Question

ABC company's ordinary shares are expected to pay $3 per share in dividends for 6 years and after which the dividends are expected to grow at 2% annually forever. Company ABC's shares have a beta of 1.75. The long-term return of ASX200 is 9% and the market risk premium is 5%.

(a) What is the expected return of ABC's shares according to the CAPM?

(b) What is the implied price per share?

Answer 1

(a) Expected rate of return as per CAPM =

Expected rate of return = Risk free Rate + Beta * (Market return - risk free rate)

Market return - Risk free rate equals market risk premium

Here, market risk premium = 5%

Thus, Risk free rate = Market return - market risk premium = 9% - 5% = 4%

(The ASX 200 index represents the market-capitalization weighted and float-adjusted stock market index of stocks listed on the Australian Securities Exchange. Thus, te 9% ASX 200 index represent the market return).

Now applying the equation:

Expected rate of return = Risk free Rate + Beta * (Market return - risk free rate)

= 4% + 1.75 * (9%-4%) = 4% + 8.75% = 12.75%

Expected rate of return = 12.75%

b. Implied price per share:

Implied price per share = Present value of all future dividends discounted at expected rate of return

= (Dividend per year * Cumulative discount factor for 6 years at 12.75%) + ((Dividend * (1+growth rate)/(rate of return of 12.75%-growth rate))* Discount factor of 6th year

= 3*((1-(1+12.75%)^-6))/12.75% + (3*((1+2%)/(12.75%-2%)))*1/(1+12.76%)^6

= $3*4.02554+($3*948.8372%)*0.4867 = $12.077+$13.855 = $25.932

Implied price per share = $25.93