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我把题目粘到这儿好了～求详细解题过程！谢谢～
1. The price of oil is currently ￡100 per barrel. Next year it will either increase by 50% to ￡150 or fall by 25% to ￡75. A firm is considering investing in a refinery. The investment must be made today or never. The cost of the investment is ￡420 million. The gross value of the project is always four million times the price of oil. The risk free interest rate is 5%. Assume that the probability of an increase in the price of oil is 50% and that all oil price risk is diversifiable.
a. Should the firm make this investment?
b. Suppose that management has the option to expand the scale of the operation after one year. At that time, it can double the gross value of the project by investing an additional ￡320 million. What is the value of this option? Should the firm invest in the refinery today?
2. SBCH has 100,000 shares outstanding. Earnings will be ￡500,000 at the end of year 1 and ￡800,000 at the end of year 2. An investment outlay of ￡200,000 at the end of year 1 has already been decided upon. SBCH is all-equity financed with a required rate of return of 16%. The firm will be liquidated after 2 years. Assume that the firm operates in a world with perfect capital markets. The firm’s policy is to pay out any surplus cash as dividends.
a. What is the current share price of SBCH stock?
b. Millicent owns 10% of SBCH and wants an income from the firm of ￡15,000 at the end of year 1. Show how she can achieve this (without a change in the firm’s dividend policy). What percentage of the firm will she own after the end of year 1 if she follows this strategy?
c. How can Millicent obtain the same income as in part b through changing the current dividend policy of the firm? How many shares will SBCH have outstanding at the end of year 1 under the new policy? What percentage of the firm will Millicent own at that time?
3. A private investor is interested in buying Stickle Tarn in the Lake District. The revenues of operating the Tarn as a camping site are determined by the weather (a random parameter w distributed uniformly on [0, 1]) and by the development programme d (the manager gets (initially at least) a share of *revenue* and pays all d cost herself). The revenue function is wd, the cost of development is 𝑑2−12 and the investor’s outside option is 𝑈̅>0. The investor needs to specify a contract paying the site manager an amount 𝜋 (if the site produces revenue R, the investor gets R-𝜋 and the manager gets 𝜋. Suppose, moreover, that the managers have to accept or reject the contract before observing w, but choose the development programme after observing it.
a. First assume that the investor can observe the revenue R but cannot separately observe d or w. You may assume that the contract takes the form 𝜋=𝛼𝑅 where 𝛼 is a (not necessarily positive) parameter. Find the manager’s optimal development as a function of 𝛼, 𝑈̅ and R, and use this to compute the value of 𝛼 that maximises the investor’s expected utility. Also, find the optimised expected value of the Tarn as a function of 𝑈̅.
b. How (if at all) would your answer differ if the manager observed w before accepting or rejecting the contract?
c. Now suppose that the investors can either choose a contract that depends on 𝜔 (𝜋=𝛼𝜔) or one that depends on d (𝜋=𝛼𝑑) but not both. In other words, they must pay off the manager before observing the value R. As before, the consultants accept or reject the offer before observing 𝜔. Which would the investors prefer to observe?
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