CHAPTER 8 B – 1
36. To answer this question, we need to compute the NPV of all three alternatives, specifically, continue
to rent the building, Project A, or Project B. If all three of the projects have a positive NPV, the project
There are several important cash flows we should not consider in the incremental cash flow analysis.
The remaining fraction of the value of the building and depreciation are not incremental and should
We will begin by calculating the NPV of the decision of continuing to rent the building first.
Continue to rent:
Rent
$50,000
Taxes
17,000
Net income
$33,000
Since there is no incremental depreciation, the operating cash flow is equal to the net income. So, the
NPV of the decision to continue to rent is:
NPV = $33,000(PVIFA12%,15)
NPV = $224,758.53
Product A:
Next, we will calculate the NPV of the decision to modify the building to produce Product A. The
income statement for this modification is the same for the first 14 years, and in Year 15, the company
Year 0 will be the cost of the equipment, and the cost of the initial building modifications, both of
which are depreciable on a straight-line basis. So, the pro forma cash flows for Product A are:
Initial cash outlay:
Building modifications
–$114,000
Equipment
–235,000
Total cash flow
–$349,000
Years 1-14
Revenue
$305,000
Expenditures
180,000
Depreciation
23,267
Restoration cost
0
EBT
$101,733
CHAPTER 8 B – 2
Tax
34,589
NI
$67,144
OCF
$90,411
The OCF each year is net income plus depreciation. So, the NPV for modifying the building to
manufacture Product A is:
Product B:
Now we will calculate the NPV of the decision to modify the building to produce Product B. The
income statement for this modification is the same for the first 14 years, and in Year 15, the company
expense in Year 15, so the income statement for that year will be slightly different. The cash flow at
Year 0 will be the cost of the equipment, and the cost of the initial building modifications, both of
which are depreciable on a straight-line basis. So, the pro forma cash flows for Product A are:
Initial cash outlay:
Building modifications
–$132,000
Equipment
–282,000
Total cash flow
–$414,000
Years 1-14
Year 15
Revenue
$372,000
$372,000
Expenditures
230,000
230,000
Depreciation
27,600
27,600
Restoration cost
0
78,000
EBT
$114,400
$36,400
Tax
38,896
12,376
NI
$75,504
$24,024
OCF
$103,104
$51,624
The OCF each year is net income plus depreciation. So, the NPV for modifying the building to
manufacture Product B is:
NPV = $278,822.17
We could have also done the analysis as the incremental cash flows between Product A and continuing
to rent the building, and the incremental cash flows between Product B and continuing to rent the
building. The results of this type of analysis would be:
NPV of differential cash flows between Product A and continuing to rent:
NPV = NPVProduct A – NPVRent
CHAPTER 8 B – 3
NPV of differential cash flows between Product B and continuing to rent:
since it has the highest marginal NPV, which is the same as our original result.
37. The discount rate is expressed in real terms, and the cash flows are expressed in nominal terms. We
interest rate. The real value of each cash flow is the present value of the Year 1 nominal cash flows,
discounted back to the present at the inflation rate. So, the real value of the revenue and costs will be:
Revenue in real terms = $345,000/1.04 = $331,730.77
Revenues, labor costs, and other costs are all growing perpetuities. Each has a different growth rate,
so we must calculate the present value of each separately. Other costs are a growing perpetuity with a
negative growth rate. Using the real required return, the present value of each of these is:
Now we can use the tax shield approach to calculate the net present value. Since there is no investment
in equipment, there is no depreciation; therefore, no depreciation tax shield, so we will ignore this in
our calculation. This means the cash flows each year are equal to net income. There is also no initial
is:
NPV = PVRevenue – PVLabor costs – PVOther costs – PVLease payments
CHAPTER 8 B – 4
each year since the cash flows were finite. Because of the perpetual nature of the cash flows in this
case, using real cash flow is the only practical method.
