Chapter 9 Homework key
I’ve edited the questions as indicated on the assignment web page. Also note that many of the
present values in the key here are shown in the key using PV factors from tables. I expect you to
do the problems with your calculator and show your calculator inputs and the result.
1.
A project has the following cash flows
C0
C1
C2
($700)
$200
$500
a. What is the project’s payback period?
b. Calculate the projects NPV at 12%.
c. Calculate the project’s IRR
C3
$244
SOLUTION:
a. The cumulative cash flow is
Year
0
1
2
3
Cash Flow
($700)
$200
$500
$244
Cumulative
($700)
($500)
0
$244
Cumulative cash flow is zero after two years, hence the payback period is two years.
b.
Year
0
1
2
3
Ci
($700)
$200
$500
$244
PVFk,i
1.0
.8929
.7972
.7118
Ck,i  PVFk,i
($700)
$179
$399
$174
NPV = $ 52
c. With the cash flows above entered in your calculator, hit the IRR key and find that the IRR
is 16.03%
3.
Clancy Inc. is considering a project with the following cash flows.
C0
C1
C2
C3
($7,800)
$2,300
$3,500
$4,153
a. Clancy has a policy of rejecting all projects that don’t pay back within three years
outright, and analyzing those that do more carefully with time value based methods.
Does this project warrant further consideration?
b. Should Clancy accept the project based on its NPV if the company’s cost of capital is
8%?
c. Based on IRR, what conclusion will the firm reach?
SOLUTION:
a. The cumulative cash flow is
Year
0
Cash Flow
($7,800)
Cumulative ($7,800)
1
$2,300
($5,500)
2
$3,500
($2,000)
3 .
$4,153
$2,153
Cumulative cash flow is negative after two years and positive after three, hence the payback
period is between two and three years (2 + 2000/4153 = 2.48). Hence Clancy’s policy would
require further evaluation using time value based methods.
1
b. and c. The project’s NPV at 8% is calculated as follows:
Year
Ci
PVF8,i
Ci  PVF8,i
0
($7,800)
1.0
($7,800)
1
$2,300
.9259
$2,130
2
$3,500
.8573
$3,001
3
$4,153
.7938
$3,297
NPV = $ 628
The project has a positive NPV which implies that it should be accepted.
The IRR, using the cash flows above is: 12%, which is above the cost of capital of 8%. Therefore
the investment should be accepted.
5.
Hamstring Inc. is considering a project with the following cash flows:
C0
($25,000)
C1
$10,000
C2
$12,000
C3
$5,000
C4
$8,000
The company is reluctant to consider projects with paybacks of more than three years. If projects
pass the payback screen, they are considered further by means of the NPV and IRR methods. The
firm's cost of capital is 9%.
a. What is the project's payback period? Should the project be considered further?
b. What is the project's NPV? Does NPV indicate acceptance on a stand-alone basis?
c. Calculate the project's IRR using your calculator. Does IRR indicate acceptance on a standalone basis?
SOLUTION:
a.
C0
Cash flows:
($25,000)
C1
C2
$10,000
$12,000
$5,000
$8,000
($3,000)
$2,000
$10,000
Cumulative cash flows:
($25,000)
($15,000)
C3
C4__
Payback period = 2.6 yrs.
Yes, since payback < 3yrs
b.
NPV = $25,000 + $10,000[PVF9,1] + $12,000[PVF9,2] + $5,000[PVF9,3] +
$8,000[PVF9,4]
NPV = $25,000 + $10,000(.9174) + $12,000(.8417) + $5,000(.7722) + $8,000(.7084)
NPV = $3,803
Yes, NPV does indicate acceptance on a stand-alone basis.
c. Enter the cash flows into your calculator and find the IRR is approximately 16.3% which
implies acceptance of the project since 16.3% > 9%.
6.
Project Alpha requires an initial outlay of $35,000 and results in a single cash inflow of
$56,367.50 after five years.
a. If the cost of capital is 8% what are Alpha's NPV? Is the project acceptable under NPV?
b. What is project Alpha's IRR? Is it acceptable under IRR?
2
c. What is Alpha's NPV if the cost of capital is 12%? Is the project acceptable under that
condition.
d. What is Alpha's payback period? Does payback make much sense for a project like Alpha?
Why?
SOLUTION:
a.
NPV = $35,000 + $56,367.50 [PVF8,5]
= $35,000 + $56,367.50 (.6806)
= $35,000 + $38,363.72
= $3,363.72
Acceptable since NPV > 0.
b. Using: N 5, PV= -35000, FV=56375.5; PMT=0: solve I = 10, so IRR = 10%
Acceptable since IRR > 8%.
c.
NPV = $35,000 + $56,367.50 [PVF12,5]
= $35,000 + $56,367.50 (.5674)
= $35,000 + $31,982.92
= $3,017.08
Unacceptable since NPV < 0.
d. 4.62 years. Yes, it payback makes sense because it takes about five years to recover the
absolute value of the investment regardless of the fact that the entire return comes in a single sum.
7.
