Reference no: EM132888563

BU5556 Real Options and Decision-Making - University of Aberdeen

You may not discuss these questions or your answers with anyone.

Answer both questions below. You should try to answer all parts of the questions.

Question 1.

An investor is considering whether or not to purchase a lease that would allow her to drill for oil at a particular site. There are two periods, period 0 and period 1. The investor must decide whether to purchase the lease in period 0, and, if she purchases the lease, whether to develop the lease in period 0, in period 1, or not at all. If the investor chooses to purchase the lease, then she must pay a price L in period 0 to the owner of the site. The investor must develop the lease to obtain any value from it. If the investor purchases the lease and decides to develop the lease in period 0, then the investor obtains a net present value from the lease in period 0 equal to V0 = 70. The investor also obtains a net present value V1 from the developed lease in period 1. For simplicity, we assume that there is no cost to develop the lease. From the perspective of period 0, the net present value V1 obtained from a developed lease in period 1 is uncertain due to uncertainty in the price of oil. The investor believes that there is a probability of 0.5 that the price of oil will be high in period 1. In this case, the net present value obtained from the lease in period 1 will take the high value VH = 290. With probability 0.5, the price of oil will be low in period 1. In this case, the net present value obtained from a developed lease in period 1 will take the low value VL = - 170. The quantity VL is negative so that the net present value in this case actually represents a loss to the investor. For simplicity, suppose that the investor cannot avoid this loss by shutting down a developed lease.Suppose that the investor is risk neutral and wishes to maximise the expected net present value from the lease including the cost L of purchasing the lease. Suppose also that the numerical values specified for the various net present values are denominated in millions of pounds. The investor has three choices in period 0.

(1) The investor can choose not to purchase the lease, in which case she obtains an expected net present value of 0.

(2) The investor can choose to purchase the lease and develop the lease in period 0.

(3) The investor can choose to pay the cost L to purchase the lease in period 0 but defer the decision as to whether or not to develop the lease until period 1.

If the investor chooses to develop the lease in period 1, the investor receives a net present value of VH = 290 or VL = - 170 depending on whether the price of oil is high or low in period 1. Moreover, by deferring the decision to develop the lease until period 1, the investor learns whether the price of oil is high or low in period 1 before she must choose whether or not to develop the lease.Hence, waiting gives the investor the opportunity to avoid a loss in period 1 by not developing the lease if the price of oil is low. On the other hand, by waiting to develop the lease untilperiod 1, the investor loses the net present value V0 that she could have obtained from the lease in period 0. In addition, the price of the lease L was paid in period 0 and is not refunded if the investor does not develop the lease.

(i) Draw a decision tree representing the decision problem facing the investor.
(ii) Suppose that L = 30 million pounds. What is the optimal policy for the investor to follow? Carefully explain your answer.
(iii) What is the largest price L that the investor should be willing to pay for the lease? Carefully explain your answer.
(iv) Suppose thatbefore the lease is offered for sale, the owner of the site adds a relinquishment requirement that requires the purchaser of the lease to develop the lease in period 0 or give up the lease. The lease price L is not refunded if the lease is given up in period 0. By how much would you expect that this relinquishment requirement has increased or decreased the value of the lease to the investor? Carefully explain your answer.

Question 2.

Suppose that the change in the price of a share of ABC stock is described by a multiplicative binomial lattice. There are three periods, period 0, period 1, and period 2. In period 0, the share price is S(0) = 180. At the beginning of each following period, the share price moves either up or down. The share price is multiplied by the factor u = 3/2 = 1.5 when there is an up move in the share price, and the share price is multiplied by the factor d = 2/3 = 0.6667 when there is a down move. Suppose also that the riskless interest rate is r = 0.10 that is 10 % per period.

(i) Calculate the market value in period 0 of a European put option to sell one share of ABC stock with an exercise price of K = 150 that expires in period 1. Carefully explain your reasoning.

(ii) Consider a project whose payoffs are determined by the share price of ABC stock. In period 2, the project pays an amount 1250 if the price of a share of ABC stock in period 2 is 405, that is, if the share price has moved upward in both period 1 and period 2. The project also pays an amount 350 in period 2 if the price of a share of ABC stock in period 2 is 180, and the project pays an amount 280 in period 2 if the price of a share of ABC stock in period 2 is 80. For simplicity, suppose that there are no other costs or payoffs associated with the project. Calculate the market value of the project in period 0. Carefully explain your reasoning.
(iii) Explain how your estimate of the market value of the project described in section (ii) would change if the project also paid an amount 150 in period 1. Assume that the amount paid by the project in period 1 is the same whether the share price of ABC stock moves up or down in period 1.

Discuss how a change in (i) the time to expiration, T, (ii) the exercise price K, and (iii) the share price at the time of expiration, S(T), is likely to affect the market value of an American call option and an American put option to buy or sell one share of some stock. For the share price at the time of expiration, consider the value of the two options at the expiration date. For the time to expiration and the exercise price, consider the value of the options at some date before the expiration date.

Attachment:- Real Options and Decision-Making.rar