Question

The current market price of the Microsoft stock is $97 and the company has just paid a 42 cents per share quarterly dividend. The Microsoft’s growth rate of dividends is 10% per year.

a. According to the constant dividend growth model, what is the annualized expected return on Microsoft?

You obtained additional information about Microsoft stock. You learned that the annual standard deviation of returns on Microsoft stock is approximately 33%. The correlation coefficient between returns on Microsoft stock and returns on the S&P 500 index is 0.8. You also estimated that the expected return on the S&P 500 index (the proxy for the market portfolio) is 10% per annum and its standard deviation is 16% per annum. The average return on 3-months Treasury bills (the proxy for the risk free rate) is 3% per annum. Use this additional information to answer the following questions:

b. According to CAPM, what is the beta of Microsoft?

c. According to CAPM, what is the expected annual return on the Microsoft stock?

Answer 1

a.

Annualized expected return of Microsoft using constant dividend growth model, is calculated below:

annualized expected return = [(Expected Dividend × 4) / Current Stock price] + Growth rate

= [($0.42 × 4) / $97] + 10%

= ($1.68 / $97) + 10%

= 1.73% + 10%

= 11.73%

annualized expected return is 11.73%.

b.

Beta of Microsoft is calculated below using following formula:

Beta = Correlation × (Standard deviation of Stock / Standard deviation of Market)

= 0.80 × (33% / 16%)

= 0.80 × 2.0625

= 1.65

Beta of Microsoft is 1.65.

c.

Expected annual return on the Microsoft stock using CAPM model is calculated in excel and screen shot provided below:

Expected annual return = Risk free rate + (Market return - Risk free rate) × Beta

= 3% + (10% - 3%) × 1.65

= 3% + (7% × 1.65)

= 3% + 11.55%

= 14.55%.

Expected annual return on the Microsoft stock using CAPM model is 14.55%.