Capital Asset Pricing Model (CAPM) A model based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification. r i =r RF + (r M – r RF ) b i

Constant Growth (Gordon) Model Used to find the value of a constant growth stock. r s = D 1 /P 0 + g P 0 = D 1 / (r s – g)

McDonald Medical Company’s stock has a beta of 1.20, the risk-free rate is 4.50%, and the market risk premium is 5%. What is McDonald Medical’s required return? (Use CAPM)

Given: Beta = 1.20 R RF = 4.5% R RP =(R M -R RF )= 5% Formula: R McDonald Medical= R RF + beta(R M -R RF ) R McDonald Medical = ?

R McDonald = 4.50% (5.00%) = 10.50%

McDonald Medical’s stock has a beta of 1.40, and its required return is 13%. Clover Dairy’s stock has a beta of If the risk-free rate is 4%, what is the required rate of return on Clover’s stock? (Hint: Find the market risk premium first)

Given: McDonald Medical beta= 1.4 R McDonald Medical = 13% Clover beta= 0.8 R RF = 4% First, calculate the market risk premium by using the McDonald Medical information: M McDonald Medical =R RF + beta(R M – R RF ) 13%=4%+1.4(R M -R RP ) 6.43%=(R M -R RP ) Now, calculate the required return for Clover: R Clover =R RF + beta(R M -R RP )= ?

R Clover =4.0% +.80(6.43%)= 9.14%

A stock is expected to pay a dividend of $1.00 at the end of the year. The required rate of return is rs= 11%, and the expected constant growth rate is 4%. What is the current stock price?

Given: Dividend=$1.00 r s =.11 g=.04 Calculate: P 0 =D 1 /(r s -g) ?

 P 0 = $1 / ( )  P 0 = $14.29

A stock just paid a dividend of $1. The required rate of return is rs = 11%, and the constant growth rate is 5%. What is the current stock price?

 P 0 = D 1 / (r s – g)  First, we need to calculate the dividend next year.  $1 * 1.05 = $1.05 Then use P 0 = D 1 / (r s – g) for current price. ?

 P 0 = $1.05 / ( )  P 0 = $17.50

Suppose you hold a diversified portfolio consisting of $10,000 invested equally in each of 10 different common stocks. The portfolio’s beta is Now suppose you decided to sell one of your stocks that has a beta of 1.00 an to use the proceeds to buy a replacement stock with a beta of What would the portfolio’s new beta be? * Write down what is given

Calculate the beta of the portfolio’s nine stocks that we are keeping. These nine represent 90% of the total value of the portfolio and 90% of the beta:.9x +.1 (1.00) = x= 1.02 X= If we add one stock with a beta of 1.75, we get: ?

.9(1.333) +.1(1.75)= =1.195

A mutual fund manager has a $20 million portfolio with a beta of The risk-free rate is 4.50% and the market risk premium is 5.50%. The manager expects to receive an additional $5.0 million which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund’s required return to be 13%. What must the average beta of the new stocks added to the portfolio be to achieve the desired required rate of return? *Write down what is given.

First, figure out what the beta of the new portfolio will be: R new =R RF +Beta(R M -R RF) 13%=4.50% +Beta(5.50%) 8.50%=Beta(5.50%) =Beta of the NEW $25million portfolio Cont….

Next, we can calculate the beta of the new stocks (New Beta). We know that the size of the portfolio will now be $25 million and the $20 million has a beta of 1.50: ($20M/$25M) ($5M/$25M)New Beta= (New Beta)= (New Beta)=.3455 New Beta= 1.73

McDonald Medical is expected to pay a dividend of $1 per share at the end of the year and that dividend is expected to grow at a constant rate of 5% per year in the future. The company’s beta is 1.2, the market risk premium is 5%, and the risk-free rate is 3%. What is the company’s current stock price? * Write down what is given.

First, we need to calculate the required return on the stock r s. We can use the CAPM: R S =R RF + beta(R M -R RF ) R S =3% + 1.2(5%) R S = 9% Now we can use this in the CGM formula to calculate the current price: P 0 =D 1 /(r s -g)

P 0 =$1/( ) P 0 = $25.00