Chapter 12 Cash Flow Estimation and Risk Analysis 383process (e.g., coal versus natural gas for generating electricity) can be changed if
input prices and/or availability change. We illustrate abandonment options here
in the text, and we cover other types of options in Web Appendix 12F.
12-7b Abandonment Options
In capital budgeting, we generally assume that a project will be operated for its full
physical life. However, this is not always the best course of action. If the " rm’s
project has an abandonment option that can be implemented if things don’t go
well, this can lower its risk, increase its expected pro" tability, and raise its calcu-
lated NPV.
Table 12-3 gives a picture of the decision tree for Project S. In the scenario
analysis in Section 12-5, we examined Project S under the best-case, base-case, and
worst-case assumptions. In the worst-case situation, the project has negative cash
! ows for its full 4-year life. However, if the company can abandon the project after
Year 1, when it sees that the project is not a success, its expected NPV can be im-
proved. The earlier analysis is reproduced in the top section of Table 12-3, labeled
“No Abandonment.” In Column C, which is Time 0, we see that the " rm must in-
vest between $750 and $1,250. Columns D through G show the annual cash! ows
under each scenario; and in Column H, we show the WACCs for each scenario.
Then in Column I, we show the NPV under each scenario when the cash! ows are
discounted at their respective WACCs. The sum of the products obtained by mul-
tiplying each probability times each branch NPV is the expected NPV, which is
$706.40. The standard deviation and the coef" cient of variation are also calculated
to provide an idea of the project’s risk. This project has a positive expected NPV;
hence, by the NPV criterion, it should be accepted.
Now suppose the company could make a second decision, at t " 1, to aban-
don (or shut down) the project if things go badly during Year 1. To see what
would happen, we add another branch to the tree, as shown in the Worst #2 row
in Table 12-3 under the “Can Abandon” situation. Here we assume that the com-
pany abandons the project at the end of Year 1, when information about the actual
production costs and demand conditions become available. If things were going
well, the project would be continued. However, if things were going badly, the
" rm would close the operation and not suffer the indicated losses during the next
3 years.^11
Given the “Can Abandon” option, the " rm would clearly prefer to abandon
the project than to continue. Therefore, we assign a zero probability to continuing
after a bad start. Therefore, the 25% probability associated with the worst case is
used for “Worst #2,” and a 0% probability is assigned to “Worst #1.”
The option to abandon raises the expected NPV from $706.40 to $1,350.09, and
it lowers the standard deviation. Those changes combine to lower the coef" cient of
variation. The coef" cient of variation is 3.05, which is above the company’s aver-
age of 2.0, which indicates that the project is still riskier than most, even after the
abandonment option has been factored in. Therefore, the 12.50% WACC is still ap-
propriate. Also note that the difference between the expected NPVs with and with-
out abandonment represents the option value to abandon this project. As shown
in the lower part of Table 12-3, this option is worth $643.68.
In this case, the ability to abandon makes the NPV look better; but it does not
reverse the accept/reject decision. However, it often turns out that if we fail to
consider abandonment, the bad case is so bad that the expected NPV is negative.
Abandonment Option
The option to abandon a
project if operating cash
flows turn out to be lower
than expected. This option
can raise expected
profitability and lower
project risk.Abandonment Option
The option to abandon a
project if operating cash
flows turn out to be lower
than expected. This option
can raise expected
profitability and lower
project risk.
Decision Tree
A diagram that lays out
different branches that
are the result of different
decisions made or the
result of different
economic situations.Decision Tree
A diagram that lays out
different branches that
are the result of different
decisions made or the
result of different
economic situations.Option Value
The difference between
the expected NPVs with
and without the relevant
option. It is the value that
is not accounted for in a
traditional NPV analysis.
A positive option value
expands the firm’s
opportunities.Option Value
The difference between
the expected NPVs with
and without the relevant
option. It is the value that
is not accounted for in a
traditional NPV analysis.
A positive option value
expands the firm’s(^11) If the assets devoted to the project could be sold, this would be a cash in" ow at the time of the sale, presum- opportunities.
ably at the end of Year 1.