Question

Fin Corp currently pays out 100% of its earnings to shareholders as dividends. It expects to yield $4 earnings per share forever starting next year (exactly one year from now). The market risk premium is 8%, and the risk-free rate is 4%. Fin Corp’s stock beta β is 1.

(a) What is the required rate of return for Fin Corp stocks?

(b) Calculate its stock’s current intrinsic value if the firm keeps its current payout policy forever.

(c)   If Fin Corp just discovers a growth opportunity, with ROE=10%. The management decides to pay out only 40% of its earnings starting from the next year’s dividend and forever after, so that it can reinvest the rest in the growth opportunity. Suppose the growth opportunity lasts forever, what is the present value of its growth opportunity (PVGO)?

(d) What is the ROE of the growth opportunity such that PVGO of Fin Corp is exactly zero, while everything else remain the same as in Question (c)?

Answer 1

1.
=risk free rate+beta*(market return-risk free rate)
=risk free rate+beta*market risk premium
=4%+1*8%
=12.0000%

2.
=Expected earnings*payout rate/(required return-RoE*(1-payout rate))-Expected earnings/required return
=4*40%/(12%-10%*(1-40%))-33.33
=-6.66

3.
=(12%-4*40%/33.33333)/(1-40%)
=12.0000%