## The Option to Abandon a Project

The final option to consider here is the option to abandon a project when its cash flows do not measure up to expectations. Generally, the option to abandon will generally increase the value of a project and make it more acceptable. To illustrate, assume that V is the remaining value on a project if it continues to the end of its life, and L is the liquidation or abandonment value for the same project at the same point in time. If the project has a life of n years, the value of continuing the project can be compared to the liquidation (abandonment) value — if it is higher, the project should be continued; if it is lower, the holder of the abandonment option could consider abandoning the project -Payoff from owning an abandonment option = 0 if V > L

These payoffs are graphed in Figure 6.10, as a function of the expected stock price.

Figure 6.10: The Option to Abandon a Projectt

PV of Cash Flows from project

Figure 6.10: The Option to Abandon a Projectt

Unlike the prior two cases, the option to abandon takes on the characteristics of a put option.

Illustration 6.12: Valuing Disney's option to abandon: A Real Estate Investment

Assume that Disney is considering taking a 25-year project which requires an initial investment of $ 250 million in a real estate partnership to develop time-share properties with a South Florida real estate developer, and where the present value of expected cash flows is $ 254 million. While the net present value of $ 4 million is small, assume that Disney has the option to abandon this project anytime by selling its share back to the developer in the next 5 years for $ 150 million. A simulation of the cash flows on this time-share investment yields a standard deviation in the present value of the cash flows from being in the partnership of 20%.

The value of the abandonment option can be estimated by determining the characteristics of the put option:

Value of the Underlying Asset (S) = PV of Cash Flows from Project = $ 254 million

Strike Price (K) = Salvage Value from Abandonment = $ 150 million Variance in Underlying Asset's Value = 0.202 = 0.04 Time to expiration = Life of the Project =5 years

Dividend Yield = 1/Life of the Project = 1/25 = 0.04 (We are assuming that the project's present value will drop by roughly 1/n each year into the project)

Assume that the five-year riskless rate is 4%. The value of the put option can be estimated as follows:

Call Value = 254 exp(004)(5) (0.9194) -150 (exp(-004)(5) (0.8300) = $ 89.27 million Put Value= $ 89.27 - 254 exp(004)(5) +150 (exp(-004)(5) = $ 4.13 million The value of this abandonment option has to be added on to the net present value of the project of $ 4 million, yielding a total net present value with the abandonment option of $ 8.13 million.

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