal cost of manufacture £33. This is irrelevant,
because fixed costs will not be saved if they are all general fixed costs.
Internal variable cost of manufacture £19. It is worth paying £18 to
save £19. Subcontracting Product C will minimize cost and will
maximize profit. (danger: cut you out…)
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四、边际成本法在企业决策中的应用
(一) 关于自制（in-house manufacture） 还是转包
（subcontracting）的决策
Product D: total internal cost of manufacture £41. This is
irrelevant, because fixed costs will not saved if they are all
general fixed costs. Internal variable cost of manufacture £24.
Therefore, it is not worth paying £26 to save £24. So carry on
with internal manufacture.
Question 3: Further information to Product D: when produce the
Product D, then need to purchase a special gauge at cost of £250,
to check each completed Product D. The gauge loses accuracy
after being used to test 50 products, and a new gauge has to be
purchase. The gauge cost is included in fixed costs. If an outside
firm makes the product, it will have to purchase its own gauges.
Does this change the decision?
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四、边际成本法在企业决策中的应用
(一) 关于自制（in-house manufacture） 还是转包
（subcontracting）的决策
Answer: Yes, this is a directly attributable fixed cost.
Each product should bear £250/50=£5 attributable fixed
cost, however, if Product D is subcontracted, then it is
worth paying £26 to save £24+ £5.
In sum, on cost consideration alone, internal
manufacture Product A and B should be continued,
Product C and D should be subcontracted.
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四、边际成本法（Marginal Costing)在企业决策中的应用
（二）Decision on further processing?
Andor Limited produces 18,000 litres of Product XP6
each month. XP6 is sold for £22 per litre. It is
proposed to further process XP6 to make
XP6(superior). Further processing will cost £ per
litre of input, and there will be additional fixed costs of
£15,000 each % of input material will be lost
in further processing. This will have no value. XP6
(superior) is expected to sell for £34 per litre.
Should XP6 be further processed into XP6 (superior)?
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四、边际成本法在企业决策中的应用
The present monthly revenue is 18,000* £22=
£396,000;
The monthly revenue for XP6(superior)
=18,000*90%*34= £550,800
Extra revenue = £154,800
The extra cost is:
Variable 18,000* £ + fixed £15,000= £132,000;
Therefore, it is worth producing XP6 (superior).
Note: Fixed cost of £15,000 is relevant to the
decision.
（二） Decision on further processing?
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（三）Price setting
The firm is a 2-product firm in Year 7, by adding budget is
:
SR5 SR6 Total
Units of production and sale 8,000 2,000 10,000
Manufacturing hours 12,000 1,000 13,000
£ £ Total (£)
Direct material cost 10,000 2,000 12,000
Variable convention costs 9,000 1,000 10,000
Fixed conversion costs have increased to £16,250.
If the firm wants to make £5,750 profit in Year 7, what will the price
to be set ?
四、边际成本法（Marginal Costing)在企业决策中的应用
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（三 ）Price setting
The product costs per unit: SR5(£) SR6(£)
Material cost
Variable conversion cost
Variable cost
Fixed cost (£ per hour)
Total cost
The budgeted total costs are: £
Direct material cost 12,000
Variable conversion cost 10,000
Fixed conversion cost 16,250
Total cost 38,250
Profit required 5,750
Sales revenue required 44,000
四、边际成本法（Marginal Costing)在企业决策中的应用
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（三）Price setting
1st Method: Mark-up: The total profit of £5,750 as a
% of total cost of £38,250 is %. The required
selling price will be:
SR5(£) SR6(£)
Total cost per unit
Add mark up %
Target selling price
In the real commercial world, the selling price are
largely decided by competition and other factors.
