Question

Since it started Business 10 years ago, Standford and sons company paid a constant dividend of $1.60 per share to its common stockholders. It paid this dividend yesterday. Next year and year thereafter., the company plans to increase the dividends at a constant rate equal to 4.5% per year. If investors require a 12% rate of return to purchase the company's common stock: A. what is the market value of the stock today? B. what is the dividend yield this year (year 1)? what is the capital gains yield this year (year 1)? D. what is the total yield this year (year 1)?

Answer 1

Answer A.

Last Dividend, D0 = $1.60
Growth Rate, g = 4.50%
Required Return, rs = 12%

D1 = D0 * (1 + g)
D1 = $1.60 * 1.045
D1 = $1.672

Current Price, P0 = D1 / (rs - g)
Current Price, P0 = $1.672 / (0.12 - 0.045)
Current Price, P0 = $1.672 / 0.075
Current Price, P0 = $22.29

Answer B.

Dividend Yield = D1 / P0
Dividend Yield = $1.672 / $22.29
Dividend Yield = 0.0750 or 7.50%

Answer C.

D2 = D1 * (1 + g)
D2 = $1.672 * 1.045
D2 = $1.747

P1 = D2 / (rs - g)
P1 = $1.747 / (0.12 - 0.045)
P1 = $1.747 / 0.075
P1 = $23.29

Capital Gain Yield = (P1 - P0) / P0
Capital Gain Yield = ($23.29 - $22.29) / $22.29
Capital Gain Yield = 0.0450 or 4.50%

Answer D.

Total Yield = Dividend Yield + Capital Gain Yield
Total Yield = 7.50% + 4.50%
Total Yield = 12.00%