Chapter 17: Problems 1,5,9
1 . A firm has the opportunity to invest in a project having an initial outlay of $20,000. Net cash
inflows (before depreciation and taxes) are expected to be $5,000 per year for five years. The firm
uses the straight-line depreciation method with a zero salvage value and has a (marginal) income
tax rate of 40 percent. The firm’s cost of capital is 12 percent.
a. Compute the internal rate of return and the net present value.
b. Should the firm accept or reject the project?
Projective evaluation:
a. NINV = $20,000 and NCF = (5000  4000)(1  .4) + 4000 = $4600/year
$20,000 = $4,600∙(Interest factor for 5 years). 20,000/4,600 = 4.3478.
Interest factor = 4.3478, which helps to find the internal rate of return (IRR) of this project. This
interest factor represents the present value of a $1 annuity for 5 years discounted at r%. Looking
up 4.3478 in Table 5, this value falls between 4.4518 and 4.3295, which corresponds to discount
rates of 4% and 5% respectively for an internal rate of return. Interpolating between these values
yields an internal rate of return of approximately 4.85%, which is far lower than the firm’s cost of
capital of 12%. Students can use a calculator or Excel to find the IRR, which is 4.847%.
For the NPV, students can use tables to find the Annuity Interest Factor at 12A% to be 3.6048) to
find: NPV = $4,600(3.6048)  $20,000 = $3,418. Alternatively, financial calculators or Excel
can find the NPV to be -3,418.03.
b. Since the NPV of the project is negative, the firm should reject the project. Likewise, by the IRR
criterion, the project should be rejected, because the internal rate of return of 4.85% is less than
the cost of capital of 12%.
5. The Charlotte Bobcats, a professional basketball team, has been offered the opportunity to
purchase the contract of an aging superstar basketball player from another team. The general
manager of the Bobcats wants to analyze the offer as a capital budgeting problem. The Bobcats
would have to pay the other team $800,000 to obtain the superstar. Being somewhat old, the
basketball player is expected to be able to play for only four more years. The general manager
figuresthat attendance, and hence revenues, would increase substantially if the Bobcats obtained
the superstar. He estimates that incremental returns (additional ticket revenues less the
superstar’s salary) would be as follows over the four-year period:
The Charlotte Bobcats is considering purchasing a superstar’s contract.
Depreciation/year = $800,000/4 = $200,000.
This involves a series of payments of unequal value.
NCF1 = (450,000  200,000)(1 .4) + 200,000 = $350,000
NCF2 = (350,000  200,000)(1 .4) + 200,000 = $290,000
NCF3 = (275,000  200,000)(1 .4) + 200,000 = $245,000
NCF4 = (200,000  200,000)(1 .4) + 200,000 = $200,000
a. The IRR calculation: $800,000 = $350,000/(1+r)1 + $290,000/(1+r)2 + $245,000/(1+r)3 +
$200,000/(1+r)4. We can find the “r” that makes the left-hand and right-hand side equal by trial
and error using PVIF tables, or with a financial calculator, or using Excel. The IRR equals
14.94%.
NPV calculation: NPV = $350,000(.89286) + $290,000(.79719) + $245,000(.71178) +
$200,000(.63552) - $800,000 = $45,176.
b.
At the given cost of capital (12%), the net present value is positive. Therefore, the Bobcats
should purchase the contract of the superstar. Likewise, since the internal rate of return (approximately
14.9%) exceeds the cost of capital, the investment should be accepted.
9. The state of Glottamora has $100 million remaining in its budget for the current year. One
alternative is to give Glottamorans a one-time tax rebate. Alternatively, two proposals have been
made for state expenditures of these funds.
In Gottamora, they could invest in a new power plant or enter into a job retraining program, both costing
$100 million.
a. The use of a relatively low discount rate results in an analysis where long-term benefits are
valued relatively highly. The higher the discount rate, the greater the emphasis on a fast return on
the investment, i.e., emphasis is placed on those returns occurring early in a project's life.
Because most capital projects have a long life relative to many human resource-type programs, it
is not unusual for the State Power Department to favor using the lower rate. Since public utilities
are regulated monopolies that do not face a threat of competition, their risks are lower as well.
b. PROJECT A: Power Plant: Cost = $100 million & benefits accrue for 20 years
Year
Benefits
1-5
0
6-20
$20M
P.V. Factor @ 5%
Present Value
4.3295
0
10.3796(.78353)=8.1327 162.65M
With P.V. Benefits = 162.65M, so NPV= $62.65M at 5%.
Year
Benefits
1-5
0
6-20
$20M
P.V. Factors @ 12%
Present Value
3.6048
0
6.8109(.56743)=3.8647 $77.29M
With P.V. Benefits = $77.29M, so NPV = -$22.71 M at 12%.
PROJECT B: Job Retraining: Cost = $100 million & benefits accrue for 20 years
Year
Benefits
P.V. Factors @ 5%
Present Value
1-5
20M
4.3295
86.59M
6-10
14M
4.3295(.78353)=3.3923
47.49M
11-20
4M
7.7217(.61391)=4.7404
18.96M
With P.V. Benefits = $153.04M, so NPV = $53.04M at 5%.
Year
Benefits
P.V. Factors @ 12%
Present Value
1-5
20M
3.6048
72.10M
6-10
14M
3.6048(.56743)=2.0455
28.64M
11-20
4M
5.6502(.32197)=1.8192
7.28M
With P.V. Benefits = $108.02M, so NPV = $8.02 M at 12%.
c. Using the 5% rate cannot be justified since this would result in a misallocation of society's
resources. If funds can earn a 12% return in the private sector, it is not optimal to reallocate them
to the public sector where the return is only 5%. In practice, the determination of the appropriate
discount rate to be used for public programs should be a function of the source of the funds
(private consumption or private investment) as well as the relative amounts coming from these
two sources. The opportunity cost for consumption source funds is likely to be lower than that
for investment source funds.
d.
We would choose B, since its NPV is still positive using the 12 percent opportunity rate.
However, estimating the benefits of a job retraining program is likely to be guess work, and the Human
Resources Department may be over-estimating its benefits. In which case, the 20 year payoff period may
well not meet expectations.