MØA 155
PROBLEM SET: Capital Budgeting
Exercise 1. Projects [3]
Consider the following projects:
Cash flows, thousands of dollars
A
B
C
C0
−1
−2
−3
C1
1
1
1
C2 C3
0
0
1
4
1
0
C4
0
1
1
C5
0
1
1
1. If the opportunity cost of capital is 10 percent, which projects have a positive NPV?
2. Calculate the payback period for each project.
3. Which project(s) would a firm using the payback rule accept if the cutoff period were 3 years?
Exercise 2. Mutually Exclusive Projects (BM 5.7) [4]
Consider the following two mutually exclusive projects A and B:
Period
A
B
0
1 2 3
−100 60 60 0
−100 0 0 140
1. Calculate the NPV of each project for discount rates of 0, 10 and 20%. Plot these on a graph with
NPV on the vertical axis and discount rate on the horizontal.
2. What is the approximate IRR of each project?
3. In what circumstances should the company accept project A?
4. Calculate the NPV of the incremental investment (B-A) for discount rates of 0, 10 and 20%. Plot these
on your graph. Show that the cases in which you would accept A are also those in which the IRR on
the incremental investment is less than the opportunity cost of capital.
Exercise 3. MacGregor Whiskey Co (BM 9.11) [4]
The MacGregor Whiskey Company is proposing to market diet scotch. The product will first be testmarketed for 2 years in Southern California at an initial cost of $500,000. This test launch is not expected
to produce any profits but should reveal consumer preferences. There is a 60 percent chance that demand
will be satisfactory. In this case, McGregor will spend $5 million to launch the scotch nationwide and will
receive an expected annual profit of $700,000 in perpetuity. If demand is not satisfactory, diet scotch will be
withdrawn.
Once consumer preferences are known, the product will be subject to an average degree of risk, and therefore,
McGregor requires a return of 12 percent on its investment. However, the initial test-market phase is viewed
as much riskier, and McGregor demands a return of 40 percent on this initial expenditure.
1. What is the NPV of the diet scotch project?
Exercise 4. Halcyon Lines (BM 3.5) [3]
Halcyon Lines is considering the purchase of a new bulk carrier for $8 million. The forecast revenues are $5
million a year and operating costs are $4 million. A major refit costing $2 million will be required after both
the fifth and tenth years. After 15 years, the ship is expected to be sold for scrap at $1.5 million.
1
1. If the discount rate is 8 percent, what is the ship’s NPV?
Exercise 5. Projects [2]
You are given the following information about three projects. Each project last for one period only.
Project
A
B
C
Investment
Outlay (C0 )
1
1
2
Rate of
return (IRR)
8%
20%
4%
1. Find the cash flow in period 1 (C1 ).
2. Suppose the opportunity cost of capital is 10%. Calculate the net present value (NPV) of each of the
three projects.
3. Which projects would you accept?
Exercise 6.
A project has costs of 1 million at startup. The project has a positive cash flow of 1 million for the next
three years and a cleanup cost of 2 million in the fourth year. Disregard taxes.
What are the internal rate(s) of return for the project?
(a) -12.45%.
(b) 0.00% and 52.15%.
(c) 2.00%.
(d) 13.38% and 52.15%.
(e) I choose not to answer.
Exercise 7.
A firm will have a stall at a summer amusement theme park. It will invest $1,000 and considers three
mutually exclusive projects; A, B and C. The cash flows of these projects are given in the table below. The
cost of capital is 10%.
Project
A
B
C
0
-100
-500
-500
Year
1
2
2200 -1210
4400 -2420
7700 -2420
What is the relative ranking of the three projects to the firm?
1. It prefers A to C, and prefers C to B.
2. It is indifferent between B and C, and prefers both to A.
3. It is indifferent between A and C, and prefers both to B.
4. It prefers C to B, and prefers B to A.
5. I choose not to answer.
2
Exercise 8.
A company is evaluating a project, developing a new computer design. The project requires an investment
of 2 million. The revenues in later years depend on the price the computer achieves in the market. The
company calculates expected cash flows for the next 5 years as 550,000 per year. However, this assumes
that the company sells computers in all the next five years. The company has the option of closing down
production early if the computer price develops unfavourably.
