Question #50102

Explain the valuation formula for a constant growth stock.Explain how the formula for a zero growth stock is related to that for a constant growth stock.

Expert's answer

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:

P0 = (D0 ( 1+g))/(r-g)= D1/(r-g)

where

P0 = the stock price,

D0 = the current dividend,

D1 = the next dividend,

g = the dividends growth rate

r = the required return on the stock

The formula for the present value of a stock with zero growth is

dividends per period divided by the required return per period,

because If there is no growth of dividends g will be equal 0:

g=0

P0 = (D0 ( 1+0))/(r-0)= D/r

the estimated dividends to be paid divided by the difference between

the required rate of return and the growth rate:

P0 = (D0 ( 1+g))/(r-g)= D1/(r-g)

where

P0 = the stock price,

D0 = the current dividend,

D1 = the next dividend,

g = the dividends growth rate

r = the required return on the stock

The formula for the present value of a stock with zero growth is

dividends per period divided by the required return per period,

because If there is no growth of dividends g will be equal 0:

g=0

P0 = (D0 ( 1+0))/(r-0)= D/r

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