123
CHAPTER 8
THE CVP APPROACH TO DECISIONS
INTRODUCTION
In Chapter 5, we briefly discussed the use of a standard cost to compare to actual costs to control
food and beverage costs. Chapter 7 identified various costs by type, knowledge of which is
necessary to facilitate understanding and their use in making rational business decisions. In
particular, Chapter 7 emphasized the importance of breaking costs into their fixed and variable
elements. This chapter continues the discussion of fixed and variable costs, and shows how they
interrelate with the volume of sales revenue and/or sales units, as well as operating income. The
resulting use of such information is the basis of Cost, Volume, Profit or CVP analysis.
TRUE OR FALSE QUESTIONS
(Correct answer indicated by T for True and F for False answers)
1. CVP analysis assumes that costs have been fairly accurately broken down into their
fixed and variable elements.
T
2. In making decisions using CVP analysis, the only information one ever needs is about
sales revenue and fixed and variable costs.
F
3. CVP analysis should be limited to individual decisions, or situations wherever
possible.
T
4. Sales revenue less fixed costs equals contribution margin.
F
5. On a graph of sales revenue and costs, the fixed cost line is drawn from the point of
intersection of the horizontal and vertical axes upward and to the right.
F
6. On a graph of sales revenue and costs, the breakeven point is that point where the
fixed cost and the sales revenue lines intersect.
F
7. In the CVP formula where the denominator is expressed in percentage terms, the
answer will be in dollars.
T
8. The CVP formula will usually give an answer more accurate than an answer from a
multi-point graph.
T
9. In a business with both fixed and variable costs, the amount by which sales revenue
has to go up to cover an increased fixed cost will be the amount of that fixed cost
increase if net income is to remain unchanged.
F
10. The CVP formula can only be used if just one item (sales revenue, fixed cost, or
variable cost) is changed at a time.
F
11. The variable cost percentage can be calculated by dividing the variable cost per unit
by the average sales revenue per unit, and multiplying by 100.
T
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12. If the variable cost per customer served in a coffee shop is $1.00 and the average
check is $3.33, the variable cost is 33.1/3%.
F
13. The CVP formula can be used to convert sales levels directly into units rather than
dollars.
T
14. In the CVP formula, the contribution margin can only be expressed in percentage
terms.
F
15. In a business with both fixed and variable costs, a 10% decrease in prices can be
offset by a 10% increase in number of units sold.
F
16. The CVP formula cannot be used to help make decisions if a business is currently in a
loss position.
F
17. If a motel is losing $1,000 a month and rents its units for an average of $20 a night, it
needs to sell 50 more units a month to break even.
F
18. A joint cost is one shared by more than one department.
T
19. CVP analysis cannot be used to make decisions about a specific department if it has
joint costs.
F
20. If two departments have the same fixed costs but different contribution margins, an
increase in sales revenue in one department will not give the same amount of addi-
tional contributory income as the same sales revenue increase in the other department.
T
21. If a department has a 30% contribution margin, each extra dollar of sales revenue will
yield a contribution margin of $0.70.
F
22. In a CVP analysis concerning two or more departments, one needs to know the sales
revenue mix, or ratio of sales revenue, for each department.
T
23. In a multi-department CVP analysis, the combined contribution margin percentage is
a figure weighted by the sales revenue mix.
T
24. In multi-department decisions, the CVP formula cannot be used for compound
changes.
F
25. Decisions made as a result of CVP analysis are not guaranteed to be the correct ones.
T
26. When a company incorporates its tax rate into the calculations for CVP analysis, the
desired profit before tax is calculated by dividing the after-tax net income by (1 – Tax
rate).
T
MULTIPLE CHOICE QUESTIONS
(Correct answer indicated by asterisk)
1. An assumption under CVP analysis is that:
(c) Variable costs will change in inverse fashion with sales revenue
(d) Total costs will not increase as sales revenue increases
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2. Sales revenue is $250,000, fixed costs are $90,000, profit is $50,000, and sales price per unit
(c) $20.00
(d) $25.00
3. On a breakeven graph, the breakeven point is the point where the:
(c) Sales revenue and variable cost lines intersect
(d) Total cost line intersects the vertical axis
4. When dealing with a problem using the CVP equation for a motel that receives rent from
leasing out its restaurant, the rent income in the equation is:
(a) Added to the room sales revenue
(b) Deducted from variable costs
5. Fixed costs are $90,000, profit required is $10,000, and variable costs are 40%. Sales revenue
will have to be (to nearest $1,000):
(c) $225,000
(d) $329,000
6. Fixed costs are $85,000, operating income required is $25,000, rent income is $5,000, and
the contribution margin is 35%. Sales revenue will have to be (to nearest $1,000):
(c) $177,000
(d) $329,000
7. In using the CVP equation, the sales level required in units to breakeven is determined by
dividing:
(c) Fixed costs plus net income by the contribution margin percent
(d) The sales level in dollars by unit variable cost
8. A college’s food operation has an average meal price of $6.00. Variable costs are $3.75 per
meal and fixed costs total $75,000. How many meals must be sold to provide an operating
income of $30,000?
