Chapter 9 ◼ Capital Budgeting Decision Models 319
Microsurgery Kit
Year
PV of CF at 10%
Remaining
cost to
recover
0
($11,000.00)
1
4,000/1.101 =
3,636.36
–7,363.64
2
4,000/1.102 =
3,305.79
–4,057.85
3
4,000/1.103
3,005.26
–1,052.59
4
4,000/1.104
2,732.05
1,679.46
5
4,000/1.105
2,483.69
4,163.15
Discounted PP (Nano) = 4.04 years; Discounted PP (Micro) = 3.385 years
With the discounted payback method, the Nano Test Tube project does not break even
until the fifth year. The Microsurgery Kit project breaks even in the fourth year.
a. Explain the rationale behind the discounted payback method.
b. Comment on the advantages and shortcomings of this method.
3. Compute the net present value for each project. BioCom uses a discount rate of
9% for projects of average risk.
a. Explain the rationale behind the NPV method.
b. State and explain the decision rule behind the NPV method.
c. Explain how the company would use the NPV method to rank mutually
exclusive projects.
320 Brooks ◼ Financial Management: Core Concepts, 4e
d. Comment on the advantages and shortcomings of this method.
e. Without performing any calculations, explain what happens to NPV if the
discount rate is adjusted upward for projects of higher risk or downward for
projects of lower risk.
4. Compute the internal rate of return (IRR) for each project.
a. Explain the rationale behind the IRR method.
b. State and explain the decision rule behind the IRR method. Assume a hurdle
rate of 9%.
c. Explain how the company would use the IRR method to rank mutually
d. Comment on the advantages and shortcomings of this method.
Chapter 9 ◼ Capital Budgeting Decision Models 323
© 2018 Pearson Education, Inc.
Because the nano project brings in a greater total amount of money, it has a higher NPV
at lower discount rates. Because the microsurgery kit project brings the money in faster,
it has a higher NPV at higher discount rates. The crossover rate is just under 9%.
Additional Problems with Solutions (Slides 9-55 to 9-68)
1. Computing Payback Period and Discounted Payback Period.
Regions Bank is debating between two the purchase of two software systems; the initial
costs and annual savings are listed below. Most of the directors are convinced that given
the short lifespan of software technology, the best way to decide between the two options
is on the basis of a payback period of two years or less. Compute the payback period of
each option and state which one should be purchased. One of the directors states, “I
object! Given our hurdle rate of 10%, we should be using a discounted payback period of
two years or less.” Accordingly, evaluate the projects on the basis of the DPP and state
your decision.
ANSWER
Year
Software
Option A
PVCF@10%
Software
Option B
PVCF@10%
0
($1,875,000)
$ (1,875,000.00)
($2,000,000)
$ (2,000,000.00)
1
$1,050,000
$ 954,545.45
1,250,000
$ 1,136,363.64
2
$900,000
$ 743,801.65
$800,000
$ 661,157.02
3
$450,000
$ 338,091.66
$600,000
$ 450,788.88
Payback period of Option A = 1 year + (1,875,000 – 1,050,000)/900,000 = 1.92 years
Payback period of Option B = 1year + (2,000,000 – 1,250,000)/800,000 = 1.9375 years
Based on the Payback Period, Option A should be chosen.
For the discounted payback period, we first discount the cash flows at 10% for the
respective number of years and then add them up to see when we recover the investment.
DPP A = –1,875,000 + 954,545.45 + 743,801.65 = –176652.9 ==> still to be recovered in
Year 3 ➔ DPP = 2 + (176652.9/338091.66) = 2.52 years
DPP B = –2,000,000 + 1, 136,363.64 + 661157.02 = –202479.34 still to be recovered in
Year 3 ➔ DPPB = 2 + (202479.34/450788.88) = 2.45 years
Based on the Discounted Payback Period and a two year cutoff, neither option is
acceptable.
328 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
To check this, let’s compute the NPVs of the two projects at 0%, 3%, 5.24%, 8%,
10.2441%, and 11.624%.
Rate
NPV(A)
NPV(B)
0.00%
167,000
187,333
3.00%
115,505
123,656
5.24%
81,318
81,309
8.00%
43,498
34,393
10.2441%
15,811
0
11.624%
0
–19,323
Note that the two projects have equal NPVs at the crossover rate of approximately5.24%.
At rates below 5.24%, Project B’s NPVs are higher, whereas at rates higher than 5.24%,
Project A has the higher NPV.