Question

g A stock just paid a dividend of $1.36. The dividend is expected to grow at 27.58% for three years and then grow at 4.00% thereafter. The required return on the stock is 12.56%. What is the value of the stock?

Answer 1

$26.64

Step-by-step explanation:

Dividend growth rate for years 1 to 3 = 27.58%

Year 1 dividend = current dividend * (1 + growth rate) = 1.36 * 1.2758 = 1.7351

Year 2 dividend = 1.7351 * 1.2758 = 2.2136

Year 3 dividend = 2.2136 * 1.2758 = 2.8241

From year 4 onward, growth rate is constant at 4%. Therefore, using the PV of an annuity formula, the PV (in year 4) of the future dividends will be

`PV=(D(1+g))/(r-g) \\PV=(2.8241(1.04))/(0.1256-0.04) \\`

PV of dividends from year 4 onward = 34.3115.

Therefore, the value of the stock

`V=(D_(1))/((1+r)^(1) ) +...+(D_(4))/((1+r)^(4) )\\V=(1.7351)/((1.1256)^(1) )+(2.2136)/((1.1256)^(2) )+(2.8241)/((1.1256)^(3) )+(34.3115)/((1.1256)^(4) )`

Therefore the value of the stock = $26.64.