CHAPTER 9 B – 1
22. Apply the accounting profit break-even point formula and solve for the sales price, P, that allows the
firm to break even when producing 40,000 calculators. In order for the firm to break even, the revenues
from the calculator sales must equal the total annual cost of producing the calculators. The depreciation
charge each year will be:
Depreciation = $137,000 per year
accounting break-even is the point at which the net income of the product is zero. So, solving the
accounting break-even equation for the sales price, we get:
23. a. The NPV of the project is sum of the present value of the cash flows generated by the project.
The cash flows from this project are an annuity, so the NPV is:
b. The company should abandon the project if the PV of the revised cash flows for the next nine
years is less than the project’s aftertax salvage value. Since the option to abandon the project
occurs in Year 1, discount the revised cash flows to Year 1 as well. To determine the level of
C2 = $4,245,536.06
24. a. The NPV of the project is sum of the present value of the cash flows generated by the project.
The annual cash flow for the project is the number of units sold times the cash flow per unit,
which is:
NPV = –$229,670.05
b. The company will abandon the project if unit sales are not revised upward. If the unit sales are
revised upward, the aftertax cash flows for the project over the last four years will be:
CHAPTER 9 B – 2
value of the expansion cash flows are in Year 1, so each of these must be discounted back to
today. So, the project NPV under the abandonment or expansion scenario is:
25. To calculate the unit sales for each scenario, we multiply the market sales times the company’s market
year. After doing these calculations, we will construct the pro forma income statement for each
scenario. We can then find the operating cash flow using the bottom up approach, which is net income
plus depreciation. Doing so, we find:
Pessimistic
Expected
Optimistic
Units per year
10,920
16,150
20,520
Revenue
$1,223,040
$1,857,250
$2,462,400
Variable costs
414,960
581,400
697,680
Fixed costs
615,000
575,000
550,000
Depreciation
310,000
290,000
270,000
EBT
–$116,920
$410,850
$944,720
Tax
–46,768
164,340
377,888
Net income
–$70,152
$246,510
$566,832
OCF
$239,848
$536,510
$836,832
Note that under the pessimistic scenario, the taxable income is negative. We assumed a tax credit in
this case. Now we can calculate the NPV under each scenario, which will be:
Challenge
26. a. Using the tax shield approach, the OCF is:
And the NPV is:
NPV = $915,432.70
b. In the worst-case, the OCF is:
The best-case OCF is:
And the best-case NPV is:
27. To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 33,000. The
OCF at this level of sales is:
OCF = $977,160
The sensitivity of changes in the OCF to quantity sold is:
OCF/Q = +$28.52
The NPV at this level of sales is:
And the sensitivity of NPV to changes in the quantity sold is:
CHAPTER 9 B – 4
NPV/Q = +$100.31
You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV
get a change in quantity. Doing so, we get:
Q = 9,126
If sales decreased by 9,126 units the NPV would be zero, so the minimum quantity is:
28. We will use the bottom up approach to calculate the operating cash flow. Assuming we operate the
project for all four years, the cash flows are:
Year
0
1
2
3
4
Sales
$10,990,000
$10,990,000
$10,990,000
$10,990,000
Operating costs
4,524,000
4,524,000
4,524,000
4,524,000
Depreciation
3,175,000
3,175,000
3,175,000
3,175,000
EBT
$3,291,000
$3,291,000
$3,291,000
$3,291,000
Tax
1,250,580
1,250,580
1,250,580
1,250,580
Net income
$2,040,420
$2,040,420
$2,040,420
$2,040,420
+Depreciation
3,175,000
3,175,000
3,175,000
3,175,000
Operating CF
$5,215,420
$5,215,420
$5,215,420
$5,215,420
Change in NWC
–$2,028,000
0
0
0
$2,028,000
Capital spending
–12,700,000
0
0
0
0
Total cash flow
–$14,728,000
$5,215,420
$5,215,420
$5,215,420
$7,243,420
Year
0
1
Sales
$10,990,000
Operating costs
4,524,000
Depreciation
3,175,000
EBT
$3,291,000
Tax
1,250,580
CHAPTER 9 B – 5
Net income
$2,040,420
+Depreciation
3,175,000
Operating CF
$5,215,420
Change in NWC
–$2,028,000
$2,028,000
Capital spending
–12,700,000
9,075,500
Total cash flow
–$14,728,000
$16,318,920
NPV = –$14,728,000 + $16,318,920/1.16
NPV = –$659,965.52
If we abandon the project after two years, the cash flows are:
Year
0
1
2
Sales
$10,990,000
$10,990,000
Operating costs
4,524,000
4,524,000
Depreciation
3,175,000
3,175,000
EBT
$3,291,000
$3,291,000
Tax
1,250,580
1,250,580
Net income
$2,040,420
$2,040,420
+Depreciation
3,175,000
3,175,000
Operating CF
$5,215,420
$5,215,420
Change in NWC
–$2,028,000
0
$2,028,000
Capital spending
–12,700,000
0
7,348,200
Total cash flow
–$14,728,000
$5,215,420
$14,591,620
CHAPTER 9 B – 6
Book value = $12,700,000 – (2)($12,700,000/4)
Book value = $6,350,000
NPV = –$14,728,000 + $5,215,420/1.16 + $14,591,620/1.162
NPV = $612,002.38
If we abandon the project after three years, the cash flows are:
Year
0
1
2
3
Sales
$10,990,000
$10,990,000
$10,990,000
Operating costs
4,524,000
4,524,000
4,524,000
Depreciation
3,175,000
3,175,000
3,175,000
EBT
$3,291,000
$3,291,000
$3,291,000
Tax
1,250,580
1,250,580
1,250,580
Net income
$2,040,420
$2,040,420
$2,040,420
+Depreciation
3,175,000
3,175,000
3,175,000
Operating CF
$5,215,420
$5,215,420
$5,215,420
Change in NWC
–$2,028,000
0
0
$2,028,000
Capital spending
–12,700,000
0
0
4,492,500
Total cash flow
–$14,728,000
$5,215,420
$5,215,420
$11,735,920
NPV = –$14,728,000 + $5,215,420(PVIFA16%,2) + $11,735,920/1.163
We should abandon the equipment after three years since the NPV of abandoning the project after
three years has the highest NPV.
NPV = –$4,800,000 + $780,000(PVIFA11%,10)
NPV = –$206,399.03
b. The company will abandon the project if the value of abandoning the project is greater than the
value of the future cash flows. The present value of the future cash flows if the company revises
+ [.50($1,260,000)(PVIFA11%,9)]/1.11
NPV = $153,459.41
30. First, determine the cash flow from selling the old harvester. When calculating the salvage value,
remember that tax liabilities or credits are generated on the difference between the resale value and
the book value of the asset. Using the original purchase price of the old harvester to determine annual
Book value = Initial Purchase Price – Accumulated Depreciation
Book value = $67,000 – ($4,466.67 5 years)
Book value = $44,666.67
CHAPTER 9 B – 8
Since the firm is able to resell the old harvester for $21,000, which is less than the $44,666.67 book
value of the machine, the firm will generate a tax credit on the sale. The aftertax salvage value of the
old harvester will be:
Aftertax salvage value = $29,046.67
Next, we need to calculate the incremental depreciation. We need to calculate depreciation tax shield
generated by the new harvester less the forgone depreciation tax shield from the old harvester. Let P
be the break-even purchase price of the new harvester. So, we find:
And the depreciation tax shield on the old harvester is:
The present value of the incremental depreciation tax shield will be: