Question

Kleine Toymakers is introducing a new line of robotic toys, which it expects to grow their earnings at a much faster rate than normal over the next three years. After paying a dividend of $2.00 last year, it does not expect to pay a dividend for the next three years. After that Kleine plans to pay a dividend of $4.00 in year 4 and then increase the dividend at a rate of 10 percent in years 5 and 6. What is the present value of the dividends to be paid out over the next six years if the required rate of return is 15 percent? (Do not round intermediate calculations. Round final answer to two decimal places.)

A) $13.24
B) $12.00
C) $6.57
D) $10.24

Answer 1

The present value of the dividends from Kleine Toymakers is computed by applying the present value formula to each year's expected dividend, discounting them back at a required rate of return of 15%. No dividends are expected for the first three years, but years 4, 5, and 6 will have dividends that need to be accounted for and added together to get the total present value.

Step-by-step explanation:

The present value of dividends from Kleine Toymakers, considering the expected growth and the required rate of return, is calculated using the formula for the present value of future cash flows. The dividends for years 4, 5, and 6 need to be discounted back to their present values separately, as they are received at different times. Since no dividends are paid in the first three years, we only need to calculate the present value of the dividends in year 4 and the growth in dividends in years 5 and 6. The expected dividend in year 4 is $4.00, and it is projected to grow by 10 percent annually in years 5 and 6.

To calculate the present value, we use the following formula: PDV = D / (1+r)^t, where PDV is the present value of the dividend, D is the expected dividend, r is the required rate of return, and t is the time in years. Implementing this formula, the present value of the $4.00 dividend in year 4 is $4.00 / (1+0.15)^4. The dividend in year 5, which is expected to be $4.40 ($4.00 increased by 10%), has a present value of $4.40 / (1+0.15)^5, and similarly, the dividend in year 6 is expected to be $4.84 ($4.40 increased by 10%), discounted back to its present value at $4.84 / (1+0.15)^6.

Finally, we add up all the present values to estimate the value of the dividends over the six-year period. The required rate of return significantly affects these calculations, influencing how much the future cash flows are worth today and hence, the decision of an investor regarding investing in this company's stocks.