Question

If the stock just paid a dividend of $5 (D₀ = $5), and has a required rate of return (k_s) of 15%, and a current price of $70, find the estimated constant growth rate using the Gordon constant growth rate model.

Answer 1

We will use the formula - Price of stock = D1 / (Re - g)

Where D1 is the dividend for year 1

Re is required rate of return

g is growth rate

Note - In the question it states that stock has just paid a dividend of $5. This is D0.

D1 = D0 (1+g)

= 5 (1 + g)

Price of stock = $70

Required rate of return = 15%

Calculation of growth rate

70 = 5 (1 + g) / (0.15 - g)

10.5 - 70g = 5 + 5g

10.5 - 5 = 5g + 70g

5.5 = 75g

g = 5.5 / 75

= 0.0733

or 7.33 %

The estimated growth rate is 7.33%

To cross check lets put the growth rate into the original formula and arrive at price $70

Price of stock = D1 / (Re - g)

D1= 5 * ( 1 + 0.0733)

= 5 * 1.0733

= 5.3665

or 5.37

Price of stock = 5.37 / (0.15 - 0.0733)

= 5.37 / 0.0767

= 70