Question

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 triples?

b. Assume that the actual price is more 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?

please breakdown calculations and provide short explanation on SML for b. thanks

Answer 1

Part A:

Calculation of Equity Rate of Return:-

= (54-48)/48

= 6/48

= 12.5%

Using the equation for the security market line,

E(r) = rf+ βold(rm–rf)

12.5% = 5% + βold(10% –5%)

βold= 1.5

If the covariance with the market triples, and if future price is triples, beta must also triples.

Therefore, the new beta must be equal to 3 * 1.5 = 4.5.

Returning to the security market line equation, E(r) = rf+ βnew(rm–rf)

E(r) = 5% + 4.5 (10% –5%)

E(r) = 5% + 22.5%

E(r) = 27.5%

Finally, given that the price is expected to be $54, and the expected return is 27.5 %, today’s current price should be:

Price = $54 / (1 + 27.5%) = $ 42.3529

Part B:

If the Actual price is more than what we have calculated in Part A, The the actual return is more than the expected return and we should buy more shares. Since SML is based in the CAPM Model and its helps us calculate the equilibrium price and if this price is less than the actual price then we should buy more shares as the share is undervalued.