Question 1
In a slow year, Deutsche Burgers will produce 3.5 million hamburgers at a total cost of $5.3
million. In a good year, it can produce 5.5 million hamburgers at a total cost of $6.2 million.
a. What are the fixed costs of hamburger production?
b. What is the variable cost per hamburger?
c. What is the average cost per burger when the firm produces 3 million hamburgers?
d. What is the average cost per burger when the firm produces 4 million hamburgers?
e. Why is the average cost lower when more burgers are produced?
Explanation
The extra 2 million burgers increase total costs by $0.9 million.
Therefore, variable cost = $0.9 million / 2 million burgers or $0.45 per burger.
$5.3 million = (3.5 million burgers × $0.45) + Fixed costs
Fixed costs = $3.725 million
a.
Fixed costs = $3.725 million
b.
Variable costs = $0.45 per burger
c.
Total cost = (3 million burgers × $0.45) + $3.725 million = $5.075 million
Average cost = $5.075 million / 3 million burgers = $1.69 per burger
d.
Total cost = (4 million burgers × $0.45) + $3.725 million = $5.525 million
Average cost = $5.525 million / 4 million burgers = $1.38 per burger
e.
The fixed costs are spread across more burgers—thus the average cost falls.
Question 2
A project currently generates sales of $9 million, variable costs equal 40% of sales, and fixed
costs are $1.8 million. The firm’s tax rate is 30%. Assume all sales and expenses are cash items.
a. What are the effects on cash flow, if sales increase from $9 million to $9.9 million?
b. What are the effects on cash flow, if variable costs increase to 55% of sales?
Explanation
Base Case
Sales $9,000,000
Variable costs40% 3,600,000
Fixed costs 1,800,000
Earnings before taxes $3,600,000
Taxes30% 1,080,000
Net income $2,520,000
a.
Sales $9,900,000
Variable costs40% 3,960,000
Fixed costs 1,800,000
Earnings before taxes $4,140,000
Taxes30% 1,242,000
Net income $2,898,000
Cash flow increases by $378,000
b.
Sales $9,000,000
Variable costs55% 4,950,000
Fixed costs 1,800,000
Earnings before taxes $2,250,000
Taxes30% 675,000
Net income $1,575,000
Cash flow decreases by $945,000
Question 3 see excel
Question 4
The following estimates have been prepared for a project:
Fixed costs: $5,400
Depreciation: $3,600
Sales price per unit: $4
Accounting break-even: 5,000 units
What must be the variable cost per unit?
Explanation
At the break-even level of sales (5,000 units) profit would be zero:
Profit = [5,000 × ($4 – Variable cost per unit)] – $5,400 – 3,600 = 0
Variable cost per unit = $2.20.
Question 5
Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be
sold for $120. The materials cost for a standard diamond is $40. The fixed costs incurred each
year for factory upkeep and administrative expenses are $212,000. The machinery costs $2.2
million and is depreciated straight-line over 10 years to a salvage value of zero.
a. What is the accounting break-even level of sales in terms of number of diamonds sold?
b. What is the NPV break-even level of diamonds sold per year assuming a tax rate of 21%, a 10-
year project life, and a discount rate of 12%?
Explanation
a.
Accounting break-even=(Fixed costs + Depreciation) / (Sales price – Variable cost per unit)
=[$212,000 + ($2.2 million / 10)] / ($120 – $40)
=5,400 units
b.
Let Q = the number of diamonds sold.
For the NPV to equal zero, the present value of the operating cash flows must equal the initial
investment.
$2.2 million = OCF (PVIFA 12%,10)
OCF = $389,365.16
OCF=[(Revenue – Expenses) × (1 – Tax)] + (Depreciation × Tax rate)
$389,365.16=({[Q × ($120 – $40)] – $212,000} × (1 – 0.21)) + [($2.2 million / 10) × 0.21]
$389,365.16=$63.2Q – $167,480 + 46,200
Q=8,080 diamonds per year
Question 6
You are evaluating a project that will require an investment of $10 million that will be
depreciated over a period of 11 years. You are concerned that the corporate tax rate will increase
during the life of the project.
a. Would this increase the accounting break-even point?
Yes
No
Correct
b. Would it increase the NPV break-even point?
Yes
Correct
No
Explanation
a.
The accounting break-even point would be unaffected since taxes paid are zero when pretax
profit is zero, regardless of the tax rate.
b.
The NPV break-even point would increase since the after-tax cash flow corresponding to any
level of sales falls when the tax rate increases.
Question 7
Modern Artifacts can produce keepsakes that will be sold for $60 each. Nondepreciation fixed
costs are $2,500 per year, and variable costs are $30 per unit. The initial investment of $4,000
will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the
discount rate is 12%.
a. What is the accounting break-even level of sales if the firm pays no taxes?
b. What is the NPV break-even level of sales if the firm pays no taxes?
c. What is the accounting break-even level of sales if the firm’s tax rate is 30%?
d. What is the NPV break-even level of sales if the firm’s tax rate is 30%?
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers
should be used for actual calculations.
a.
Accounting break-even=(Fixed costs + Depreciation) / (Sales price – Variable cost per unit)
=[$2,500 + ($4,000 / 5)] / ($60 – $30)
=110 units
b.
Let Q = the number of units sold.
For the NPV to equal zero, the present value of the operating cash flows must equal the initial
investment.
