Valuing an Option to Abandon: An Illustration

Assume that Disney is considering taking a 25-year project which requires an initial investment of $ 250 million in an 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 variance in the present value of the cash flows from being in the partnership is 0.09.

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 = 0.09

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 7%. The value of the put option can be estimated as follows:

Call Value = 254 exp(0.04)(5) (0.9105) -150 (exp(-0.07)(5) (0.7496) = $ 110.12 million

Put Value= $ 110.12 - 254 exp(0.04)(5) +150 (exp(-0.07)(5) = $ 7.86 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 $ 11.86 million.