Question

You are contemplating an investment in the stock of Apple.You know that the price of apple stock is estimated using the constant-growth dividend discount model and its required return (cost of equity) is estimated using the CAPM.  

Yesterday, apple paid a dividend of $3.00 per share. The dividend is expected to grow at an annual rate of 4% throughout the foreseeable future. Apple’s trailing P/E ratio is 18, its debt/equity ratio is 1.25, and its bonds are rated BB.  The yield to maturity (cost of debt) for the bonds of Apple is 8% (which represents a 500 basis point spread over the risk-free rate).   You also know that the expected market return (S&P 500) is 11%, with a standard deviation of 14%. The correlation coefficient between Apple and the market (S&P 500) is .81, the correlation between Apple and the risk-free rate is .49, and Apple's stock has a standard deviation of 18%.  

Calculate the price per share of the Apple stock.

Answer 1

Under Constant-growth dividend discount model price of a stock can be calculated with following equation -

where,

D = last dividend

g = constant growth rate

Ke = Required rate of return of equity

In above question, D=$3 , g=4% provided but we need to calculate Required rate of return (Ke) to find out per share price of Apple stock.

Under CAPM, we can find required rate of return with following equation -

Where,

rf = risk free return

rm = Market return

B = Beta

Provided,

Market Return (rm) = 11%

Bond's YTM = 8% which is 5% over the risk free return , thus -

Risk free return (rf) = 8%-5% = 3%

Beta of Apple stock is not provided in question, thus we need to calculate beta first. we can calculate Beta with following equation -

Where,

M = Market

A = Apple

= Standard deviation

Provided,

Correlation(M,A) = 0.81

Standard deviation of Market = 14%

Standard deviation of Apple = 18%

Putting the values to calculate Beta -

Now, Calculate Required rate of return of equity(Ke), using above values

Thus, Required rate of return of equity (cost of equity) = 11.33%

Now, Using the above value, calculate the per share price of Apple stock.

Price of a Apple Stock = $42.46

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.