The project is to be evaluated at a required rate of return of 10%.
Which of the following statements is correct?
1. The NPV of the project is above 84,933.
2. The NPV of the project equals 84,933.
3. The NPV of the project is below 84,933.
4. There is not enough information to state whether the NPV of the project is above, equal to, or below
84,933.
5. I choose not to answer.
Exercise 9.
A company named Magne Jernilden ASA is evaluating a move to a new location. The local community is
offering a sweetener to encourage the move. The local community is offering Magne Jernilden ASA a 5 year,
zero coupon, interest free loan of kr 5 million. Magne Jernilden ASA is paying 10% interest on its current
debt.
What is the value to Magne Jernilden ASA of the offer made by the local community?
1. kr 0
2. kr 0,2 million
3. kr 0,5 million
4. kr 1,9 million
5. I choose not to answer.
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Empirical
Solutions
MØA 155
PROBLEM SET: Capital Budgeting
Exercise 1. Projects [3]
Project
A
B
C
NPV
-91
4044
39
Payback
1
2
4
c) Using payback, I will accept A and B. However, I should accept B and C, since those are the positive-NPV
projects.
Exercise 2. Mutually Exclusive Projects (BM 5.7) [4]
A
B
C0
-100
-100
C1
60
0
C2
60
0
C3
0
140
NPV:
A
B
0%
20
40
10%
4.13
5.18
20%
-8.33
-18.98
IRR
13.066
11.869
NPV
6
r
c) When A has a higher (positive) NPV than B. This can easiest be seen in the figure above.
An alternative way is to find when the IRR on the difference investment is higher than the opportunity cost
of capital (In this case, it is when 10.278 ≤ r ≤ 13.066).
d) Incremental investment.
Cash flows:
B–A
C0
0
C1
-60
4
C2
-60
C3
140
NPV:
0%
20
B–A
10%
1.051
20%
-10.641
IRR
10.278
Exercise 3. MacGregor Whiskey Co (BM 9.11) [4]
N P V2 if unsuccessful = 0
700
N P V2 if successful = −5000 +
= 833
.12
(.4 · 0) + (.6 · 833)
= −$245, 000
N P V0 = −500 +
1.42
Exercise 4. Halcyon Lines (BM 3.5) [3]
1. First, look at the table of cash flows: (all numbers in millions)
Year
Income
Refit
Scrap
1
1
···
···
···
···
2
1
4
1
5
1
-2
···
···
···
···
1
1
1
PV = 1 ·
−
r
(1 + r)15 r
+
···
···
···
···
10
1
-2
14
1
15
1
1.5
(−2)
1.5
(−2)
+
+
(1 + r)5
(1 + r)10
(1 + r)15
= 1 · 8.559 − 2 · 0.681 − 2 · 0.463 + 1.5 · 0.315
= 6.743
N P V = P V − C0 = 6.743 − 8.000 = −1.256
Since the NPV is negative, don’t invest.
Exercise 5. Projects [2]
1.
0=
C1
− C0 ⇒ C1 = C0 (1 + r)
1+r
A
B
C
2.
NPV =
1.08
1.20
2.08
C1
− C0
1+r
−0.018
0.090
−0.109
A
B
C
3. Accept B only, it has positive NPV, which could also be seen from the fact that it was the only project
with an IRR higher than the opportunity cost of capital.
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Exercise 6.
The cashflows sum to zero, one IRR is zero. 52.15% is also correct.
(b) is correct.
Exercise 7.
Exercise 8.
Calculate the NPV assuming the company maintains production for five years
NPV
= −2
0.55
(1 + 0.1)1
0.55
+
(1 + 0.1)2
0.55
+
(1 + 0.1)3
0.55
+
(1 + 0.1)4
0.55
+
(1 + 0.1)5
= 0.0849327,
+
or 84.933. The option to abandon early can only add
(a) is correct
Exercise 9.
Beregn nåverdien av tilbudet.
t
0
5
NPV = 5 + −
to this NPV. Hence
Ct
5
−5
5
= 1.89539
(1 + 0.1)5
(d) is correct.
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