Question

Assume Highline Company has just paid an annual dividend of

$0.97.

Analysts are predicting an

11.5%

per year growth rate in earnings over the next five years. After​ then, Highline's earnings are expected to grow at the current industry average of

5.6%

per year. If​ Highline's equity cost of capital is

8.8%

per year and its dividend payout ratio remains​ constant, for what price does the​ dividend-discount model predict Highline stock should​ sell?

Answer 1

Given the following information,

Dividend just paid = D0 = 0.97

short term growth rate = gs = 11.5% = 0.115

long term growth rate gL = 5.6% = 0.056

cost of capital = r = 8.8% = 0.088

We know that value of the stock can be calculated using the following formula,

P = D0(1+gs)/(1+r)^1 + D0(1+gs)^2/(1+r)^2 + D0(1+gs)^3/(1+r)^3 + D0(1+gs)^4/(1+r)^4 + D0(1+gs)^5/(1+r)^5 + D0(1+gs)^5/(1+r)^5 * (1+gL)/ (r-gL)

Where

D0(1+gs)/(1+r)^1 = 0.97(1+0.115)/(1+0.088)^1 = 0.97(1.115)/(1.088) = 0.9941

D0(1+gs)^2/(1+r)^2 = 0.97(1+0.115)^2/(1+0.088)^2 = 0.97*1.2432/1.1837 = 1.0187

D0(1+gs)^3/(1+r)^3 = 0.97(1+0.115)^3/(1+0.088)^3 = 0.97*1.3862/1.2879 = 1.0440

D0(1+gs)^4/(1+r)^4 = 0.97(1+0.115)^4/(1+0.088)^4 = 0.97*1.5456/1.4012 = 1.0699

D0(1+gs)^5/(1+r)^5 = 0.97(1+0.115)^5/(1+0.088)^5 = 0.97*1.7234/1.5246 = 1.0965

D0(1+gs)^5/(1+r)^5 * (1+gL)/ (r-gL) = 1.0965* (1+0.056)/ (0.088-0.056) = 1.0965*1.056/ 0.032 = 36.1839

Substituting these values in the above equation, we get

P = 0.9941 + 1.0187 + 1.0440 + 1.0699 + 1.0965 + 36.1839

P = 41.41

Therefore, price of the stock is $41.41