$4,00
=OCF (PVIFA )
012%, 5
OCF =$1,109.64
OCF=[(Revenue – Expenses) × (1 – Tax)] + (Depreciation × Tax rate)
$1,109.6
=({[Q × ($60 – $30)] – $2,500} × (1 – 0)) + [($4,000 / 5) × 0]
4
$1,109.6
=$30Q – $2,500 + 0
4
Q=120 units
c.
Accounting break-even=(Fixed costs + Depreciation) / (Sales price – Variable cost per unit)
=[$2,500 + ($4,000 / 5)] / ($60 – $30)
=110 units
d.
Let Q = the number of units sold.
For the NPV to equal zero, the present value of the operating cash flows must equal the initial
investment.
$4,00
=OCF (PVIFA )
012%, 5
OCF =$1,109.64
OCF=[(Revenue – Expenses) × (1 – Tax)] + (Depreciation × Tax rate)
({[Q × ($60 – $30)] – $2,500} × (1 – 0.30)) + [($4,000 / 5) ×
$1,109.64=
0.30]
$1,109.64=$21Q – 1,750 + 240
Q=125 units
Question 8
You estimate that your cattle farm will generate $0.15 million of profits on sales of $3 million
under normal economic conditions and that the degree of operating leverage is 2.
a. What will profits be if sales turn out to be $1.5 million?
b. What will profits be if sales turn out to be $4.5 million?
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers
should be used for actual calculations.
a.
%ΔProfi
=%ΔSales × DOL
t
=[($1.50m – 3m) / $3m] × 2
=–1, or –100%
New
=Old profit × (1 + %ΔProfit)
profit
=$0.15m × [1 + (–1)]
=$0
Profits will decrease to $0.
b.
%ΔProfi
=%ΔSales × DOL
t
=[($4.5m – 3m) / $3m] × 2
=1, or 100%
%ΔProfiOld profit × (1 +
=
t %ΔProfit)
=$0.15m × [1 + 1]
=$0.3m
Profits will increase to $0.3 million.
Question 9
Modern Artifacts can produce keepsakes that will be sold for $40 each. Nondepreciation fixed
costs are $600 per year, and variable costs are $30 per unit. The initial investment of $1,800 will
be depreciated straight-line over its useful life of 6 years to a final value of zero, and the discount
rate is 8%.
a. What is the degree of operating leverage of Modern Artifacts when sales are $4,000? (Do not
round intermediate calculations. Round your answer to 2 decimal places.)
b. What is the degree of operating leverage when sales are $7,360? (Do not round intermediate
calculations. Round your answer to 2 decimal places.)
c. Why is operating leverage different at these two levels of sales?
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers
should be used for actual calculations.
Fixed costs (including depreciation)
DOL=1+
Profits
a.
Profi
=Revenues – Variable costs – Fixed costs – Depreciation
t
=$4,000 – $3,000 – $600 – $300
=$100
$900
DOL=1+ =10.00
$100
b.
Profi
=Revenues – Variable costs – Fixed costs – Depreciation
t
=$7,360 – $5,520 – $600 – $300
=$940
$900
DOL=1+ =1.96
$940
c.
When a firm has fixed costs, the DOL is higher when profits are lower because a $1 change in
sales leads to a greater percentage change in profits.
Question 10
A silver mine can yield 16,000 ounces of silver at a variable cost of $34 per ounce. The fixed
costs of operating the mine are $56,000 per year. In half the years, silver can be sold for $50 per
ounce; in the other years, silver can be sold for only $25 per ounce. Ignore taxes.
a. What is the average cash flow you will receive from the mine if it is always kept in operation
and the silver always is sold in the year it is mined?
b. Now suppose you can costlessly shut down the mine in years of low silver prices. What
happens to the average cash flow from the mine?
Explanation
a.
Average cash (Best-case cash flow × % of time) + (Worst-case cash flow × % of time) –
=
flowVariable costs – Fixed costs
=($50 × 16,000 × 0.50) + ($25 × 16,000 × 0.50) – ($34 × 16,000) – $56,000
=$0
b.
Average cash (Best-case cash flow × % of time) + (Worst-case cash flow × % of time) –
=
flowVariable costs – Fixed costs
=($50 × 16,000 × 0.50) + $0 – ($34 × 16,000 × 0.50) – ($56,000 × 0.50)
=$100,000
Question 11
An auto plant that costs $200 million to build can produce a line of flexfuel cars that will
produce cash flows with a present value of $280 million if the line is successful but only $90
million if it is unsuccessful. You believe that the probability of success is only about 40%. You
will learn whether the line is successful immediately after building the plant.
a-1. Calculate the expected NPV.
a-2. Would you build the plant?
Suppose that the plant can be sold for $150 million to another automaker if the auto line is not
successful.
b-1. Calculate the expected NPV.
b-2. Would you build the plant?
Explanation
a-1.
Expected (Successful cash flow × Probability of success) + (Unsuccessful cash flow ×
=
NPVProbability of unsuccess)
=[($280m – 200m) × 0.40] + [($90m – 200m) × 0.60]
= –$34.0m
a-2.
Since the NPV is negative, you should not build the plant.
b-1.
Expected (Successful cash flow × Probability of success) + (Unsuccessful cash flow ×
=
NPVProbability of unsuccess)
=[($280m – 200m) × 0.40] + [($150m – 200m) × 0.60]
=$2.00m
b-2.
Since the NPV is positive, you should build the plant.
