## 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.

## Retirement Planning For The Golden Years

If mutual funds seem boring to you, there are other higher risk investment opportunities in the form of stocks. I seriously recommend studying the market carefully and completely before making the leap into stock trading but this can be quite the short-term quick profit rush that you are looking for if you am willing to risk your retirement investment for the sake of increasing your net worth. If you do choose to invest in the stock market please take the time to learn the proper procedures, the risks, and the process before diving in. If you have a financial planner and you definitely should then he or she may prove to be an exceptional resource when it comes to the practice of 'playing' the stock market.

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