四、边际成本法（Marginal Costing)在企业决策中的应用
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（三）Price setting
2nd method: Variable cost+Contribution=Selling Price
The required contribution is£5,750 + £16,250=£22,000. As
the planned hours are 13,000, so the required contribution per
hours is £22,000/13,000= £. This would give the
required selling prices of:
SR5 SR6
£ £
Material cost per unit
Variable conversion cost per unit
Variable cost per unit
Contribution at £ per hour
Selling price
四、边际成本法（Marginal Costing)在企业决策中的应用
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（三） Price setting
Contribution
Hours to make
Contribution per hour
The 3rd method: Added value+Direct material=Selling Price
The required added value is £44,000 less material of
£12,000= £32,000. And an added value per hour is
£32,000/13,000= £ per hour. This would give required
selling price of : SR5 (£) SR6(£)
Direct materials
Added value @ £ per hour
Target selling price
四、边际成本法（Marginal Costing)在企业决策中的应用
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（四）Closure decision
The management of Company X are considering the closure of
Branch 10. Annual sales of this branch are £860,000. An average
gross margin of 60% is earned. £345, 000 is paid for staff wages and
salaries. In addition, sales staff are paid a commission of 2% of sales
turnover. Staff with salaries totaling £75,000 would be absorbed in
other branches. The remaining staff would be made redundant. This
would involve one-off redundancy costs of £36,700. An amount of
£80,000 is apportioned to branch 10 from Head Office costs, which
would be unaffected in total by the closure of Branch 10. Other
expenses amount to £55,000, and these would be saved by the
closure of Branch 10. It is estimated that sales of £340,000
normally made at Branch 10 would be picked up at other branches.
The rest of the sales would be lost.
How should this closure proposal be evaluated?（Saving or costing is
from the firm point of view, not the branch along.）
四、边际成本法在企业决策中的应用
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（四）Closure decision
Lost of sales: £
Lost sales from Branch 10 860,000
Sales picked up at other branches (340,000)
Net lost sales 520,000
Gross margin 60% 312,000
Cost Savings: £
Staff wages and salaries 345,000
Less wages and salaries not saved (75,000)
Other expense 55,000
Commission 2% on £520,000 10,400
335,400
Net saving from closure of Branch 10 23,400
四、边际成本法（Marginal Costing)在企业决策中的应用
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四、边际成本法（Marginal Costing)在企业决策中的应用
One-off redundancy payment 36,700
Net loss from closure 13,300
Note:
The Branch 10 should not be closed, however, it reflects a point
which is included in many questions of this type: the redundancy
payment is only paid once. In all future years the company will be £
23,400 (335,400 - 312,000) better off if Branches 10 is closed. (Net
saving of £ 23,400)
It has been assumed that staff transferred to other branches are
additional staff. If they are being placed in jobs for which people
would otherwise have to be recruited, then the £75,000 should not be
deducted. From firm’s point of view, £75,000 is not saved.
（四）Closure decision
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第二节 边际贡献
Contribution: Sales value less variable cost of
sales. It may be expressed as total contribution,
contribution per unit or as a percentage of sales.
The definition of contribution refers to the
variable cost of sales.
Contribution in relation to a scarce resource can
be used to allocate that resource most profitably.
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第二节 边际贡献的计算—举例
Example 1: At Year 3, the company X plans to make
900 units of product X1 and 400 units product X2, the
prime costs for each products as followings:
X1 X2
Material 40kg*@ £ 20
100kg*@ £ 50
Direct labour 20hrs@ £ 5hr 100
5hrs@ £ 5hr 25
Prime cost 120 75
Selling price 200 135
Fixed cost £ 50,000
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第二节 边际贡献的计算—举例
Using the marginal costing method:
X1 X2
Direct material 20 50
Direct labour 100 25
Variable cost 120 75
Selling price 200 135
Contribution per unit 80 60
Unit 900 400
Total contribution 72,000 24,000 96,000
Fixed costs 50,000
Profit 46,000
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Decision making: Scarce Resource (Example 2)
Using data from above example , for Year 3, 900 units of
X1 and 400 units of X2 will be made. If there is only £
30,000 of material will be available for the whole year.
What is the best profit can be made?
(Key point: the contribution per £ of material should be
calculated)
X1 X2
Contribution per unit 80 60
Material used per unit 20 50
Contribution per £ of Material 4
第二节 边际贡献在企业决策中的应用
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第二节 边际贡献在企业决策中的应用
From the calculation, the X1 give the best contribution
in relation to the scarce material used. It is preferred to
allocated scare labour to X1 first:
As X1 need £ 20 material per unit, therefore, 900 units
needs 900* £ 20=18,000; this leaves £ 30, 000- £ 18,
000= £ 12, 000 for product X2.
This will make £ 12, 000/ £ 50=240 units of X2
The best (or optimal) profit is therefore:
(900* £ 80)+(240* £ 60)- £ 50, 000= £ 36, 400
Decision making: Scarce Resource (Example
2)
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第二节 边际贡献在企业决策中的应用
If the direct labour hours will be limited to 16, 000
hours. What is the best profit can be made?
