Question

. Mike works for a prominent technology company. His company just paid a $1.50 dividend per share. The required return for his company’s stock is 12%.

A. If the dividend that Mike’s company just paid is a perpetual dividend, what is the price of the stock today? (Hint: Zero-growth Dividend Stock)

B.(QUESTION 22) Mike’s company has decided to increase the company’s dividend by 6% forever, on an annual basis starting with the next dividend. If this is the case, what will the value of the dividend be in year 8? (Hint: D0=$1.50; g=6%)

C.Given the growth information from problem 22 and the required rate of return of 12%, what is the price of the stock today? (Hint: Constant Dividend Growth Stock; D0=$1.50)

D. Given the information from problem 22 and the required rate of return of 12%, what is the stock price at year 13? (Hint: D0=$1.50; g=6%)

E.Consider the following information. Suppose Mike’s company is expected to increase dividends by 12% in one year, and by 8% in two years. After that, his company’s dividends will increase at a rate of 6% indefinitely. If the last dividend was $1.50 and the required rate of return in 12%, what is the current price of the stock.

Answer 1

a) Price = D / r = 1.50 / 12% = $12.50

b) Dividend in year 8, D8 = D0 x (1 + g)^8 = 1.50 x (1 + 6%)^8 = $2.39

c) Price today, P0 = D0 x (1 + g) / (r - g) = 1.50 x (1 + 6%) / (12% - 6%) = $26.50

d) Price in year 13, P13 = D14 / (r - g) = 1.50 x (1 + 6%)^14 / (12% - 6%) = $56.52

e) Price today, P0 = D1 / (1 + r) + D2 / (1 + r)^2 + D3 / (r - g) / (1 + r)^2

= 1.50 x (1 + 12%) / 1.12 + 1.50 x (1 + 12%) x (1 + 8%) / 1.12^2 + 1.50 x 1.12 x 1.08 x 1.06 / (12% - 6%) / 1.12^2

= $28.50