The Sampson Company is considering a project that requires an initial outlay of $75,000
and produces cash inflows of $20,806 each year for five years. Sampson's cost of capital is 10%.
a. Calculate the project's payback period by making a single division rather than accumulating
cash inflows. Why is this possible in this case?
b. Calculate the project's IRR recognizing the fact that the cash inflows are an annuity. Is the
project acceptable?
c. What is the project's NPV? Is it acceptable according to NPV rules?
SOLUTION:
a.
$75,000 / $20,806 = 3.6 years
The calculation is possible because the returns are constant in amount and regular in time (an
annuity).
b. N=5, PV= -75000; FV=0; PMT= 20806; solve I = 12%; IRR=12%
The project is acceptable since IRR > k = 10%.
c. NPV = $75,000 + $20,806 [PVFA10,5]
= $75,000 + $20,806 (3.7908)
= $75,000 + $78,871
= $3,871
The project is acceptable since NPV > 0.
15.
Bagel Pantry Inc. is considering two mutually exclusive projects with widely differing
lives. The company's cost of capital is 12%. The project cash flows are summarized as follows:
C0
Project A
($25,000)
Project B
($23,000)
3
C1
C2
C3
C4
C5
C6
C7
C8
C9
$14,742
$14,742
$14,742
$
$
$
$
$
$
$
$
$
6,641
6,641
6,641
6,641
6,641
6,641
6,641
6,641
6,641
a. Compare the projects by using Payback.
b. Compare the projects by using NPV.
c. Compare the projects by using IRR.
e. Compare the projects by using the EAA method.
f. Chose a project and justify your choice.
SOLUTION:
a.
Payback Period
A: P/B = $25,000 / $14,742 = 1.7 years
B: P/B = $23,000 / $6,641 = 3.5 years
Project A is preferred.
b.
c.
e.
NPV = C0 + C [PVFAk,n]
A: NPV = $25,000 + $14,742 [PVFA12,3]
= $25,000 + $14,742 (2.4018)
= $10,407
B: NPV = $23,000 + $6,641 [PVFA12,9]
= $23,000 + $6,641 (5.3282)
= $12,385
Project B is preferred.
Enter CFs into calculator
A: IRR
= 35%
B: IRR
= 25%
Project A is preferred.
A: N=3, I=12; PV= -10407; solve PMT = $4,333 = EAA
B: N=9; I=12; PV= -12385; solve PMT = $2324 = EAA
Project A is preferred, because it has the larger EAA.
f.
Project A is preferred on all counts except the original NPV calculation, and that
disparity is due to the time horizon problem. Hence, if A can be repeated, then A is the best
choice.
17.
Provide the missing information for the following projects.
4
Project
Initial
Investment
Length
(in years)
Annual
Cash Flow
Cost of
Capital
NPV
A
$100,000
5
$35,000
8%
B
$200,000
4
13%
C
$300,000
7
$50,000
D
$400,000
$56,098
9%
E
6
$75,000
10%
SOLUTION:
A.
PMT = 35,000
N=5
I/Y = 8
FV = 0
PV = ? = 139,744.85 which make the NPV = $39,744.85
18.
$35,000
$15,000
$20,000
$25,000
B.
PV = (235,000)
N=4
I/Y = 13
FV = 0
PMT = ? = $79,005.64
C.
PV = (315,000)
PMT = 50,000
N=7
FV = 0
I/Y = ? = 2.71%
D.
PV = (420,000)
I/Y = 9
PMT = 56,098
FV = 0
N = ? = 13
E.
PMT = 75,000
N=6
I/Y = 10
FV = 0
PV = ? = 326,644.55
which means the Initial investment was $25,000 less or $301,644.55
Calculate IRRs for the projects in the previous problem.
SOLUTION:
PV
PMT
N
FV
I/Y
A
(100,000)
35,000
5
0
22.11%
B
(200,000)
79,005.64
4
0
21.19%
C
(300,000)
50,000
7
0
4.01%
D
(400,000)
56,098
13
0
9.93%
E
(301,644.55)
75,000
6
0
12.78%
5
23.
Zuker Distributors handles the warehousing of perishable foods and is considering
replacing one of its primary cold storage units. One supplier has offered a unit for
$250,000 with an expected life of 10 years. The unit is projected to reduce electricity
costs by $50,000 per year. However, it requires a $20,000 refurbishing every two years,
beginning two years after purchase. Another supplier has offered a cold storage unit with
similar capabilities for $300,000. It will produce the same savings in electricity costs, but
requires refurbishing every five years at a cost of $40,000. Zuker’s cost of capital is
8.5%. Use NPV to determine which cold storage unit Zuker should select.
SOLUTION:
2-year
refurb.
5-year
refurb.
CF0
CF1
CF2
CF3
CF4
CF5
CF6
CF7
CF8
CF9
CF10
(250,000)
50,000
30,000
50,000
30,000
50,000
30,000
50,000
30,000
50,000
30,000
(300,000)
50,000
50,000
50,000
50,000
10,000
50,000
50,000
50,000
50,000
10,000
I = 8.5%
NPV
15,129
(16,226)
NPV tells us to select the $250,000 storage unit.
6