Question

Jacobson, Inc. paid $3.00 in dividends to common stockholders last year. Dividends are expected to grow at sustainable growth rate for an indefinite number of years. Jacobson has a return on equity of 30% with dividend payout ratio of 60%.

1. If Jacobson’s stock current market price is $33.60, what is the stock’s expected rate of return?

2. If your required rate of return is 18 percent, what is the value of the stock for you?

Answer 1

a. The rate of return is computed as follows:

= [ Dividend paid x (1 + growth rate) ] / current price ] + growth rate

growth rate is computed as follows:

= (ROE x b) / (1 - ROE x b)

b is computed as follows:

= 1 - dividend payout ratio

= 1 - 0.60

= 0.40

So, the growth rate will be as follows:

= (0.30 x 0.40) / (1 - 0.30 x 40)

= 0.12 / 0.88

= 13.63636363%

So, the expected rate will be as follows:

= [ ($ 3 x 1.136363636) / $ 33.60 ] + 13.63636363%

= 10.1461039% + 13.63636363%

= 23.78246753% or 23.78%

b. The price is computed as follows:

= [ Dividend just paid x (1 + growth rate) ] / (rate of return - growth rate)

= [ $ 3 x 1.1363636363 ] / (23.78246753% - 13.63636363%)

= $ 3.409090908 / 10.1461039%

= $ 33.60