Question

Wonderland Ltd. is considering building a new Rapid Ride facility in its theme park. One year from now the company will know whether the ride will be accepted by park visitors. If the demand for the ride is high, the company estimates that the present value of cash flows in one year will be $24 million. If the demand is low, the present value of cash flows in one year will be $9 million. The value of the facility today under these assumptions is $18 million. Suppose that the company can sell the facility for $12 million in one year if the demand is low. The risk-free rate is 5 percent per annum Required: Calculate the value of the option to abandon.

Answer 1

Answer:

Let P(H) denote the probability that demand for the ride one year hence will be high, and P(L) denote the probability that demand for the ride one year hence will be low; such that P(H) + P(L) = 1.

Value of facility today = $18 million = P(H) * $24 million + P(L) * $9 million

On solving the above equations, we come to know that P(H) = 0.60 or 60%, and P(L) = 0.40 or 40%.

Expected profit = P(H) * $(24 - 18) million + P(L) * $(9 - 18) million = $0 ...(A)

Now, if there is an option to sell the facility for $12 million one year from now, if the demand is low.

Present value of $12 million today = $12 million / (1+5%)^1 = $ 11.43 million

Expected profit (with the option in hand) = P(H) * $(24 - 18) million + P(L) * $(11.43 - 18) million = $0.97 million ...(B)

Therefore, value of option = (B) - (A) = $0.97 million.