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Question 4-1An abandonment option is the option to stop
investing in a venture and to liquidate any othe ventures assets.
An entrepreneur can benefit from an abandonment option in avariety
of ways. For one, if the venture is abandoned, the entrepreneur can
stop devoting
effort and resources to the venture and can recommit them to
other activities that may bemore valuable. Another benefit is that
abandoning may give the entrepreneur theliquidation return on any
existing assets that are invested in the venture but could have
ahigher value in alternative use.
Problem 4-2
Accept/Reject Decision
High Demand NPV:
000,000,1$
000,000,3$000,000,2$
NPV
NPV
Moderate Demand NPV:
000,500$
000,500,1$000,000,2$
NPV
NPV
Low Demand NPV:
000,000,1$
000,000,1$000,000,2$
NPV
NPV
Calculate NPV of investment:
000,75$
)000,000,1$(*)35.0()000,500$(*)25.0()000,000,1($*)4.0(
NPV
NPV
You should not invest because the Net Present Value of the
investment is negative.
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Problem 4-3
Expansion Option
Moderate Demand
(0.25)
High Demand (0.4)
Expand NPV = -$2.5 million + $4 million
Do Not Expand NPV = -$2 million + $3 million
NPV = $1.5 million
NPV = $1 million
NPV = -$2 million + $1 millionLow Demand (0.35)
NPV = -$1 million
Expand NPV = -$2.5 million + $2.5 million
NPV = $0
Do Not Expand NPV = -$2 million + $1.5 million
NPV = -$500,000
Expanding dominates not expanding in the high and moderate
demand states. The NPV
rom investing in the business and expanding in the high or
moderate demand state is the
ollowing:
000,250$)000,000,1($*)35.0()0($*)25.0()000,500,1($*)4.0(
NPVNPV
The Value of the Expansion Option
NPV with expansion = $250,000 compared to rejecting
venture$325,000 compared to negative NPV of accept/reject
decision
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Problem 4-6
Evaluation Sequential Options
No (0.7)
Success(0.3)
No (0.6)
Success
(0.4)
No (0.8)
Success
(0.2)
Invest $3
million
Probability of not succeeding:
336.0)(
)8.0(*)6.0(*)7.0()(
noP
noP
Probability of succeeding:
664.0)(
336.01)(
)(1)(
successP
successP
noPsuccessP
Expected value of investment:
000,656,2$)(
)000,000,4($*)664.0()(
)000,000,4($*)()(
xE
xE
successPxE
Net Present Value:
000,344$
000,656,2$000,000,3$
NPV
NPV
Do not undertake the project
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Problem 4-7
Staging of Investment Decisions
a.
No (0.7)
Success
(0.3)
Invest $1
million
Abandon
No (0.6)
Success
(0.4)
Invest $1
million
Problem 4-7 continued
b.
Conditional Value in Stage 3Expected Value of Success:
000,800$)(
)000,000,4($*)2.0()(
xE
xE
NPV of Conditional Investment:
000,200$
000,800$000,000,1$
NPV
NPV
Do not invest in Stage 3.
Conditional Value in Stage 2
Expected Value of Success:
000,600,1$)(
)000,000,4($*)4.0()(
xE
xE
NPV of Conditional Investment:
000,600,1$000,000,1$
NPV
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c.
Whereas the NPV in problem 6 is negative, it is positive in
problem 7. This result is dueto the abandonment options, rather
than committing all three million at the beginning othe venture.
The total difference in value between the approaches in problems 6
and 7 is$964,000. However, because the NPV is negative in problem
6, the approach in problem6 would not be pursued. The value added
by the options in problem 7 is, thus, the netamount of $620,000.
This example illustrates that the options values are not
additive.More generally, because some options can only be exercised
if others are exercised (thethird stage cannot be exercised without
the second stage) the option value are notadditive.
