Question

Suppose that the rate of return on the market portfolio is 10% and the risk-free rate is 5%. Consider a stock with beta is 1.3. The firm is expected to have no earnings in the first year (E1 = 0), and then $10 earnings-per-share in the second year (E2 = 10). After that, earnings are expected to grow at a constant annual rate of 8%. The retention ratio is 80% in all periods.

If the market P/E is 8, do your calculations suggest that stock is under- or over- priced?

Answer 1

Step 1: Calculation of cost of equity using Capital Asset Pricing Model

Cost of Equity Ke = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 5%

b – Beta = 1.3

Rm – Expected return on market portfolio = 10%

Cost of Equity Ke = 5+1.3*(10-5)

= 5+6.5

= 11.50%

Step 2: Calculation of share price using Gordon Growth Model

P1 = D2 / (Ke – g)

Where,

P1 - Market price at the end of year 1 =?

D2 - Expected dividend in year = E2*(1-retention ratio) = 10*.2 = 2

Ke – Cost of equity = 11.5%

G – Growth rate in dividend = 8%

P1 = 2/(.115-.08)

= 2/.035

P 1 = 57.14

Fair market price P0 = P1/1.115^1

= 57.14/1.115

= $51.25

Actual market price using PE ratio = P2 = 10*8 = 80

P0 = 80/1.115^2

= 64.35

​​​​​​​STock is overvalued.