Question

Global Logistics just announced it is increasing its annual dividend to $1.68 next year and establishing a policy whereby the dividend will increase by 3.25 percent annually thereafter. How much will one share of this stock be worth ten years from now if the required rate of return is 13.5 percent?

Answer 1

As per Gordon model, share price is given by:

Share price = D1 / k -g

where, D1 is next years' dividend, k is the required rate of return = 13.5% and g is the growth rate = 3.25%

For calculating the share price 10 from now, we will amend the formula to below:

Share price (after 10 years) = D11 / k -g

where, D11 is the dividend after 11 years

First we will calculate dividend after 11 years. Dividend will grow at the rate of 3.25% annually. So we will calculate the D11 by future value formula as per below:

FV = P * (1 + r)¹⁰

where, FV = Future value, which is the dividend after 11 years,  P is next years' dividend = $1.68, r is the rate of interest = 3.25% and n is 10 years

Now, putting these values in the above formula, we get,

FV = $1.68 * (1 + 3.25%)¹⁰

FV = $1.68 * (1 + 0.0325)¹⁰

FV = $1.68 * (1.0325)¹⁰

FV = $1.68 * 1.3768943

FV = 2.31

So, the value of D11 is $2.31

Now, we will calculate the share price after 10 years by putting the values in the below formula:

Share price (after 10 years) = D11 / k -g

Share price (after 10 years) = $2.31 / 13.5% - 3.25%

Share price (after 10 years) = $2.31 / 10.25%

Share price (after 10 years) = $22.54