You are considering investing in Apple stock its beta coeffi

You are considering investing in Apple stock. its beta coefficient, which is equal to 2. The risk free rate is currently 2% and the return on the S&P 500 index (which you use as a proxy for the market portfolio) is 15%. You estimate that Apple\'s dividends are expected to grow at 5% per year.

1) What is the return on equity for Apple?

2) If the standard deviation of returns on Apple is 40% per annum and the standard deviation of the S&P 500 is 20%, what is the correlation coefficient between returns on Apple and returns on S&P 500 index?

3) What price should you pay for this stock, if it just paid $2 per share dividend?

Solution

1) Required return on equity using CAPM can be computed as -

Return on equity = Risk free rate + beta x (market return - risk free rate) = 2% + 2 x (15% - 2%) = 28%

2) Beta_Apple = (Standard deviation_Apple x Correlation) / Standard deviation_market

or, 2 = (40% x Correlation) / 20%

or, Correlation = 1

3) Price as per constant dividend growth model can be computed as -

P0 = [ D0 x (1 + g) ] / (Ke - g)

where, P0 = price of stock today, D0 = last dividend paid, g = constant growth rate, Ke = return on equity

P0 = [ $2 x (1 + 5%) ] / (28% - 5%) = $9.1304348 or $9.13