Question

Example 5: Nonconstant Growth

Suppose a stock will pay the following dividends and has the following required return:

Year 1:	$               1.00
Year 2:	$               2.00
Year 3:	$               2.50
Required return:	10.0%

After the third year, the dividends will grow at:

5.0%

What is the price of the stock? First, we need to find the price of the stock when it begins a constant growth rate, which is in Year 3. The price of the stock in Year 3 will be:

Price in Year 3:

The price today is the present value of the future dividends, plus the present value of the future price, so:

Price today:

Please help answer the question above: "Price in Year 3" and "Price Today"

Thank you

Answer 1

D1 = $1.00
D2 = $2.00
D3 = $2.50

Growth Rate, g = 5.00%
Required Return, r = 10.00%

D4 = D3 * (1 + g)
D4 = $2.50 * 1.05
D4 = $2.625

Stock Price in Year 3, P3 = D4 / (r - g)
Stock Price in Year 3, P3 = $2.625 / (0.10 - 0.05)
Stock Price in Year 3, P3 = $52.50

Current Stock Price = $1.00/1.10 + $2.00/1.10^2 + $2.50/1.10^3 + $52.50/1.10^3
Current Stock Price = $43.88

So, current stock price is $43.88