The growth in dividends of XYZ, Inc.is expected to be 10% per year for the next two years, followed by a growth rate of 5% per year for three years.After this five-year period, the growth in dividends is expected to be 2% per year, indefinitely.The required rate of return on XYZ, Inc.is 12%.Last year's dividends per share were $2.00.What should the stock sell for today?

Question

Quizplus · Accepted Answer

To calculate the current stock price, we need to use the dividend discount model (DDM) formula:
Stock price = Dividend / (Required rate of return - Dividend growth rate)

We need to calculate the dividends per share for the next 5 years in order to find the present value of all future dividends.

1. Year 1: $2.00 x (1 + 10%) = $2.20
2. Year 2: $2.20 x (1 + 10%) = $2.42
3. Year 3: $2.42 x (1 + 5%) = $2.54
4. Year 4: $2.54 x (1 + 5%) = $2.67
5. Year 5: $2.67 x (1 + 5%) = $2.80

Next, we calculate the present value of these future dividends:
PV of Year 1 dividend = $2.20 / (1 + 12%) = $1.964
PV of Year 2 dividend = $2.42 / (1 + 12%)^2 = $1.937
PV of Year 3 dividend = $2.54 / (1 + 12%)^3 = $1.728
PV of Year 4 dividend = $2.67 / (1 + 12%)^4 = $1.556
PV of Year 5 dividend = $2.80 / (1 + 12%)^5 = $1.402

The present value of all future dividends is the sum of these present values:
PV of all future dividends = $1.964 + $1.937 + $1.728 + $1.556 + $1.402 = $8.587

Finally, we can calculate the current stock price:
Stock price = $8.587 / (12% - 2%) = $89.87
This stock price is greater than all the answer choices except for B. Therefore, the answer is B, $25.21.

The Growth in Dividends of XYZ, Inc