(a) 13,333
(b) 33,333
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9. Given the facts in the Question 8, how many meals would have to be sold if variable costs
increased 20%?
(a) 50,000
10. Given the facts in Question 8, how many meals would have to be sold if fixed costs declined
by 20%?
(c) 46,667
(d) 70,000
11. An establishment has three departments with variable costs as a percentage of sales revenue
of 30%, 40%, and 50%, respectively. Each department has the same level of sales revenue.
The weighted average contribution margin is:
(c) 67.0%
(d) 33.0%
12. A restaurant has a food operation with a 30% variable cost and a bar operation with a 25%
variable cost. The food operation produces 60% of total sales revenue and the bar 40%. If the
restaurant wanted an extra $7,500 in operating income, by how much would bar sales
revenue only have to increase to provide this added profit?
(a) $30,000
(b) $18,750
13. Using the data from the previous question, by how much would sales revenue have to
increase if the added operating income had to be provided by a joint increase in sales
revenue, keeping the sales revenue mix the same?
(a) $26,786
(b) $23,810
14. When a company incorporates its tax rate into the calculations for CVP analysis, the desired
operating income (before tax) is calculated by:
(c) Multiplying the operating income before tax by (1 − Tax rate)
(d) Dividing the operating income before tax by (1 – Tax rate)
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15. A restaurant has sales revenue of $500,000, variable costs of $200,000, and fixed costs of
$200,000. The owner wants net income after tax of $40,000. The tax rate is 30%. What is the
operating income (before tax)?
(a) $ 17,143
(b) $ 40,000
16. A restaurant specializes in a seafood buffet serving dinner only, at a price of $15.75 per
person. Its average variable cost is $6.30 per person. The fixed cost is $6,000 per month.
How many buffet meals must be served monthly to break even if they are open 20 days per
month?
(a) 952
(b) 380
EXERCISE SOLUTIONS
E8.1 Find breakeven sales revenue.
E8.2 Find breakeven sales revenue.
E8.3 Find breakeven sales revenue.
E8.4 Find breakeven sales revenue in units.
E8.5 Find breakeven units.
128
E8.6 Find the unit contribution margin, breakeven units, variable cost percentage, contribution
margin percentage, and breakeven sales revenue in dollars.
a. CM[u] = SP[u] − VC[u] = $12.75 − $4.85 = $7.90
E8.7 Find operating income (before tax) and income tax.
Net income after tax is: $200,000 × 20% = $40,000
E8.8 Find the additional sales revenue required to support the desired net income after tax.
a. NI [AT] / [1 − Tax Rate] = Additional OI [BT]
E8.9 Find additional sales revenue required.
E8.10 Calculate the amount of sales revenue each cost item requires.
Fixed Cost: $120,000 / 38% = $315,789
$700,000 / $14.00
=
Customers
$640,000 / $14.00
=
Customers
PROBLEM SOLUTIONS
P8.1 a. Find breakeven sales revenue:
b. Find operating income if the restaurant’s actual sales revenue were to be $640,000
rather than $700,000. Variable costs as a percentage of sales revenue will not
change.
Contribution Margin Income Statement
$640,000
( 396,800)
$243,200
( 168,000)
$ 75,200
c. If sales revenue is $640,000 instead of $700,000, how many fewer customers would
be served?
P8.3 a. Find breakeven sales revenue.
VC% = 38% + 27% + 10% = 75%
Depreciation expense: $150,000 x 20% = $30,000
131
P8.4 a. Find the present annual operating income:
Contribution Margin Income Statement
Sales Revenue:
$582,000
Variable Costs:
Cost of Sales [38% × $582,000]
( 221,160)
Contribution Margin
$360,840
Expenses
Other variable costs [28% × $582,000]
$162,960
Fixed costs
150,000
( 312,960)
Operating income [BT]
$ 47,880
b. Find increase to operating income with a new cost added:
Liquor variable costs: [38% × $582,000]
=
$221,160
Other variable costs: [28% × $582,000]
=
$162,960
Total variable costs
=
$384,120
c. Find the new operating income if menu prices are raised by 6%.
