Principles of Corporate Finance_ 12th Edition

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Chapter 22 Real Options 581


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abandonment later? In this case you have an abandonment option that does not have to be
exercised immediately.
We can value the abandonment option as a put. Assume for simplicity that the put lasts one
year only (abandon now or at year 1) and that the one-year standard deviation of the crusher proj-
ect is 30%. The risk-free interest rate is 4%. We value the one-year abandonment put using the
Black–Scholes formula and put–call parity. The asset value is $5 million and the exercise price
is $5.5 million. (See Table 22.2 if you need a refresher on using the Black–Scholes formula.)


Call value = .480 million or $480,000 (from the Black–Scholes formula)


Put value = call value + PV(exercise price) − asset value (put–call parity)


= .480 + (5.5/1.04) − 5.0 = .768, or $768,000


Therefore you decide not to abandon now. The project, if alive, is worth $5 + .768 = $5.768
million when the abandonment put is included but only $5.5 million if it is abandoned
immediately.
You are keeping the project alive not out of stubbornness or loyalty to the crusher, but
because there is a chance that cash flows will recover. The abandonment put still protects on
the downside if the crusher project deals up further disappointments.
Of course we have made simplifying assumptions. For example, the recovery value of the
crusher is likely to decline as you wait to abandon. So perhaps we are using too high an exer-
cise price. On the other hand, we have considered only a one-year European put. In fact you
have an American put with a potentially long maturity. A long-lived American put is worth
more than a one-year European put because you can abandon in year 2, 3, or later if you wish.


Abandonment Value and Project Life


A project’s economic life can be just as hard to predict as its cash flows. Yet NPVs for cap-
ital-investment projects usually assume fixed economic lives. For example, in Chapter 6 we
assumed that the guano project would operate for exactly seven years. Real-option techniques
allow us to relax such fixed-life assumptions. Here is the procedure:^7



  1. Forecast cash flows well beyond the project’s expected economic life. For example, you
    might forecast guano production and sales out to year 15.

  2. Value the project, including the value of your abandonment put, which allows, but
    does not require, abandonment before year 15. The actual timing of abandonment
    will depend on project performance. In the best upside scenarios, project life will be
    15 years—it will make sense to continue in the guano business as long as possible.
    In the worst downside scenarios, project life will be much shorter than seven years.
    In intermediate scenarios where actual cash flows match original expectations,
    abandonment will occur around year 7.


This procedure links project life to the performance of the project. It does not impose an
arbitrary ending date, except in the far distant future.


Temporary Abandonment


Companies are often faced with complex options that allow them to abandon a project tempo-
rarily, that is, to mothball it until conditions improve. Suppose you own an oil tanker operat-
ing in the short-term spot market. (In other words, you charter the tanker voyage by voyage,


(^7) See S. C. Myers and S. Majd, “Abandonment Value and Project Life,” in Advances in Futures and Options Research, ed. F. J. Fabozzi
(Greenwich, CT: JAI Press, 1990).

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