Question

A stock just paid an annual dividend of $2.8. The dividend is expected to grow by 10% per year for the next 4 years. The growth rate of dividends will then fall steadily by 1.75% per year, from 10% in year 4 to 3% in year 8 and stay at that level forever. The required rate of return is 12%. Attempt 2/10 for 10 pts. Part 1 What is the expected dividend in 8 years

Answer 1

$39.53

Step-by-step explanation:

The first step is to find the dividends growth

D1 $2.80 * 1.10 = $3.08

D2 $3.08 * 1.10 = $3.388

D3 $3.388 * 1.10 = $3.727

D4 $3.727 * 1.10 = $4.1

D5 $4.1 * 1.0175 = $4.171

D6 $4.171 * 1.0175 = $4.244

D7 $4.244 * 1.0175 = $4.318

D8 $4.318 * 1.03 = $4.448

From the year 8 onward, the growth remains at 3% forever. So the value of the stock at the year end 8 would be:

Perpetuity at the year 8 = $4.448 * (1 + 3%) / (12%-3%) = $50.9

Now, we will discount all the dividends to the year 8 and the stock value at 12% required rate of return to find the value of stock at year zero.

Value of Stock at Y0 = D1 / (1 + 12%)^1 + D1 / (1 + 12%)^2 + D1 / (1 + 12%)^3 + D1 / (1 + 12%)^4 + D1 / (1 + 12%)^5 + D1 / (1 + 12%)^6 + D1 / (1 + 12%)^7

+ D1 / (1 + 12%)^8 + Stock Value / (1 + 12%)^8

= $39.53