Question

Megatrends stock will generate earnings of $2 per share this year. The discount rate for the stock is 10%, and the rate of return on reinvested earnings also is 10%. 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%; (ii) 20%; (iii) 40%. (Do not round intermediate calculations. Enter the growth rates as a whole percent.) b. Redo part (a) now assuming that the rate of return on reinvested earnings is 15%. What is the present value of growth opportunities (PVGO) for each reinvestment rate

Answer 1

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