Risk Topics and Real Options in Capital Budgeting
M
O R E
C
O M P L E X
D
E C I S I O N
T
R E E S
: E
X A M P L E S
1 2 - 2
A N D
1 2 - 3
(
PA G E S
5 3 2
A N D
5 3 4 )
9.
Work Station Inc. manufactures office furniture.
The firm is interested in “ergonomic” products that are designed to
be easier on the bodies of office workers’ who suffer from aliments such as back and neck pain due to sitting for long
periods.
Unfortunately customer acceptance of ergonomic furniture tends to be unpredictable, so a wide range of
market response is possible.
Management has made the following two-year, probabilistic estimate of the cash flows
associated with the project arranged decision tree format ($000).
Path
$7,000
1
.3
$4,000
.7
.
6
$5,000
2
$6,000
.
4
$3,000
3
.
8
$2,000
.
2
$2,400
4
Work Station is a relatively small company, and would be seriously damaged by any project that lost more than $1.5
million.
The firm’s cost of capital is 14%.
a.
Develop a probability distribution for NPV based on the forecast.
I.e., calculate the project’s NPV along each
path of the decision tree and the associated probability.
b.
Calculate the project’s expected NPV.
c.
Analyze your results and make a recommendation about the project’s advisability considering both expected NPV
and risk
SOLUTION:
a.
The NPV along each of the project’s four paths and the probability of each of those outcomes is calculated as
follows:
Path 1
NPV
= -6000 + 4000(PVF14,1) + 7000(PVF14,2)
= -6000 + 4000(.8772) + 7000(.7695)
= -6000 + 3508.8 + 5386.5
= 2895.3
Probability
= .6
.3 = .18
Path 2
NPV
= -6000 + 4000(.8772) + 5000(.7695)
= -6000 + 3508.8 + 3847.5
= 1356.3
Probability
= .6
.7 = .42
3

4
Path 3
NPV
= -6000 + 2000(.8772) + 3000(.7695)
= -6000 + 1754.4 + 2308.5
=
-1937.1
Probability
= .4
.8 = .32
Path 4
NPV
= -6000 +1754.4 + 2400(.7695)
= -6000 + 1754.4 + 1846.8
=
-2398.8
Probability
= .4
.2 = .08
1.00
b.
The expected NPV for the entire project is the sum of the products of each path’s NPV and probability.
Expected NPV = 2895.3(.18) + 1356.3(.42)
1937.1(.32) – 2398.8(.08)
= 521.2 + 569.6 – 619.9 – 191.9
= 279.0
c.
Recommendation:
The project has a positive expected NPV, which is quite small relative to the size of the
initial investment.
This argues weakly for acceptance.
However, risk considerations tell another story.

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- Corporate Finance, Investing, Net Present Value