Question

A company currently pays a dividend of $1.75 per share (D₀ = $1.75). It is estimated that the company's dividend will grow at a rate of 16% per year for the next 2 years, and then at a constant rate of 7% thereafter. The company's stock has a beta of 1.95, the risk-free rate is 6.5%, and the market risk premium is 4%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Current dividend = D0 = $1.75

Growth rate of dividend for first 2 years = g1 = 16%

Dividend in year 1 = D1 = D0 (1+g1) = 1.75 (1+16%) = 1.75 x 1.16 = $2.03

Dividend in year 2 = D2 = D1(1+g1) = 2.03(1+16%)= 2.03 x 1.16 = 2.3548

Growth rate of dividend after year 2 = g

Dividend in year 3 = D2(1+g) = 2.3548(1+7%) = 2.3548 x 1.07 = 2.5196

Now according to CAPM

Required rate of return of stock = r = Risk free rate + Beta x market risk premium = 6.5% + 1.95 x 4% = 6.5% + 7.8% = 14.30%

Let V2 = Price of stock or terminal value of stock at end of year 2

Using constant growth rate model

V2 = D3 / (r - g) = 2.5196 / (14.30% - 7%) = 2.5196 / 7.30% = $34.5150

Now

Current price of stock = Present value of dividend for year 1 to year 2 + Present value of Terminal value at end of year 2

Current price of stock = D1 / (1+r) + D2(1+r)² + V2 / (1+r)² = 2.03 / (1+14.30%) + 2.3548 / (1+14.30%)² + 34.5150 / (1+14%)² = 1.7760 + 1.8024 + 26.4189 = 29.9973 = 30.00 (rounded to two decimal places)

Current price of stock = $30.00