Answer:
a. Find both the growth rate of dividends and the price of the stock if the company reinvests the following fraction of its earnings in the firm:
(i) 0% ⇒ g = 0, P₀ = $2/10% = $20
(ii) 20% ⇒ g = 0.2 x 10% = 2%, P₀ = $1.632/8% = $20.40
(iii) 40% ⇒ g = 0.4 x 10% = 4%, P₀ = $1.248/6% = $20.80
b. Redo part (a) now assuming that the rate of return on reinvested earnings is 15%.
(i) 0% ⇒ g = 0, P₀ = $2/10% = $20
(ii) 20% ⇒ g = 0.2 x 15% = 3%, P₀ = $1.648/7% = $23.54
(iii) 40% ⇒ g = 0.4 x 15% = 6%, P₀ = $1.272/4% = $31.80
What is the present value of growth opportunities (PVGO) for each reinvestment rate
ROE = 10%, reinvestment rates:
(i) 0%: PVGO = $20 - $2/10% = $0
(ii) 20%: PVGO = $20.40 - $2/10% = $0.40
(iii) 40%: PVGO = $20.80 - $2/10% = $0.80
ROE = 15%, reinvestment rates:
(i) 0%: PVGO = $20 - $2/10% = $0
(ii) 20%: PVGO = $23.54 - $2/10% = $3.54
(iii) 40%: PVGO = $31.80 - $2/10% = $11.80
Explanation:
sustainable growth rate = g = retention rate x ROE
PVGO = stock price - earnings/Re
