Sample Capital Budgeting Problems
1. A company is considering a project that requires an initial investment of $24M to build a new
plant and purchase equipment. The investment will be depreciated as a MACRS 7-year class
(see p. 21 in the text) asset. The new plant will be built on some of the company's land
which has a current, after-tax market value of $4.3M. The company will produce units at a
cost of $130 each and will sell them for $420 each. There are annual fixed costs of $0.5M.
Unit sales are expected to be 150,000 each year for the next 6 years, at which time the project
will be abandoned. At that time, the plant and equipment is expected to be worth $8M
(before tax) and the land is expected to be worth $5.4M (after tax). To supplement the
production process, the company will need to purchase $1M worth of inventory. That
inventory will be depleted during the final year of the project. The company has $100M of
debt outstanding with a yield-to-maturity of 8%, and has $150M of equity outstanding with a
beta of 0.9. The expected market return is 13% and the risk-free rate is 5%. The company's
marginal tax rate is 40%. Should the project be accepted?
Solution
WACC:
wd = $100M / $250M = 0.4
kd = 8%
ws = $150M / $250M = 0.6
ks = 5% + 0.9(13% - 5%) = 12.2%
 WACC = 0.48%(1-0.4) + 0.612.2% = 9.24%
Capital Expenditure:
-$24M at date 0
Date
0
1
2
3
4
5
6
7
8
MACRS %
14.29%
24.49%
17.49%
12.49%
8.93%
8.92%
8.93%
4.46%
Depreciation
$3.430
$5.878
$4.198
$2.998
$2.143
$2.141
$2.143
$1.070
Salvage Cash Flow of New Equipment:
Salvage CF = $8M - 0.4($8M - $3.212M) = $6.085M
Change in Net Working Capital:
-$1M at date 0
+$1M at date 6
Book Value
$24.000
$20.570
$14.692
$10.494
$7.496
$5.353
$3.212
$1.070
$0.000
Operating Cash Flows:
Sales = 150,000  $420 = $63,000,000
Costs = 150,000  $130 + $0.5M = $20,000,000
OCF = ($63,000,000 - $20,000,000)  (1-0.4) + D  0.4 = 25,800,000+D0.4
Date
0
1
2
3
4
5
6
Depreciation
OCF
$3.430
$5.878
$4.198
$2.998
$2.143
$2.141
$27.172
$28.151
$27.479
$26.999
$26.657
$26.656
Other Relevant Cash Flows: Land
The $4.3M is an opportunity cost and must be included at date 0.
If the project is accepted, however, the land can be sold in 6 years for $5.4M. Is this an
incremental cash flow? Yes, because we wouldn't be selling it then if we reject the
project.
Total Expected Cash Flows
Date
0
1
2
3
4
5
6
Cap. Exp.
-$24M
NWC
-$1M
Salvage
OCF
$27.172M
$28.151M
$27.479M
$26.999M
$26.657M
$1M $6.085M $26.656M
Other (Land)
-$4.3M
$5.4M
Total
-$29.300M
$27.172M
$28.151M
$27.479M
$26.999M
$26.657M
$39.141M
NPV = -29.3 + 27.172/ 1.0924 + … + 39.141/1.09246 = $99.37M > 0, so accept the project.
IRR = 92.53% > 9.24%, so accept the project.
2. A company is considering the purchase of new equipment to replace some old, existing
equipment. The old equipment is fully depreciated and has a current market value of $1.2M.
The new equipment costs $10.4M and will be depreciated using the 5 year MACRS class.
The equipment is used to produce items with constant annual revenues of $18M. Current
costs (using the old equipment) are $3M per year. The new equipment will not change the
expected revenues (they will remain at $18M per year), but will allow the company to cut
costs by $1M per year. The project is expected to last for 4 years, at which time the new
equipment would be worth $6.0M. If the old equipment is kept, it will be worthless in 4
years. The company's marginal tax rate is 35%. The company is financed with $50M of
preferred stock and $150M of common stock. The preferred stock has a current value of $20
and pays constant dividends of $2 annually. The expected return on the common stock is
14.4%. Should the project be accepted?
