Solutions to End-of-Chapter Problems
13-1 a. Equipment $ 9,000,000
NWC Investment 3,000,000
Initial investment outlay $12,000,000
b. No, last year’s $50,000 expenditure is considered a sunk cost and does not represent an
incremental cash flow. Hence, it should not be included in the analysis.
c. The potential sale of the building represents an opportunity cost of conducting the
project in that building. Therefore, the possible after-tax sale price must be charged against
the project as a cost.
13-2 a. Project cash flows: t = 1
Sales revenues $10,000,000
Operating costs 7,000,000
Depreciation 2,000,000
Operating income before taxes $ 1,000,000
Taxes (40%) 400,000
Operating income after taxes $ 600,000
Add back depreciation 2,000,000
Project cash flow $ 2,600,000
b. The cannibalization of existing sales needs to be considered in this analysis on an
after-tax basis, because the cannibalized sales represent sales revenue the firm would
realize without the new project but would lose if the new project is accepted. Thus, the
after-tax effect would be to reduce the project’s cash flow by $1,000,000(1 – T) =
$1,000,000(0.6) = $600,000. Thus, the project’s cash flow would now be $2,000,000
rather than $2,600,000.
c. If the tax rate fell to 30%, the project’s cash flow would change to:
Operating income before taxes $1,000,000
Taxes (30%) 300,000
Operating income after taxes $ 700,000
Add back depreciation 2,000,000
Project cash flow $2,700,000
Thus, the project’s cash flow would increase by $100,000.
13-3 Equipment’s original cost $20,000,000
Depreciation (80%) 16,000,000
Book value $ 4,000,000
Gain on sale = $5,000,000 – $4,000,000 = $1,000,000.
Tax on gain = $1,000,000(0.4) = $400,000.
AT net salvage value = $5,000,000 – $400,000 = $4,600,000.
13-4 Cash outflow = $40,000.
Increase in annual after-tax cash flows: CF = $9,000.
Place the cash flows on a time line:
0 1 2 10
| | | • • • |
-40,000 9,000 9,000 9,000
With a financial calculator, input the appropriate cash flows into the cash flow register,
input I/YR = 10, and then solve for NPV = $15,301.10. Thus, Chang should purchase the
new machine.
13-5 First, solve for each project’s NPV.
Project A: CF0 = -20000, CF1 = 6000, Nj = 6, I/YR = 10; solve for NPV = $6,131.56.
Project B: CF0 = -12000, CF1 = 6000, Nj = 3, I/YR = 10; solve for NPV = $2,921.11.
The appropriate EAAs are:
Project A: N = 6, I/YR = 10, PV = -6131.56, FV = 0; solve for PMT = $1,407.85.
Project B: N = 3, I/YR = 10, PV = -2921.11, FV = 0; solve for PMT = $1,174.62.
Choose Project A, whose EAA = $1,407.85
13-6 a. The applicable depreciation values are as follows for the two scenarios:
Scenario 1 Scenario 2
Year (Straight-Line) (MACRS)
1 $200,000 $264,000
2 200,000 360,000
3 200,000 120,000
4 200,000 56,000
b. To find the difference in net present values under these two methods, we must determine
the difference in incremental cash flows each method provides. The depreciation expenses
cannot simply be subtracted from each other, as there are tax ramifications due to
depreciation expense. The full depreciation expense is subtracted from Revenues to get
operating income, and then taxes due are computed Then, depreciation is added to
after-tax operating income to get the project’s operating cash flow. Therefore, if the tax
rate is 40%, only 60% of the depreciation expense is actually subtracted out during the
after-tax operating income calculation and the full depreciation expense is added back to
calculate operating income. So, there is a tax benefit associated with the depreciation
expense that amounts to 40% of the depreciation expense. Therefore, the differences
between depreciation expenses under each scenario should be computed and multiplied by
0.4 to determine the benefit provided by the depreciation expense.
Depreciation Expense Depreciation Expense
Year Difference (2 – 1) Diff. 0.4 (MACRS)
1 $ 64,000 $25,600
2 160,000 64,000
3 -80,000 -32,000
4 -144,000 -57,600
Now to find the difference in NPV to be generated under these scenarios, just enter the
cash flows that represent the benefit from depreciation expense and solve for net present
value based upon a WACC of 10%.
CF0 = 0; CF1 = 25600; CF2 = 64000; CF3 = -32000; CF4 = -57600; and I/YR = 10. Solve
for NPV = $12,781.64
So, all else equal the use of the accelerated depreciation method will result in a higher
NPV (by $12,781.64) than would the use of the straight-line depreciation method.
13-7 E(NPV) = 0.05(-$70) + 0.20(-$25) + 0.50($12) + 0.20($20) + 0.05($30)
= -$3.5 + -$5.0 + $6.0 + $4.0 + $1.5
= $3.0 million.
sNPV = [0.05(-$70 – $3)2 + 0.20(-$25 – $3)2 + 0.50($12 – $3)2 + 0.20($20 – $3)2 +
0.05($30 – $3)2]
= $23.622 million.
13-8 a. The net cost is $178,000:
Cost of investment at t = 0:
Base price ($140,000)
Modification (30,000)
Increase in NWC (8,000)
Cash outlay for new machine ($178,000)
b. The annual cash flows follow:
Year 1 Year 2 Year 3
After-tax savings $30,000 $30,000 $30,000
Depreciation tax savings 22,440 30,600 10,200
Salvage value $60,000
Tax on SV (19,240)
Return of NWC 8,000
Project cash flows $52,440 $60,600 $88,960
Notes:
1. The after-tax cost savings is $50,000(1 – T) = $50,000(0.6) = $30,000.
2. The depreciation expense in each year is the depreciable basis, $170,000, times the
MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively.
Depreciation expense in Years 1, 2, and 3 is $56,100, $76,500, and $25,500. The
depreciation tax savings is calculated as the tax rate (40%) times the depreciation expense
in each year.
3. Tax on SV = ($60,000 – $11,900)(0.4) = $19,240.