38. We are given the real revenue and costs, and the real growth rates, so the simplest way to solve this
problem is to calculate the NPV with real values. While we could calculate the NPV using nominal
real labor costs will increase at a real rate of two percent per year, and the real energy costs will
increase at a real rate of three percent per year, so the real costs each year will be:
Year 1
Year 2
Year 3
Year 4
Real labor cost each year
$19.25
$19.64
$20.03
$20.43
Real energy cost each year
$7.35
$7.57
$7.80
$8.03
depreciation to net income to find the operating cash flow each year. Doing so, we find the cash flow
of the project each year is:
Year 0
Year 1
Year 2
Year 3
Year 4
Revenues
$82,400,000.00
$95,275,000.00
$126,175,000.00
$72,100,000.00
Labor cost
41,387,500.00
48,498,450.00
59,081,715.00
39,835,095.30
Energy cost
1,323,000.00
1,627,657.50
2,183,332.20
1,345,283.53
Depreciation
20,432,692.31
19,646,819.53
18,891,172.62
18,164,589.06
EBT
$19,256,807.69
$25,502,072.97
$46,018,780.18
$12,755,032.11
Taxes
6,547,314.62
8,670,704.81
15,646,385.26
4,336,710.92
Net income
$12,709,493.08
$16,831,368.16
$30,372,394.92
$8,418,321.19
OCF
$33,142,185.38
$36,478,187.69
$49,263,567.54
$26,582,910.25
Capital sp.
–$85,000,000
CHAPTER 8 B – 5
Total cash flow
–$85,000,000
$33,142,185.38
$36,478,187.69
$49,263,567.54
$26,582,910.25
We can use the total cash flows each year to calculate the NPV, which is:
NPV = –$85,000,000 + $33,142,185.38/1.08 + $36,478,187.69/1.082 + $49,263,567.54/1.083
+ $26,582,910.25
NPV = $35,607,615.92
project cash flows is to use the real cash flows. In doing so, we must be sure to adjust the depreciation,
which is in nominal terms. We could analyze the cash flows using nominal values, which would
require calculating the nominal discount rate, nominal price, and nominal production costs. This
method would be more complicated, so we will use the real numbers. We will calculate the NPV of
We can find the real revenue and production costs by multiplying each by the units sold. We must be
sure to discount the depreciation, which is in nominal terms. We can then find the pro forma net
income, and add back depreciation to find the operating cash flow. Discounting the depreciation each
year by the inflation rate, we find the following cash flows each year:
Year 1
Year 2
Year 3
Sales
$45,175,000
$45,175,000
$45,175,000
Production costs
22,100,000
22,100,000
22,100,000
Depreciation
11,217,949
10,786,489
10,371,624
EBT
$11,857,051
$12,288,511
$12,703,376
Tax
4,031,397
4,178,094
4,319,148
Net income
$7,825,654
$8,110,417
$8,384,228
OCF
$19,043,603
$18,896,906
$18,755,852
And the NPV of the headache only pill is:
NPV = –$35,000,000 + $19,043,603/1.06 + $18,896,906/1.062 + $18,755,852/1.063
NPV = $15,531,617.34
For the headache and arthritis pill project, the equipment has a salvage value. We will find the aftertax
salvage value of the equipment first, which will be:
Market value
$1,000,000
Taxes
–340,000
Total
$660,000
CHAPTER 8 B – 6
Remember, to calculate the taxes on the equipment salvage value, we take the book value minus the
market value, times the tax rate. Using the same method as the headache only pill, the cash flows each
year for the headache and arthritis pill will be:
Year 1
Year 2
Year 3
Sales
$62,550,000
$62,550,000
$62,550,000
Production costs
36,900,000
36,900,000
36,900,000
Depreciation
12,500,000
12,019,231
11,556,953
EBT
$13,150,000
$13,630,769
$14,093,047
Tax
4,471,000
4,634,462
4,791,636
Net income
$8,679,000
$8,996,308
$9,301,411
OCF
$21,179,000
$21,015,538
$20,858,364
So, the NPV of the headache and arthritis pill is:
NPV = –$39,000,000 + $21,179,000/1.06 + $21,015,538/1.062
+ ($20,858,364 + 660,000)/1.063
40. Since the project requires an initial investment in inventory as a percentage of sales, we will calculate
the sales figures for each year first. The incremental sales will include the sales of the new table, but
we also need to include the lost sales of the existing model. This is an erosion cost of the new table.
