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Faculty of Economics and Business
FINANCE I (102329) – Group 3 – 2012 - 13 Third exam (60% of the final grade)
9 th^ January 2013
Question 1 ( 4 points ): CAPM
On the stock exchange of Crocodilandia , where the CAPM holds strictly, following financial assets are traded:
Expected return
Standard deviation
Stock 1 correlation
Stock 2 correlation
Stock 3 correlation
Stock 4 correlation Stock 1 2 % 8% 1 0. 75 0.6 - 0. 75 Stock 2 10 % 12% 0. 75 1 - 0.5 0. Stock 3 15 % 20% 0. 6 - 0.5 1 0. Stock 4 25 % 30% - 0. 75 0.5 0.8 1 r = 5% M 18.9119% 20.6313%
On this stock exchange the efficient frontier of risky assets is expressed by the next equation:
E(R) = 0. 072628038 + (0. 380738249 ·σ^2 – 0. 00263597 )1/
Other significant data about the stocks listed in Crocodilandia are:
Stock 1 Stock 2 Stock 3 Stock 4 Weight in M 11.6050% 21.2758% 2.2755% 64. 8437 % Covariance with M - 0. 91 79% 1. 5 298% 3. 0 596% 6. 119 2% Beta - 0. 215642 0. 359404 0. 718807 1. 437614 Systematic risk - 4. 4490 % 7. 4150 % 14. 8300 % 29. 6599 % Specific risk 6. 6488 % 9. 4349 % 13. 4191 % 4. 5044 % Total risk 8 % 12 % 20 % 3 0% Contribution to M - 0.51630% 1 .57759% 0. 33745 % 19. 23259 %
Questions:
1.1 Explain the meaning of the market portfolio, its relationship with the separation theorem and with market indices. Comment on the composition of the market portfolio in Crocodilandia and relate it with the design of market indices that you know. Justify the values of the expected rate of return and the standard deviation of the market portfolio. Explain the properties upon which you have based your calculations.
1.2 Prove that the expected rate of return on stock 1 is only 2% and interpret your calculation. Why are its systematic risk and contribution to M negative while total risk and specific risk are positive? Could stock 1 be considered as a close substitute of the risk-free asset? Why?
1.3 Fifí Carambola has invested all her savings (10000€) in stock 4 because she likes assuming high risk and stock 4 is the security with the highest risk in Crocodilandia. Is her choice efficient? Why? If you can suggest a better alternative to her, calculate the expected rate of return and the composition of her new investment. How much money is invested in stock 4? Illustrate your answer with a suitable diagram.
Question 2 (2 points): SHARE VALUATION
On the stock exchange of The Paparines Islands the most popular firm listed is Together-We-Shall- Conquer Ltd , whose name reflects the idiosyncrasy of the inhabitants of this island.
Book value per share is 110€ while current stock price is 1 40 €. The coefficient beta of present investments is 0.75.
Earnings per share are expected to be 20€. The dividend policy is explained by a payout ratio of 40%. Retained profits are entirely devoted to finance a new investment expected to yield 22% and to be financed at a cost of capital determined by a coefficient beta of 0.7.
The risk-free interest rate on The Paparines Islands is 5% and the expected return on the market index reaches 25% in this optimistic country.
Questions:
2.1 Are the shares of Together-We-Shall-Conquer Ltd fairly valued? Why? Is this firm a value company or a growth company?
2.2 Break down the market value calculated in the previous question identifying all possible present values. Explain the meaning of the PVGO, the NPV incorporated into the stock price and the NPV of the transaction identified in question 2.1.
2.3 Calculate the price-earnings ratio (using the fair price) and interpret it. Is it true that the average cost of capital of Together-We-Shall-Conquer Ltd can be inferred from its P/E ratio? Why?
FINANCE I (102329) Examination paper 9th^ January 2013 - ANSWER SHEET Name: __________________________________________________________________ Group 3
If you need more space to answer, please turn the page
Question 1 (4 points ): CAPM
1.1 Explain the meaning of the market portfolio, its relationship with the separation theorem and with market indices.
Comment on the composition of the market portfolio in Crocodilandia and relate it with the design of market indices that you know.
Justify the values of the expected rate of return and the standard deviation of the market portfolio. Explain the properties upon which you have based your calculations.
1.2 Prove that the expected rate of return on stock 1 is only 2% and interpret your calculation.
Why are its systematic risk and contribution to M negative while total risk and specific risk are positive?
Could stock 1 be considered as a close substitute of the risk-free asset? Why?
Is this firm a value company or a growth company?
2.2 Break down the market value calculated in the previous question identifying all possible present values.
Meaning of the PVGO:
Meaning of the NPV incorporated into the stock price:
Meaning of the NPV of the transaction identified in question 2.1.:
2.3 Calculate the price-earnings ratio (using the fair price) and interpret it.
Is it true that the average cost of capital of Together-We-Shall-Conquer Ltd can be inferred from its P/E ratio? Why?
Question 3 (2 points): OPTIONS
3.1 Calculate the value of the call option. Explain the meaning of the method used in your calculation.
3.2 Calculate the put value using the put-call parity. Explain why you have been capable of applying this equation.
3.3 If there is an arbitrage opportunity, explain why, identify its main features and develop it.
