University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights sum to 100. YOU MAY ANSWER IN ENGLISH OR NORWEGIAN. Some advice: It is better to try to do something on each question than to get bogged down with one question. None of these questions requires a lot of complicated calculations. If you find you are spending too much time on one question, stop working on it and plan to get back to it if you have time at the end. Make sure you state any assumptions you make. Explain and show the steps of any calculations you do. Keep discussions clear and brief. You will be rewarded for answers emphasizing intuition. Exercise 1. Bond [10] A 2 year coupon bond is paying 10% coupon. The current interest rate is 5% (with annual compounding). The bond has a face value of 1000. 1. What is the price of the bond? 2. What is the duration of the bond? Exercise 2. Stock [5] Stocks in company A are priced at 100. Last years dividend was 10. The current interest rate relevant for valuing A is 10% (with annual compounding). 1. Using the dividend discount model, what is the implicit growth rate in this price? Exercise 3. Project [10] A project is planned to give the following cash flows for the next four years: t = 1 2 3 4 C t = 200 250 300 300 The project requires an initial investment of 740. The relevant continously compounded interest rate is 14%. Disregard taxes. 1. Should you invest in this project? Exercise 4. Term [10] A treasury zero coupon bill that pays 100 one period from now is priced at 90. A treasury zero coupon bill that pays 100 two periods from now is priced at 80. 1
1. Determine the price of a two year treasury bond paying 10% annual interest payments with face value of 1000. 2. How would you describe the term structure of interest rates in this economy? Exercise 5. Mean Variance [15] Consider a risk averse investor that puts together a portfolio based on the following properties of the investment portfolio: 1. Expected return E[r p ]. 2. variance of return σ 2 (r p ), i.e. the investor has a utility function U(E[r p ], σ 2 (r p )). a. What is the sign of the partial derivative with respect to expected return, U() E[r p]? b. What is the sign of the partial derivative with respect to variance, U() σ(r p) 2? This investor has access to two possible investment opportunities A and B, with the given expected returns and standard deviations: E[r i ] σ(r i )) A 12% 20% B 10% 30% c. If you can only invest in one of the assets, which one would you choose? d. If the correlation between these two assets is highly negative, what do you expect your portfolio will look like? Exercise 6. Short answer questions [25] Answer the following questions in at the most a paragraph each. 1. Does the internal rate of return method always give the same ranking as the NPV method in investment analysis? 2. A corn farmer in Iowa faces two major risks: The crop may fail, or the price of the corn may be low. Which of these risks can be hedged using financial means? Can hedging of one of these risks be done independently of the other? 3. Suppose there are traded options written on the price of Statoil. One is a call option with exercise price 150. Another is a digital option paying one NOK if the price of Statoil is higher than 150. Is the digital option always less worth than the call option? 4. What is the underlying financial principle used to develop put-call parity of options? 2
5. There are three methods for dealing with interactions between investment decisions and financing: Adjusted Present Value, Flow to Equity, and WACC. Which of these account for expected bankruptcy costs? 6. An event study is a test of how financial markets incorporate information. How does it do that? 7. What is the difference between an open end and closed end mutual fund? 8. Financial analysts often use the so called P/E method which says that the value of a firm can be found as an estimate of next year s net earnings multiplied by a P/E multiple. How can such a procedure be reconciled with the standard stock valuation formula based on expected future dividends? 9. How can you compare the costs of machines with different times to replacement? 10. In risk management we discussed three dimensions of risk transfer: Hedging, Insuring, and Diversifying. Which of these three are futures suited for? What about options? 11. What types of corporations typically have severe mismatch of duration of assets and liabilities? 12. In consumption savings decisions, what does interest rates represent? 13. In pricing of forwards/futures, one direction of the cost of carry relationship (F = S(1+r f ) for an asset without storage costs) does not need to hold if there are limits to short selling the asset. Which? And why? 14. What is implied volatility? 15. How can one represent the firm s equity as an option written on the assets of the firm? Exercise 7. XZY [10] The current price of XZY stock is 50. XZY is not expected to pay dividends the next few years. It has a cost of equity capital of 10% and a cost of debt capital of 5%. The beta of the equity is one, and the market risk premium is 6%. Interest rates are stated with annual compounding. 1. What is the one year forward price for XZY stock? Exercise 8. CBA [20] The current price of CBA stock is 80. CBA is not expected to pay dividends for the next few years. During the next two years, CBA stock is expected to either increase by 15 percent or decrease by 10 percent each year. The one year continously compounded interest rate is 5%. 1. What are the possible stock prices after two years? 3
2. Price a (European) call option with exercise price 95 written on CBA stock and maturity one year. 3. Price a (European) call option with exercise price 95 written on CBA stock and maturity two years. 4
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