4 KAPLAN SCHWESER Here are data on two companies The Tbill r

4 KAPLAN SCHWESER Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%. Company Forecast returm Standard deviation of returns Beta S1 Discount Store Everything $5 12% 8% 1.5 11% 1096 1.0 Page 225 What would be the fair return for each company, according to the capital asset pricing model (CAPM)? (LO 7-1) 5 KAPLAN SCHWESER Characterize each company in the previous problem as underpriced, overpriced, or properly priced.(LO 7-2) 6 KAPLAN SCHWESER What is the expected rate of return for a stock that has a beta of l if the expected return on the market is 15%? (LO 7-2) a. 15%. b. More than 15%. C. Cannot be determined without the risk-free rate

Solution

Answer 4. Information Given:

Risk Free Rate (Rf)= 4%

Market Risk Premium= 6%

As Per CAPM: Required Rate of Return = Rf+B(Rm-Rf)

Market Risk Premium (MRp)= Return of Market(Rm) - Risk Free Rate (Rf)

Calculation of Fair Return of $1 Discount Store if Beta is 1.5

Fair Return of $1 Discount Store as per CAPM Model = 4+1.5*(6) = 13%

Calculation of Fair Return of Everything $5 if Beta is 1.0

Fair Return of Everything $5 as per CAPM Model = 4+1.0*(6) = 10%

Answer 5. The forecast return of the $1 Discount Store is 12% while Return as per CAPM Model is 13% it clearly shows that the stock of $ 1 Discount Store is overpriced.

Similarly,

The forecast return of the Everything $5 is 11% while Return as per CAPM Model is 10% it clearly shows that the stock of Everything $5 is underpriced.

To see this we can choose a pricing model and values for that pricing model we need to show the relationship between the market price and CAPM price. Remember that the relationship between the market price and CAPM price is not dependent on the pricing model we choose.

Calculation of two prices of each stock using Forcasted Return and CAPM Return by the use of Constant Dividend Growth Pricing Model. (Assuming Next Year Dividend of both companies (D1) = $2 and Growth Rate of both companies (g) = 5%)

Price of Stock(P0)= D1/(r-g)

Forecasted Return : $1 Discount Store= 12%

Everything $5= 11%

P0 of $ 1 Discount Store = 2/(0.12-0.05) = $28.57

P0 of Everything $5 = 2/ (0.11-0.05)= $33.33

CAPM Return : $1 Discount Store= 13%

Everything $5= 10%

P0 of $ 1 Discount Store = 2/(0.13-0.05) = $25.00

P0 of Everything $5 = 2/ (0.10-0.05)= $40.00

According to CAPM and our Pricing Model i.e. Constant Dividend Growth Pricing Model, Price of $1 Discount Store stock should be $25 but the market price is $28.57 Hence it is overpriced.

According to CAPM and our Pricing Model i.e. Constant Dividend Growth Pricing Model, Price of Everything $5 stock should be $40 but the market price is $33.33 Hence it is underpriced.

Note: Prices of stock will change if we choose different pricing model but the relationship between prices will not change.

Answer 6. Correct Answer is option a. i.e. 15%

According to the CAPM Model, If Beta is 1 then expected return of stock must be equal to the expected return of Market. In the given case, Beta is 1 and Expected Return of Market is 15% so expected rate of return for a stock also 15%.

As Per CAPM: Required Rate of Return = Rf+B(Rm-Rf) Market Risk Premium (MRp)= Return of Market(Rm) - Risk Free Rate (Rf) Calculation of Fair Return of $1 Discount Store if Beta is 1.5 Fair Return of $1 Discount Store as per CAPM Model = 4+1.5*(6) = 13% Calculation of Fair Return of Everything $5 if Beta is 1.0 Fair Return of Everything $5 as per CAPM Model = 4+1.0*(6) = 10% Answer 5. The forecast return of the $1 Discount Store is 12% while Return as per CAPM Model is 13% it clearly shows that the stock of $ 1 Discount Store is overpriced. Similarly, The forecast return of the Everything $5 is 11% while Return as per CAPM Model is 10% it clearly shows that the stock of Everything $5 is underpriced. To see this we can choose a pricing model and values for that pricing model we need to show the relationship between the market price and CAPM price. Remember that the relationship between the market price and CAPM price is not dependent on the pricing model we choose. Calculation of two prices of each stock using Forcasted Return and CAPM Return by the use of Constant Dividend Growth Pricing Model. (Assuming Next Year Dividend of both companies (D1) = $2 and Growth Rate of both companies (g) = 5%) Price of Stock(P0)= D1/(r-g) Forecasted Return : $1 Discount Store= 12% Everything $5= 11% P0 of $ 1 Discount Store = 2/(0.12-0.05) = $28.57 P0 of Everything $5 = 2/ (0.11-0.05)= $33.33 CAPM Return : $1 Discount Store= 13% Everything $5= 10% P0 of $ 1 Discount Store = 2/(0.13-0.05) = $25.00 P0 of Everything $5 = 2/ (0.10-0.05)= $40.00 According to CAPM and our Pricing Model i.e. Constant Dividend Growth Pricing Model, Price of $1 Discount Store stock should be $25 but the market price is $28.57 Hence it is overpriced. According to CAPM and our Pricing Model i.e. Constant Dividend Growth Pricing Model, Price of Everything $5 stock should be $40 but the market price is $33.33 Hence it is underpriced. Note: Prices of stock will change if we choose different pricing model but the relationship between prices will not change. Answer 6. Correct Answer is option a. i.e. 15% According to the CAPM Model, If Beta is 1 then expected return of stock must be equal to the expected return of Market. In the given case, Beta is 1 and Expected Return of Market is 15% so expected rate of return for a stock also 15%.