Question

Assume a common stock currently just paid a dividend of $5 per share. The stock’s current price is $50 per share. It is estimated that the dividend will grow at a constant rate of 6% per year forever. What is the cost of equity?

Answer 1

Solution:

As per the Gordon growth Model, price of a share is calculated using the following formula:

P₀ = D₀ * [ ( 1 + g ) ] / ( k_e – g )

Where

P₀ = Current Price of the share;      D₀ = Dividend paid in Year 0 i.e., Recent dividend paid ;     

g = growth rate ;        k_e = Cost of equity    ;

As per the information given in the question we have ;

D₀ = $ 5 ;       g = 6 % = 0.06 ;        P₀ = $ 50 ;     k_e = To find   ;

Applying the above values in the formula we have

$ 50 = [ 5 * ( 1 + 0.06 ) ] / ( k_e – 0.06 )

$ 50 = ( 5 * 1.06 ) / ( k_e – 0.06 )

$ 50 = $ 5.30 / ( k_e – 0.06 )

$ 50 * ( k_e – 0.06 ) = $ 5.30

( k_e – 0.06 ) = $ 5.30 / $ 50

( k_e – 0.06 ) = 0.1060

k_e = 0.06 + 0.1060 = 0.1660

k_e = 16.60 %

The cost of equity = 16.60 %