Final answer:
To calculate the intrinsic value of stock XYZ with varying growth rates and a required return of 8%, we use the Dividend Discount Model for the initial years and the Gordon Growth Model for the perpetual growth rate. The dividends for the first two years are found and discounted to present value, and the Gordon Growth Model is used to determine the present value of the perpetual dividends. Adding up these present values gives us an intrinsic value of $39.42 for stock XYZ.
Step-by-step explanation:
To calculate the intrinsic value of stock XYZ that pays a current annual dividend of $2, expected to grow at 10% for two years and then at 2% thereafter, with a required return of 8%, we must use the Dividend Discount Model (DDM). We'll compute the present value of dividends for the first two years using the growth rate of 10%, and after that, we'll use the Gordon Growth Model to find the present value of all future dividends growing at a perpetual rate of 2%. The formula for the Gordon Growth Model is D / (r - g), where D is the dividend, r is the required rate of return, and g is the growth rate.
First, let's find the dividends for the first two years:
- Year 1 Dividend: $2.00 * (1 + 0.10) = $2.20
- Year 2 Dividend: $2.20 * (1 + 0.10) = $2.42
Now, calculate the present value of these dividends:
- Present Value Year 1: $2.20 / (1 + 0.08) = $2.04
- Present Value Year 2: $2.42 / (1 + 0.08)2 = $2.08
For the perpetual growth from Year 3 onward, the dividend in Year 3 would be $2.42 * (1 + 0.02) = $2.4684.
Using the Gordon Growth Model:
Present Value of Perpetual Dividends: $2.4684 / (0.08 - 0.02) = $41.14
However, this $41.14 needs to be discounted back two years to the present:
Present Value of Perpetual Dividends today: $41.14 / (1 + 0.08)2 = $35.3
Adding up the present values, the intrinsic value of the stock is $2.04 + $2.08 + $35.3 = $39.42.