Question

The following information has been provided on a popular Hitech stock:

Market risk premium is given as 9% and rate of return on Treasury bills is 3%. The stock has a beta of 1.2. Furthermore, the stock recently commenced dividend payment and paid a dividend of $3.40 per stock. You expect the dividend to grow rapidly for the first three years at 20%, 15% and 10% and, thereafter, smoothen at 8%. What is the maximum you should pay for this stock?

SHOW ALL WORK

Answer 1

Using CAPM method, required rate of return = risk free rate + beta ( market risk premium )

Using CAPM method, required rate of return = 0.03 + 1.2 ( 0.09)

required rate of return = 0.138 or 13.8%

Dividend at year 0 = 3.4

Dividend at year 1 = 3.4 * 1.2 = $4.08

Dividend at year 2 = 4.08 * 1.15 = 4.692

Dividend at year 3 = 4.692 * 1.1 = 5.1612

The dividend paid at the end of year 3 will increase constantly at 8%. Therefore we can find the price at year 2 by applying constant growth model.

Present value at year 2 = D1 / (K - G)

Prsent value at year 2 = 5.1612 / (0.138 - 0.08)

Present value at year 2 = 5.1612 / 88.9862

Present value today = 88.9862 / ( 1 + 0.138)²

Present value today = 68.712878

Present value of dividend paid in year 2 = 4.692 / ( 1 + 0.138)²

Present value of dividend paid in year 2 = 3.623043

Present value of dividend paid in year 1 = 4.08 /  ( 1 + 0.138)¹

Present value of dividend paid in year 1 = 3.585237

Price of stock = 3.585237 + 3.623043 + 68.712878 = $75.92