Question

Solve the problem. Show your work and equations! Please do not show screenshots of Excel as your work shown.

4. The company yesterday paid their annual dividend of $2.00 and the expected price in 2 years is $100. The dividend payment is expected to grow at 7%. i) What is the stock's required return? ii) what is the price today? Use annual compounding

Answer 1

As per Gordon model, share price is given by:

Share price (P₀) = D1 / k -g

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

(i) For calculating the required rate of return, we will amend the above formula, as per be below:

Share price 2 from now, we will amend the formula to below:

Share price (after 2 years) = D3 / k -g

where, D3 is the dividend after 3 years

First we will calculate dividend after 3 years. Dividend will grow at the rate of 7% annually. So we will calculate the D3 by future value formula as per below:

FV = P * (1 + r)¹⁰

where, FV = Future value, which is the dividend after 3 years,  P is current years' dividend = $2, r is the rate of interest = 7% and n is 3 years

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

FV = $2 * (1 + 7%)³

FV = $2 * (1 + 0.07)³

FV = $2 * (1.07)³

FV = $2 * 1.225043

FV = $2.45

So, the value of D3 is $2.45

Now, we will calculate the required rate of return by putting the values in the below formula:

Share price (after 2 years) = D3 / k -g

$100 = $2.45 / k - 7%

$100 * (k - 0.07) = $2.45

k - 0.07 = $2.45 / $100

k - 0.07 = 0.0245

k = 0.0245 + 0.07

k = 0.0945 or 9.45%

(ii) Calculation of share price today:

Share price (P₀) = D1 / k -g

First we will calculate the value of D1 by the future value formula:

FV = PV * (1 + r)ⁿ

FV = $2 * (1 + 7%)¹

FV = $2 * 1.07 = $2.14

So, D1 = $2.14

Now, share price today is:

Share price = D1 / k - g

where, D1 = $2.14, k = 9.45% (as calculated in point (i) , g = 7%

Share price = $2.14 / 9.45% - 7%

Share price = $2.14 / 2.45%

Share price = $87.35