Question

A company is expecting a period of intense growth and has decided to retain more of their earnings to help finance that growth. As a result, the company is going to reduce the annual dividend by 12.75% a year for the next three years. After those three years, the company will maintain a constant dividend of $0.65 a share. Recently, the company paid $1.45 as the annual dividend per share. What is the market value of this stock if the required rate of return is 9.75%?

Answer 1

Given about a company,

Most recent dividend D0 = $1.45

dividend are expected to decrease at the rate of 12.75% a year for next 3 years

So, D1 = 1.45*(1-0.1275) = $1.2651

D2 = 1.2651*(1-0.1275) = $1.1038

D3 = 1.1038*(1-0.1275) = $0.9631

thereafter, company will maintain constant dividend of D = $0.65

required rate of return r = 9.75%

So, Value of stock at year 3 using perpetual model is

P3 = D/r = 0.65/0.0975 = $6.6667

So, present value of stock is sum of PV of future dividends and P3 discounted at r

=> P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + P3/(1+r)^3

=> P0 = 1.2651/1.0975 + 1.1038/1.0975^2 + 0.9631/1.0975^3 + 6.6667/1.0975^3 = $7.84

So, current market value of this stock is $7.84