Question

Company ABC currently pays $5 dividend. Dividends have been growing at a 3% annual rate and are expected to continue growing with same rate for the foreseeable future. What is the current value of this stock if the required rate of return is 18%?

Answer 1

The formula for the present value of a stock with constant growth is the estimated dividends to be paid divided by the difference between the required rate of return and the growth rate.

The present value of a stock with constant growth is one of the formulas used in the dividend discount model, specifically relating to stocks that the theory assumes will grow perpetually. The dividend discount model is one method used for valuing stocks based on the present value of future cash flows, or earnings.

HERE IN THE PROBLEM IS GIVEN UNDER A CONSTANT GROWTH MODEL

The Gordon Growth Model (GGM) is a variation of the standard discount model. The key difference is that the GGM model assumes the dividends will grow at a constant rate till perpetuity. here under the problem its given that the growth rate is constant forever. so that we can find that the present value of stock could be find out from the constant growth model formula, the formula is:

V₀ = D₁/(k_e – g_c)

V₀= PRESENT VALUE OF STOCK

D₁=EXPECTED DIVIDENT

k_e= RATE OF RETURN

g_c= GROWTH RATE

CURRENT YEAR DIVIDEND = $ 5

If the current year’s dividends are D0, and the dividend growth rate is g_c, the next year’s dividend D₁ will be D₀ = (1+g_c). D₂ will be D₀(1+g_c)^2 and so on.

GROWTH RATE = 3%

RATE OF RETURN =18%

D₁=5(1+0.03) = $ 5.15

V = $5.15 /(0.18 –.03)

= 5.15/.15 = 34.33