CHAPTER 6: Practice questions
Exercise No.8. Consider the following projects:
Co
(1.000)
(2.000)
(3.000)
Project
A
B
C
C1
1.000
1.000
1.000
Cash Flows
C2
C3
1.000
4.000
1.000
-
C4
C5
1.000
1.000
1.000
1.000
a) If the opportunity cost of capital is 10%, which projects have a positive NPV?
NPVA = − $1000 +
$1000
= −$90.91
(1.10)
NPVB = − $2000 +
$1000 $1000 $4000 $1000 $1000
+
+
+
+
= +$4,044.73
(1.10) (1.10) 2 (1.10) 3 (1.10) 4 (1.10) 5
NPVC = − $3000 +
$1000 $1000 $1000 $1000
+
+
+
= +$39.47
(1.10) (1.10) 2 (1.10) 4 (1.10) 5
b) Calculate the payback period for each project.
Remember that: Payback period of a project is found by counting the number of years it
takes before the cumulative forecasted cash flow equals the initial investments. So:
Payback A = 1 year
Payback B = 2 years
Payback C = 4 years
c) Which project(s) would a firm using the payback rule accept if the cutoff period is 3 years?
The firm would accept only those projects with a payback period < 3 years; in this case
only projects A and B would be accepted.
d) Calculate the discounted payback period for each project.
From a) we know that:
Project
A
B
Co
-1.000
-2.000
C1
909,09
909,09
Discounted Cash Flows
C2
C3
C4
826,45 3.005,26
683,01
C5
620,92
NPV
(90,91)
4.044,73
C
-3.000
909,09
826,45
-
683,01
620,92
39,47
So the discounted payback period for each project would be:
Disc. Payback A = Project A never exceeds the initial outlay.
Disc. Payback B = 3 years
Disc. Payback C = 5 years
e) Which project(s) would a firm using the discounted payback rule accept if the cutoff period
was 3 years?
If the cutoff period is 3 years the firm would choose Project B.
Exercise No 9. Respond to the following comments:
a) “I like the IRR rule. I can use it to rank projects without having to specify a discount
rate”
When using the IRR rule, the firm must still compare the IRR with the opportunity cost
of capital. Thus, even with the IRR method, one must specify the appropriate discount
rate.
b) “I like the payback rule. As long as the minimum payback period is short, the rule makes
sure that the company takes no borderline projects. That reduces risk”
Risky cash flows should be discounted at a higher rate than the rate used to discount less
risky cash flows. Using the payback rule is equivalent to using the NPV rule with a zero
discount rate for cash flows before the payback period and an infinite discount rate for
cash flows thereafter.
Exercise No 10. Calculate the IRR (or IRRs) for the following project:
Co
(3.000)
C1
3.500
C2
4.000
C3
(4.000)
For what range of discount rates does the project have positive NPV?
r = -17.44%
0.00% 10.00%
Year 0 -3,000.00 -3,000.00 -3,000.00 -3,000.00
Year 1 3,500.00 4,239.34 3,500.00 3,181.82
Year 2 4,000.00 5,868.41 4,000.00 3,305.79
Year 3 -4,000.00 -7,108.06 -4,000.00 -3,005.26
PV =
-0.31
500.00
482.35
15.00%
-3,000.00
3,043.48
3,024.57
-2,630.06
437.99
20.00%
-3,000.00
2,916.67
2,777.78
-2,314.81
379.64
25.00%
-3,000.00
2,800.00
2,560.00
-2,048.00
312.00
45.27%
-3,000.00
2,409.31
1,895.43
-1,304.76
-0.02
The two IRRs for this project are (approximately): –17.44% and 45.27%. Between these two
discount rates, the NPV is positive.
Exercise No. 12. Mr. Cyrus Clops, the president of Giant Enterprises, has to make a choice
between two possible investments:
Project
Cash Flows ($ thousands)
Co
C1
C2
IRR
A
(400)
250
300
23
B
(200)
140
179
36
The opportunity cost of capital is 9%. Mr. Clops is tempted to take B, which has the higher
IRR.
(a) Explain to Mr. Clops why this is not the correct procedure.
Taking a decision based only on the IRR is not the correct procedure because Project A
requires a larger capital outlay; it is possible that Project A has both a lower IRR and a
higher NPV than Project B. (In fact, NPVA is greater than NPVB for all discount rates
less than 10 percent.) Because the goal is to maximize shareholder wealth, NPV is the
correct criterion.
(b) Show him how to adapt the IRR rule to choose the best project.
To use the IRR criterion for mutually exclusive projects, we can calculate the IRR for the
incremental cash flows as follows:
Cash Flows ($ thousands)
Project
Co
C1
C2
A
-400
250
300
B
-200
140
179
Incremental CF (A-B)
-200
110
121
IRR
23%
36%
10%
Given that the IRR for the incremental cash flows exceeds the cost of capital, the
additional investment in A is worthwhile.
(c) Show him that this project has the higher NPV.
NPVA = − $400 +
$250 $300
+
= $ 81.86
1.09 (1.09) 2
NPVB = − $200 +
$140
$179
+
= $79.10
1.09
(1.09) 2
Exercise No.13. The Titanic Shipbuilding Company has a noncancelable contract to
build a small cargo vessel. Construction involves a cash outlay of $250.000 at the end
of each of the next two years. At the end of the third year the company will receive
payment of $650.000. The company can speed up the construction by working an extra
shift. In this case there would be a cash outlay of $550.000 at the end of the first year
followed by a cash payment of $650.000 at the end of the second year. Use the IRR rule
to show the (approximate) range of opportunity costs of capital at which the company
should work the extra shift.
Problem setting (in $ thousands):
Year
1
2
3
Projected
schedule
Accelerated shift
(250)
(550)
(250)
650
650
Using incremental analysis:
Current arrangement
Extra shift
Incremental flows
C1
-250.000
-550.000
-300.000
C2
-250.000
+650.000
+900.000
C3
+650.000
0
-650.000
The IRRs for the incremental flows are (approximately): 21.13% and 78.87%. If the cost of
capital is between these rates, Titanic should work the extra shift.