Question

In March of 2018, Domestic Paper stock sold for $73 per share. Security analysts were forecasting a long-term earnings growth rate of 8.5%. The company’s most recent annual dividend was $0.68 per share.

A. If dividends are expected to grow along with earnings at g = 8.5% per year in perpetuity, what rate of return (r_E) were investors expecting?

B. Analysts just revised their previous estimates and now expect Domestic Paper will earn 12% on book their equity (ROE), which they believe is a good proxy for the return on their retained earnings. They expect Domestic Paper will retain 50% of its earnings going forward. Based on these new forecasts, what rate of return (r_E) were investors expecting?

Notes: If possible, please provide the formulas and steps. Our class doesn't use a financial calculator either - only using time value of money math. Thank you!

Answer 1

a.

Current price of stock (P0) = 73

D0 = 0.68

growth rate (g) = 8.5%

D1 = D0*(1+g)

=0.68*(1+8.5%) =0.7378

Investor required return formula = (D1/P0)+g

=(0.7378/73)+8.5%

=0.09510684932 or 9.51%

So investor are expecting or required rate of return is 9.51%

b.

new return on equity = 12%

retention ratio = 50%

new growth rate (g) = return on equity * retention ratio

=12%*50%

=6%

new D1 = D0*(1+g)

=0.68*(1+6%)= 0.7208

Investor required return formula = (D1/P0)+g

=(0.7208/73)+6%

=0.0698739726 or 6.99%

So investor are expecting or required rate of return is 6.99%