Contribution Margin Income Statement
Sales revenue [$582,000 × 106%]
$616,920
Variable costs (no change)
(384,120)
Contribution Margin
$232,800
Fixed costs [$150,000 + $12,000]
(162,000)
Operating income
$ 70,800
d. Determine how much sales revenue can decrease before operating income falls
below $30,000 per year.
($150,000 + $30,000 + $12,000) / [1 – ($384,120 / $616,920)]
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P8.5 a. Calculate motel’s breakeven level of occupancy:
Assuming 10 rooms Rms. × % × Rate = Tot. Rev.
4.5 × $60 = $270 70 × 45% × $60 = $1,890
3.5 × $74 = $259 70 × 35% × $74 = $1,813
b. Find the occupancy % to provide OI [BT] of $65,000 per year.
c. Find the occupancy percentage to provide an operating income operating income
(OI) before tax of $65,000 if the average room rate is decreased by 20%.
New selling price = $70.90 – 20% = $70.90 – $14.18 = $56.72
d. Find the occupancy percentage to provide $65,000 OI [BT], average room rate
increase is 10%, VC per unit is $16.00 and $30,000 is wanted for advertising.
New average rate 10% increase = $70.90 × 110% = $77.99
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P8.6 a. What is the motel’s occupancy breakeven level?
VC VC per Room Sold
Room’s × Occupancy % × 365
b. What level of sales revenue is required to provide operating income before tax?
c. Room rate is increased by $8.00 and $100,000 of OI is still wanted. How many
fewer rooms per night need to be sold as compared to rooms to be sold in part b.
above?
New room rate = $65.60 + $8.00 = $73.60
d. Cost changes: (1) + $2.00 VC per room variable (housekeepers)
(2) + $1.00 other variable costs
(3) + $48,000 fixed cost increase ($4,000 × 12 months)
(4) + $30,000 added for advertising costs
134
P8.7 a. Total sales revenue is provided jointly by both departments.
Rooms:
$600,000 / $800,000
=
75.0%
Food:
$200,000 / $800,000
=
25.0%
Totals:
$800,000
100.0%
Rooms variable costs: $180,000 / $600,000 = 30.0%
b. Cost / CM% = $1,000 / 20% = $5,000
P8.8 a. Determine the contribution margin of the café.
b. Determine the contribution margin of the bar.
c. Determine the combined contribution margin of the café and bar.
d. Determine the additional sales revenue necessary to cover the additional $50,000
operating income if provided by both the café and the bar.
Additional Sales Revenue:
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P8.9 Calculate changes to contributory income. Total FC is $335,000.
Rooms
Food
Totals
Sales revenue
$440,000
$110,000
$550,000
Variable costs
( 132,000)
( 66,000)
( 198,000)
Contribution margin
$308,000
$ 44,000
$352,000
a. Increase Rooms Contribution Margin (CM) by $20,000:
Rooms CM = $440,000 − $132,000 = $308,000
b. Increase Food CM by $20,000
Food CM = $110,000 − $66,000 = $44,000
c. Doubling present OI [BT] with no change to direct VC costs.
d. Doubling present Food OI [BT] with no change to direct VC costs.
Combined CM – Fixed costs = OI [BT]
e. Doubling present operating income [BT] jointly with no change to direct (VC) costs.
f. Calculate the required total sales revenue if provided jointly by both departments.
• Doubling OI [BT] by both departments
• Add an additional $5,000 on advertising.
136
P8.10 a. Find the desired OI [BT].
Food
Item
SP
–
VC
=
CM
/
SP
=
CM%
×
SR%
=
CCM%
1
$15.00
–
$7.75
=
$7.25
/
$15.00
=
48.3%
×
16.0%
=
7.7%
2
12.95
–
7.50
=
5.45
/
12.95
=
42.1%
×
20.0%
=
8.4%
3
11.00
–
5.50
=
5.50
/
11.00
=
50.0%
×
22.0%
=
11.0%
4
8.95
–
2.85
=
6.10
/
8.95
=
68.2%
×
14.0%
=
9.5%
5
9.95
–
6.50
=
3.45
/
9.95
=
34.7%
×
8.0%
=
2.8%
*Beverage CM% = 1 – VC% = 1 – 55% =
45.0%
×
20.0%
=
9.0%
Total combined CM%
100%
48.4%
Fixed costs + OI $546,000 + $25,000 $571,000 $1,179,752 Sales revenue
CM% 48.4% 48.4%
b. Removal of Item 5 and its sales revenue are evenly split over the remaining items.
Beverage VC% will decrease and its CM% will increase to 48% (1 − 52%).