Solution:
X1 X2
Contribution per unit 80 60
Direct labour hours per unit 20 5
Contribution per direct labour hour 4 12
Decision making: Scarce Resource (Example 3)
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Decision making: Scarce Resource (Example 2)
From the calculation, we can see the X2 give the best
contribution in relation to the scarce labour used. It is
preferred to allocated scare labour to X2 first:
X2 need 5 hours per units
Therefore, 400 units needs400*5=2,000 hours
This leaves 16,000-2,000=14,000 hours for product X1.
This will make 14,000/20 hours=700 units of X1
The best (or optimal) profit is therefore:
(700* £ 80+400* £ 60)-50,000= £ 30, 000
第二节 边际贡献在企业决策中的应用
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第三节 保本点(盈亏临界点)的计算-公式
Break-Even Calculations:
Break-even is where neither a profit nor a loss
is made. The aggregate contribution must just
be enough to cover the fixed cost.
Formula:
Fixed costs/ Contribution per unit= units to
break-even
Fixed costs/CS ration= sales value to break-
even
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第三节 保本点的计算-举例
Break-Even Calculations
Company X starts production on 1 January Year 1. It
makes one product and budgets to make and sell 1000
units during Year 1. The product will be sold direct to
the public from its factory premises. ( there will be no
distribution costs). A selling price of £ 200 per unit has
been set. The prime costs have been forecast as :
Material 40kg@ £ kg £ 20
Direct labour 20 hours@ £ 5hour £ 100
Overheads (all fixed)are budgeted @ £ 50000
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第三节 保本点的计算-举例
Break-Even Calculations
Using the same data as above example:
Units to break-even= £ 50,000/ £ 80=625 units
Sales value to break-even= £ 50,000/40%= £ 125,000
(CS ratio= £ 80/ £ 200=40%)
Prove that this is correct: £
Sales 625 units*200 125,000
Variable cost 625*120 75,000
Contribution 50,000
Fixed costs 50,000
Profit/Loss Nill
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实现目标利润的销售数量与销售金额的计算
Required Profit Calculation
Example 5: Data as above, what do the sales need
to be, to make a profit of £ 40,000
(Fixed cost+ required profit)/Contribution per
unit
=(£ 50,000+ £ 40,000)/ £ 80=1,125 units
Or (Fixed cost+required profit)/ CS ratio=(£
50,000+ £ 40,000)/40%= £ 225,000
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第四节 本量利图 (保本图)----概述
The Definition of Breakeven Chart
CIMA defines a breakeven chart as:
A chart which indicates approximate profit or loss at
different levels of sales volume within a limited range.
Few points regarding definition:
1. The breakeven chart is a visual representation of
relationship between cost, volume and profit.
2. “approximate” indicates that readings from a graph can
never have the accuracy of calculations.
The following data to demonstrate a breakeven chart in
traditional format:
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第四节 本量利图（保本图)----传统式举
例：
The Example of Breakeven Chart (example
1)
Baber Limited produces and sells a single product at
selling price of £28 per unit. In any year, sales are never
less than 9,000 units and never more than 14,000 units.
The variable cost of each unit produced is £12, and fixed
costs for the year amount to £160,000.
Required:
(a) Construct a traditional/conventional breakeven chart.
(b) On the chart:
Indicate the breakeven point, and the relevant range of the
company’s activity. And read and indicate the breakeven
sales in £ and units.
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第四节 本量利图（保本图)----传统式举
例：
The Example of Breakeven Chart (example
1)
Solution:
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第四节 本量利图（保本图)----传统式举例：
The Example of Breakeven Chart
Example 2: Company X makes one product, which
it sells for £40 per unit. The variable cost per unit is
£30, and fixed costs in total are £30,000. The
maximum output is 5,000 units.
1. Use the x-axis to represent units of output, use the y-
axis to represent £; and choose the maximum values
on each scale. In this example the maximum output
is 5,000 units. Therefore, scale the x-axis from 0
units to 5,000 units;
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第四节 本量利图（保本图）----传统式举例：
The Example of Breakeven Chart
the y-axis must therefore allow for the sales revenue
from 5,000 units. This will be 5,000*40=£200,000.
Therefore, scale the y-axis from 0 to £200,000.
2. For a traditional chart, the fixed costs are plotted first. So find the
£30,000 point on the y-axis, and extend the fixed cost line parallel
to the base line.
3. Plot the variable costs over the fixed cost. It is the total cost line that
is therefore being plotted. Find two points (x=0;y=30,000) and
(x=5,000; y=180,000) and the total cost line by connecting the two
points.