Solution
WACC:
wd = 0
ws = $150 / ($150 + $50) = 0.75
ks = 14.4%
wps = $50 / ($150 + $50) = 0.25
kps = D1/P0 = $2 / $20 = 10%
 WACC = 0.7514.4% + 0.2510% = 13.3%
Capital Expenditure:
-$10.4M at date 0
Date
0
1
2
3
4
5
6
MACRS %
Depreciation
20.00%
32.00%
19.20%
12.52%
12.52%
5.76%
$2.080M
$3.328M
$1.997M
$1.198M
$1.198M
$0.599M
Book Value
$10.4M
$8.320M
$4.992M
$2.995M
$1.797M
$0.599M
$0.000M
Salvage value of new equipment (date 4):
CF = $6.0M - ($6.0M - $1.797M)0.35 = $4.529M
Salvage value of old equipment (date 0): $1.2M - 0.35($1.2M-$0M) = $0.78M
Operating Cash Flow:
We are only interested in the incremental cash flow. In this case, the incremental
change to revenues is $0 and the incremental change to costs is $1M. This gives and
incremental OCF of
OCF = (S-C)  (1-T) + TD = (0 - (-$1M))  (1-0.35) + 0.35$2.08M = $1.378M
Year
0
1
2
3
4
Depreciation
Sales
Costs
OCF
$2.08
$3.328
$1.976
$1.248
$0
$0
$0
$0
-$1M
-$1M
-$1M
-$1M
$1.378M
$1.815M
$1.349M
$1.069M
Change in NWC:
$0
Total Expected Cash Flows
Date
0
1
2
3
4
Cap. Exp.
-$10.4M
NWC
$0
Salvage
$0.78M
$4.529M
OCF
$1.378M
$1.815M
$1.349M
$1.069M
Total
-$9.62M
$1.378M
$1.815M
$1.349M
$5.598M
NPV = -9.62 + 1.378/1.133 + $1.815 / 1.1332 + $1.349 / 1.1333 + $5.598 / 1.1334
= -$2.665M < 0, so reject the project.
IRR = 1.72% < 13.3%, so reject the project.
3. A firm is considering a project that requires an investment of $10M in equipment. The
equipment will be depreciated using the 3-year MACRS class, but will be used for a five year
project. At the end of the project, the equipment should be worth $3M. The equipment will
be used to produce items at a cost of $35 each. Those items will be sold for $60 each.
Projected sales are 60,000 each year. Historically, the firm has maintained a inventory to
sales ratio of 0.1 (measured in units, not dollars). The firm's marginal tax rate is 35% and its
WACC is 12%. Should the firm take the project?
Solution
Capital Expenditure:
-$10M at date 0
Date
0
1
2
3
4
MACRS %
Depreciation
33.33%
44.45%
14.81%
7.41%
$3.333M
$4.445M
$1.481M
$0.741M
Book Value
$10.000M
$6.667M
$2.222M
$0.741
$0.000
Salvage value in five years: $3M - ($3M-$0M)0.35 = $1.95M
Year
0
1
2
3
4
5
Date
0
1
2
3
4
5
Depreciation
Sales
Costs
OCF
$3.333M
$6060,000
= $3.6M
$3.6M
$3.6M
$3.6M
$3.6M
$3560,000
= $2.1M
$2.1M
$2.1M
$2.1M
$2.1M
$2.142M
$2.531M
$1.493M
$1.234M
$0.975M
$4.445M
$1.481M
$0.741M
$0.000M
Cap. Exp. NWC
-$10M -$0.21M
$0.21M
Salvage
OCF
$1.95M
$2.142M
$2.531M
$1.493M
$1.234M
$0.975M
Total
-$10.210M
$2.142M
$2.531M
$1.493M
$1.234M
$3.135M
NPV = -$10.21 + $2.142/1.12 + +$2.531/1.122 + $1.493/1.123 + $1.234/1.124 + $3.135/1.125
= -$2.6541M
IRR: 1.03
 reject the project
4. As the director of a firm's capital budgeting department, you have been asked to evaluate a
project. After collecting information from various sources, you have determined the
following. The firm's preferred stock pays a constant annual dividend of $2.25 and is
currently selling for $20. The firm is expected to pay a common stock dividend of $3 in one
year, with anticipated growth of 2% each year thereafter. Currently, the common stock is
