Question

Question 1 (10 Marks) Tilda Co. stock is currently priced at $48. You expect its price in one year to be $54 and do not expect any dividends to be paid. The risk free rate is 5%, and the overall market is expected to return 10%. a) What will be the current price of Tilda Co. if the expected future price remains the same but its covariance with the market doubles? (4 Marks) b) Assume that the actual price is less than what you have calculated in A. What does this say about its actual return compared to what is predicted by the security market line? (4 Marks) c) If it is true that properly priced securities fall on the security market line, what would you expect to happen to the price of Tilda Co. given that it is currently less than your calculation from part a? Explain why you believe that a price change would occur. (2 Marks)

Answer 1

Solution:

Given the current prices and expected price, the expected return is equal to $54 − $48 48 = 12.5%

Using the equation for the security market line,

E(r) = r f + β old (r m – r f )

12.5% = 5 % + β old (10% – 5%)

β old = 1.5

If the covariance with the market doubles, all else equal, beta must also double. Therefore, the new beta must be equal to 2 * 1.5= 3. Returning to the security market line equation,

E(r) = r f + β new (r m – r f )

E(r) = 5% + 3 (10% – 5%)

E(r) = 20%

Finally, given that the price is expected to be $54, and the expected return is 20 %, today’s current price should be:

Price = $54 / (1 + 20%) = $45