4. Finally draw in the sales revenue line. This will connect the points
(x=0;y=0) and (x=5,000;y=200,000)
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第四节 本量利图（保本图）----传统式
Breakeven Point
CIMA defines a breakeven point as:
The level of activity at which there is neither profit nor loss.
Read the breakeven point from the graph; The reading can be
checked. Breakeven is F/C, which in this case is
£30,000/(£40- £30)=3,000 units.
If the company normally makes and sells between 2,500 and
4,000 units( the relevant range ), then what happens to the
cost and revenue lines outside that range is less important.
Marginal of safety: if the company was planning to make and
sell 3,800 units this year, the margin of safety would be 800
units (3,800 units less 3,000 units).
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第四节 本量利图（保本图）----贡献式
Contribution breakeven charts
The contribution breakeven charts is another
way of presenting the same information as
breakeven chart;
The contribution breakeven charts has the
same x and y axes as a traditional chart, but
draws the variable cost line first instead of the
fixed cost line.
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第四节 本量利图（保本图）----贡献式
Contribution breakeven charts
Construct a contribution breakeven chart using the information given in
example 1,and clearly indicating the “contribution Wedge”.
Solution:
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第四节 本量利图 （保本图）----贡献式
Contribution breakeven charts
Example 2:
Use the same date as example 2 in the lesson 1.
1. The x-axis and y-axis must be scaled and labeled as example 1.
2. Draw the variable cost line first. The plotting points for variable cost line are
(x=0; y=0); (x=5,000;y=150,000);
3. Draw the sale revenue line. The plotting points are (x=0;y=0) and
(x=5,000;y=200,000). Joining these two points will give the sales revenue
line.
4. Show the wedge of contribution as the area between the sales revenue line and
the variable cost line.
5. Finally, put on fixed costs to show the total cost line. The fixed costs are added
to the variable costs. The plotting points for total costs line are (x=0;y=3,000)
and (x=5,000;y=180,000).
Note: The breakeven point must be same as example 1. The
breakeven point is reached when the contribution
wedge increases until the contribution=fixed costs.
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第五节 利量图（PV图）—概述
The Introduction to Profit graphs
A PV graph or chart is a type of breakeven chart.
It allows direct readings of profit or loss. On a traditional or
contribution breakeven chart, profit has to be read as a space
between the total cost line and the total revenue line.
PV图反映出产量的变化（量）对营业收益（利润）的影响。
The profit graph has an x-axis which represents output. Output
can be measured in units(for one-product firm), or in sales value,
or in machine hours, or in any other measure of output. The units
and sales £ are the most usual.
The y-axis represents profit or the x-axis it represents
profit and below is loss.
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第五节 利量图（PV图）—举例
Example to Profit graphs---Example 3
Example 3:
Hartopp Limited makes and sells a single product.
For year 10, sales were £180,000, sold at £9 per
unit. Variable costs were £4 per unit and a profit
of £35,000 was made.
Required:
Construct a profit graph for Year 10.
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第五节 利量图（PV图）—举例
Example to Profit graphs---Example 3
Solution:
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第四节 利量图（PV图）—举例
Example 4 :
A company makes one product. Its results for the current
year show:
£ £
Sales 180,000
Variable cost 72,000
Fixed costs 90,000
Total cost 162,000
Profit 18,000
Prepare a profit graph for these figure.
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第四节 利量图（PV图）—举例
Notes:
1. As no units have been mentioned, although the firm
does only make one product. Therefore, the x-axis will
be scaled in Sales £. Sales of £180,000 must be taken to
x-axis.
2. For the maximum loss must be equal to the fixed costs.
3. The plotting points are (x=0;y=90,000 loss) and
(x=180,000;y=18,000 profit).
4. The breakeven point is where the drawn line crosses the
x-axis.
56
第四节 利量图（PV图）—举例
Example 4:
Produce a profit graph for the following company: £
Sales 240,000
Total cost 220,000
Profit 20,000
The company breaks even at sales of £190,000.
Note:Get two Points: (240,000; 20,000); (190,000; 0). Extend these two
points and finished the graph;
Sale 240,000 190,000
Profit 20,000 Nil
Increase in sale is £50,000 and £20,000 for profit , (because of fixed costs ,
the change in profit equal in contribution)therefore c/s
ratio=20,000/50,000=40%, the contribution is 40% £190,000=£76,000. As
the the £190,000 is the breakeven sale, so the contribution =fixed cost, so the
fixed cost is £76,000