selling at a price of $23.75. The firm has 8 year bonds outstanding with a coupon rate of
8.75%, paid annually. The bonds are currently selling at par. The firm is currently being
financed with $10,000,000 of debt, $20,000,000 of common equity, and $5,000,000 of
preferred stock. The project requires the use of equipment valued at $6,200,000. The
equipment currently has a book value of $3,000,000 with two years of straight-line
depreciation (to zero) remaining ($1,500,000 each year). You anticipate that the equipment
can be sold in three years for $2,100,000. Anticipated sales are 1,000,000 units per year
based on a sale price of $11 per unit. The cost of producing each unit is $8.50. If the project
is accepted, the firm will need to hire an additional manager with an annual salary of
$80,000. The product complements another of the firm's products. As a result, you
anticipate increased sales of $700,000 per year for that product. Total research (information
gathering for project analysis) expenses to date are $26,000. If the project is accepted, the
firm will have to forego another project that has a NPV of $584,000. The firm's marginal tax
rate is 40%. Should the project be accepted?
Solution
kps = $2.25/$20 = 11.25%
P0 = D1/(ks-g)  ks = D1/P0 + g = $3/$23.75 + 2% = 14.63%
kd = 8.75%
wps = $5,000,000/$35,000,000 = 0.1429
ws = $20,000,000/$35,000,000 = 0.5714
wd = $10,000,000/$35,000,000 = 0.2857
WACC = 0.142911.25% + 0.571414.63% + 0.2857(1-0.4)8.75% = 11.47%
Capital Expenditure: -$6,200,000 at date 0 (note that this is an opportunity cost)
Date
0
1
2
3
Depreciation
$1.5M
$1.5M
$0M
Book Value
$3.0M
$1.5M
$0M
$0M
Salvage CF = $2,100,000 - ($2,100,000 - $0)0.4 = $1.26M at date 3
Year
0
1
Depreciation
Sales
Costs
OCF
$1.5M
$11M + $0.7M =
$11.7M
$8.5M + 0.08M =
8.58M
$2.472M
2
3
$1.5M
$0M
Date
0
1
2
3
Cap. Exp.
-$6.2M
$11.7M
$11.7M
NWC
$0
$0
$0
$0
8.58M
8.58M
Salvage
OCF
$1.26M
$2.472M
$2.472M
$1.872M
$2.472M
$1.872M
Total
-$6.2M
$2.472M
$2.472M
$3.132M
Notice that the $26,000 research expense does not appear. It is a sunk cost and
therefore should not affect our analysis.
NPV = -$6.2 + $2.472/1.1147 + $2.472/1.11472 + $3.132/1.11473 = $0.268M
IRR = 13.86%
payback = 2.40 years
 Normally, we would accept the project, but doing so would result in us giving up a
$0.584M project (a net loss of $0.316M). We therefore must reject the project.
5. A company is considering two projects and can only accept one of them. The projected cash
flows are as follows:
Year
0
3
Project A Cash Flow
-$10,000,000
$15,000,000
Project B Cash Flow
-$15,000,000
$21,700,000
The company's WACC is 10%. Compute the payback, NPV, and IRR for each project.
Which project should be chosen? Explain the logic behind your choice.
Solution
NPVA = -$10 + $15/1.13 = $1.270M
NPVB = -$15 + $21.7/1.13 = $1.304M
IRRA = ($15/$10)1/3 - 1 = 14.47%
IRRB = ($21.7/$15)1/3 - 1 = 13.10%
paybackA = 2.67 years
paybackB = 2.69 years
The choice is a judgement call. The NPVs are very close, but the IRR for A is a good bit
higher than the IRR for B. Because we might have errors in our projections, I would
tend to favor project A.