Question

Set-up for all parts: 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.

a) Suppose the company decided to payout 90% of its earnings as dividends, what would be the fundamental value of the stock today? (t=0)

Answer 1

a) The fundamental value of stock today is :

The cost of equity is :

Re = Rf + beta * (Rm - Rf)

= 5 + 1.3* 5

= 11.5%

E1 = 0

E2 = $10

E3= $10.8

So, the dividends paid is :

D1 = 0

D2= $9

D3= $9.72 ($9 *1.08)

P2 = D3/ Re - g

= $9.72  / 0.115 - 0.08

= $277.7143

So, the current value of stock is : ($9 + $277.7143)/1.115^2

= $230.62 ( rounded off to two decimal places)