03-PS5-OP_sol

# B it is the same as short a put option plus cash now

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(b) It is the same as short a put option plus cash. Now assume that the cashflow generated next year can only take two values, 0 and 100, with equal likelihood. (c) We need to determine the risk-neutral probabilities. Assume the risk-free rate is zero for simplicity. Notice that p * 100 + (1 - p ) * 0 + 30 = 100, so p = 0.7. So the value of the project is 0.7*35 = 24.5, so it has negative NPV. If the management rejects the project, the stock holders get nothing if the asset produces 0 and get 70 if the asset generates 100. Therefore the value of the stock is 49. Now if the manage takes the project, the stock holders still get 0 if asset produces 0 but get 75 if the asset generates cash. Therefore the value of stock is increased to 52.5. If the management cares only about stockholders but not debtholders, they will undertake the new project, hurting the debtholders. This illustrates the agency problem that the shareholders is inclined to make the company more risky, even if it may not be efficient. This makes the debt more risky, thus have a lower value and the shareholders benefit from that. (d) Assume the asset pay 35 in the down state (because 30 won’t give you a positive NPV) The value of the project = 0.3*35 = 10.5, so NPV is positive. Now repeat the exercise as above. The shareholders still get 0 if the company produces low cashflow but now only 60 if the company produces high cashflow. Thus the value of stock drops to 42, but the risk of debt has greatly decreased. 3
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• Fall '03
• Wang
• Options, Strike price

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