1. Suppose that the market contains three stocks, A, B, and C and two systematic risk- factors 1 and 2 that have the following relationship:
E(rA) = 1.2λ1 + 2.0λ2
E(rB) = -0.2λ1 - 0.4λ2
E(rC) = 0.5λ1 + 0.8λ2
The zero-beta return, λ0, equals zero and all three stocks currently sell for 240 pence.
a. If the risk-premium on factor 1 is 6% and the risk premium on factor 2 is 8%, calculate the price expected next year on each stock assuming that none of them will pay a dividend
b. Following analysis of the stocks you are convinced that the price of each stock in one year will be PA = 310, PB = 235, PC = 265. Create and demonstrate a riskless, arbitrage investment that takes advantage of any mispricing.
c. Assuming that prices move as your analysis predicts, what is the profit from your investment?
2. Trent Fixtures expects net cash flow of £50,000 in perpetuity if the firm makes no new investments. The firm has the opportunity to add a new production line to the business. The immediate outlay for this opportunity is £100,000 and the net cash flows from the line will begin one year from now. The new line will generate £32,000 in additional net cash flows in perpetuity. These net cash flows will also grow at 3%. The firm's discount rate is 13%, and 200,000 shares of Trent Fixtures stock are outstanding. Assume that all net cash flows can be paid out as dividends.
a. What is the price per share of Trent Fixtures stock without the new production line?
b. What is the value of the growth opportunities that the new line offers?
c. Once Trent Fixtures adds the new line, what will be the price per share of Trent's stock?
3. An oil company is considering whether to invest in one or both of two oil wells. Well A is expected to produce oil worth £3 million a year for ten years; Well B is expected to produce £2 million for 15 years. These cash flows are real (inflation-adjusted).
The beta for producing wells is 0.9. The market risk-premium is 8%, the nominal risk-free interest rate is 6%, and the expected inflation rate is 4%. Although the two Wells develop an existing oil field there is still a 20% chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the £10 million investment.
a. What is the correct real discount rate for developed Wells?
b. A company executive proposes adding 20 percentage points to the real discount rate calculated in a) above to offset the risk of a dry hole. Explain briefly why this is not a good idea.
c. Calculate the NPV of each Well and recommend whether or not the company should undertake the investment.