Item
CM%
×
SR%
=
CCM%
1
48.3%
×
18.0%
=
8.7%
2
42.1%
×
22.0%
=
9.3%
3
50.0%
×
24.0%
=
12.0%
4
68.2%
×
16.0%
=
10.9%
*Beverage
48.0%
×
20.0%
=
9.6%
Total combined CM%
50.5%
Sales revenue: (Fixed costs + OI) / CM% = $571,000 / 50.5% = $1,130,693
c. New Operating Income before tax:
137
P8.11 Alternative (1): Analysis of the first alternative, using owner’s capital.
Management & supervisory salaries expense
$49,200
Rent expense
32,000
Insurance expense
4,800
Depreciation expense [20% × $160,000]
32,000
Total (Known) Fixed Costs
$118,000
Return on investment [18% × $200,000]
36,000
Operating Income [BT]
$154,000
Total Variable Costs = 35% + 30% + 18% = 83%
100% of SR − Total VC % = 100% − 83% = 17% Known cost %
OI [BT] / Known FC % = SR
$154,000 / 1 – 83% = $154,000 / 17% = $905,882 Sales revenue
Alternative (2): By borrowing $60,000 and renting equipment for $40,000 reduces the
use of owner’s capital to $100,000. The operating income [BT] return on investment is
$18,000 (18% × $100,000) compared to the 1st alternative, which was $40,000.
The effect of using the alternative (2) of assuming debt is summarized:
Management and supervisory salaries expense
$49,200
Rent expense
32,000
Insurance expense
4,800
Depreciation expense [20% × $120,000]
24,000
Interest expense [8% x $60,000]
4,800
Equipment rental expense
10,000
Total Fixed Costs
$124,800
Return on investment [18% x $100,000]
18,000
Operating Income [BT]
$142,800
Fixed costs / 1 − VC% = SR
$142,800 / [1 – (35% + 30% + 18%)] = $142,800 / 17% = $840,000 SR
The required sales revenue is $65,882 lower with the loan option alternative 2, than with
alternative 1, using 100% of invested capital. Since the contribution margin percentage
is the same for both options, the owner would be better to borrow $60,000 to lower the
required sales. As well, the owner still has $100,000 to invest in another project.
138
P8.12 a. Calculate the hotel’s breakeven point.
b. Operating income [BT] of 15% on $1,200,000 is $180,000.
c. Complete an analysis of the renegotiations of the hotel’s land lease.
i. Acceptance of a variable lease will reduce fixed costs $80,000 ($570,000 −
$490,000) and variable costs will increase by 6.5%.
35% + (10% × 65%) = 35% + 6.5% = 41.5%
ii. The indifference point (or breakeven sales) at which fixed rental cost and
variable rental cost for one year are identical is:
Fixed Cost Lease / Change of VC
iii. Should management accept the variable lease if sales revenue is forecast to be
$1,200,000 next year?
Sales Revenue $1,200,000
Variable Costs at 35% ( 420,000)
iv. Should management accept the variable lease if sales revenue is forecasted to be
$1,400,000 next year?
Sales Revenue $1,400,000
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CASE 8 SOLUTIONS
Variable
Fixed
Analysis of restaurant costs, Year 2007
Cost %
Costs
Cost of Sales Food & Beverage [$220,626 / $639,111]
$220,626
34.5%
Salaries and wages expense
$223,543
Fixed portion
(156,400)
$156,400
Variable portion [$67,143 / $639,111]
$ 67,143
10.5%
Laundry [$16,609 / $639,111]
16,609
2.6%
Kitchen fuel
7,007
Fixed portion
( 3,800)
3,800
Variable portion [$3,207 / $639,111]
$ 3,207
0.5%
China & tableware expense [$12,214 / $639,111]
12,214
1.9%
Glassware expense [$1,605 / $639,111]
1,605
0.3%
Contract cleaning expense [$3,207 / $639,111]
5,906
5,906
Licenses
3,205
3,205
Other operating expenses [$4,101 / $639,111]
4,101
0.6%
Administrative and general expenses
15,432
15,432
Marketing expense
6,917
6,917
Utilities expenses
7,918
Fixed portion
( 3,100)
3,100
Variable portion [$4,818 / $639,111]
$ 4,818
0.8%
Insurance expense
1,895
1,895
Rent expense
24,000
24,000
Interest expense
23,981
23,981
Depreciation expense [$13,752 + $6,372]
20,124
20,124
Totals
51.7%
$264,760
a. Total variable costs as a percentage of sales revenue is: 51.7%
b. Total fixed costs are: $264,760
c. Breakeven Sales Revenue / Average check per guest (from Case 3)
d. To increase operating income to 10% [10% – 6.9%] = 3.1% increase in sales revenue]
(1) $639,111 × 3.1% = $19,812