The lost sales of the existing table are constant for every year, but the table will be discontinued after
Year 1
Year 2
Year 3
Year 4
Year 5
New
$14,405,000
$14,941,000
$17,152,000
$14,606,000
$11,658,000
Lost sales
–1,225,000
–1,225,000
–1,225,000
0
0
Total
$13,180,000
$13,716,000
$15,927,000
$14,606,000
$11,658,000
Now we will calculate the initial cash outlay that will occur today. The company has the necessary
New table
–$1,440,500
Old table
122,500
Total
–$1,318,000
CHAPTER 8 B – 7
depreciation, or:
Book value = $5,203,870
The taxes on the salvage value will be:
Taxes on salvage = ($5,203,870 – 7,320,000)(.38)
Taxes on salvage = –$804,129
So, the aftertax salvage value of the equipment in five years will be:
Sell equipment
$7,320,000
Taxes
–804,129
Total
$6,515,871
Next, we need to calculate the variable costs each year. The variable costs of the lost sales are included
as a variable cost savings, so the variable costs will be:
Year 1
Year 2
Year 3
Year 4
Year 5
New
$6,482,250
$6,723,450
$7,718,400
$6,572,700
$5,246,100
Lost sales
–490,000
–490,000
–490,000
0
0
Total
$5,992,250
$6,233,450
$7,228,400
$6,572,700
$5,246,100
Adding back depreciation to net income to calculate the operating cash flow, we get:
Year 1
Year 2
Year 3
Year 4
Year 5
Sales
$13,180,000
$13,716,000
$15,927,000
$14,606,000
$11,658,000
VC
5,992,250
6,233,450
7,228,400
6,572,700
5,246,100
Fixed costs
3,100,000
3,100,000
3,100,000
3,100,000
3,100,000
Dep.
0
0
1,700,510
2,914,310
2,081,310
EBT
$4,087,750
$4,382,550
$3,898,090
$2,018,990
$1,230,590
Tax
1,553,345
1,665,369
1,481,274
767,216
467,624
NI
$2,534,405
$2,717,181
$2,416,816
$1,251,774
$762,966
Dep.
0
0
1,700,510
2,914,310
2,081,310
OCF
$2,534,405
$2,717,181
$4,117,326
$4,166,084
$2,844,276
CHAPTER 8 B – 8
the end of period inventory. The sign of this calculation will tell us whether the inventory change is a
in Year 3. This is an opportunity cost. The inventory each year, and the inventory change, will be:
Beginning
$1,440,500
$1,494,100
$1,715,200
$1,460,600
$1,165,800
Ending
1,494,100
1,715,200
1,460,600
1,165,800
0
Existing
0
0
–122,500
0
0
Change
–$53,600
– $221,100
$132,100
$294,800
$ 1,165,800
Year 1
Year 2
Year 3
Year 4
Year 5
OCF
$2,534,405
$2,717,181
$4,117,326
$4,166,084
$2,844,276
Equipment
0
–11,900,000
0
0
6,515,871
Inventory
–$53,600
– $221,100
$132,100
$294,800
$ 1,165,800
Total
$2,480,805
–$9,403,919
$4,249,426
$4,460,884
$10,525,946
+ $4,460,884/1.144 + $10,525,946/1.145
NPV = $4,598,423.84
b. You can perform an IRR analysis, and would expect to find up to three IRRs since the cash flows
change signs three times.
c. The profitability index is intended as a “bang for the buck” measure; that is, it shows how much
shareholder wealth is created for every dollar of initial investment. In this case, the largest
negative cash flow is discounted, the profitability index will still measure the amount of
shareholder wealth created for every dollar spent today.