Expected NPV
= $1,177,400 (.9) - $911,300 (.1)
= $1,059,660 – $91,130
= $968,0530
e.
Recommendation:
The project has a positive expected NPV, which is substantial relative to the size
of the initial investment.
This argues strongly for acceptance.
There is substantial risk, however, since
there is a modest chance of a significant loss.
Most managers would probably accept this project
unless the underlying business is so weak that the loss would seriously damage it.
More Complex Decision Trees: Examples 12-2 and 12-3 (pages 522 and 524)
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 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(PVF
14,1
) + 7000(PVF
14,2
)
= -6000 + 4000(.8772) + 7000(.7695)
= -6000 + 3508.8 + 5386.5
= 2895.3
Probability
= .6
.3 = .18
46

Risk Topics and Real Options in Capital Budgeting
Path 2
NPV
= -6000 + 4000(.8772) + 5000(.7695)
= -6000 + 3508.8 + 3847.5
= 1356.3
Probability
= .6
.7 = .42
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.
Two paths with probabilities totaling 40% have ruinously negative NPVs.
That means
accepting the project has as much as a 40% probability of seriously damaging or sinking the company.
Most rational managers would forego such a project in spite of the positive overall expected NPV.
Abandonment Options: Example 12-5 (page 528)

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