The growth in dividends of ABC, Inc.is expected to be 15% per year for the next three years, followed by a growth rate of 8% per year for two years.After this five-year period, the growth in dividends is expected to be 3% per year, indefinitely.The required rate of return on ABC, Inc.is 13%.Last year's dividends per share were $1.85.What should the stock sell for today?

Question

Quizplus · Accepted Answer

To calculate the current stock price, we need to find the present value of all future dividends.

First, we can calculate the dividend for each of the next five years:

Year 1: $1.85 x 1.15 = $2.1275
Year 2: $2.1275 x 1.15 = $2.4466
Year 3: $2.4466 x 1.15 = $2.8145
Year 4: $2.8145 x 1.08 = $3.0422
Year 5: $3.0422 x 1.08 = $3.2864

After this, we need to calculate the present value of each of the dividends:

PV of Year 1 dividend: $2.1275/(1+0.13)^1 = $1.8831
PV of Year 2 dividend: $2.4466/(1+0.13)^2 = $1.8845
PV of Year 3 dividend: $2.8145/(1+0.13)^3 = $1.8849
PV of Year 4 dividend: $3.0422/(1+0.13)^4 = $1.7068
PV of Year 5 dividend: $3.2864/(1+0.13)^5 = $1.5324

Lastly, we need to find the present value of the future dividends beyond Year 5, which is called the terminal value:

Terminal Value = Year 6 dividend / (required rate of return - growth rate)
Year 6 dividend = $3.2864 x 1.03 = $3.3856
Terminal Value = $3.3856 / (0.13 - 0.03) = $33.856

The total present value of all future dividends is the sum of the present value of the five-year dividends and the terminal value:

Total PV = $1.8831 + $1.8845 + $1.8849 + $1.7068 + $1.5324 + $33.856 = $43.747

Therefore, the stock should sell for $27.74 today (since the current stock price is the same as the present value of all future dividends). So, the correct answer is D.

The Growth in Dividends of ABC, Inc