If expected dividends grow at 7% and the appropriate discount rate is 9%, what is the value of a stock with an expected dividend one year from now of $1.00?

The value of a stock whose dividends are expected to grow at a constant percentage is calculated using the constant growth model of DDM or dividend discount model. The DDM values the stock based on the present value of the expected future dividends from the stock. The formula for price of the stock today under this model is,

P0 = D1 / (r - g)

Where,

D1 is the dividend expected for the next period
r is the required rate of return or discount rate
g is the growth rate in dividends

To calculate the price today or P0, we use D1. Thus, as the constant growth rate will apply from Year 2, we will first calculate the price of the stock at Year 1 or P1 using the D2. Then we will discount this P1 back to P0 by dividing it by (1+r).

P1 = 1 * (1+0.07) / (0.09 - 0.07)

P1 = $53.5

Price of the stock today is,

P0 = P1 / (1+r)

P0 = 53.5 / (1+0.09)

P0 = $49.0825 rounded off to $49.08

andromache andromache · Answer 2 · 2022-01-04T11:26:26+01:00

andromache andromache

04-01-2022

The value of the stock should be $50.

The calculation is as follows;

The value of the stock is

= Expected dividend ÷ (required rate of return - growth rate)

= $1 ÷ (9% - 7%)

= $50

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