Question

A7X Corp. just paid a dividend of $1.70 per share. The dividends are expected to grow at 20 percent for the next eight years and then level off to a growth rate of 5 percent indefinitely. If the required return is 15 percent, what is the price of the stock today

Answer 1

To calculate the price of the stock today, we can use the Dividend Discount Model (DDM). By discounting the estimated future dividends back to their present value, we can determine the value of the stock. In this case, the dividends are expected to grow at 20% for the next eight years and then level off to a growth rate of 5% indefinitely. The price of the stock today is $17.42.

Step-by-step explanation:

To calculate the price of the stock today, we need to use the Dividend Discount Model (DDM). DDM is a method used to value a stock by discounting its estimated future dividends back to their present value. In this case, the dividends are expected to grow at 20% for the next eight years and then level off to a growth rate of 5% indefinitely.

Step 1: Calculate the present value of dividends during the first eight years using the formula:

PV(div) = D1 / (1 + r)¹ + D2 / (1 + r)² + ... + D8 / (1 + r)⁸

Where D1 = dividend in year 1, and r = required return.

Step 2: Calculate the present value of dividends after the eighth year using the formula:

PV(terminal) = D8 * (1 + g) / (r - g) / (1 + r)⁸

Where g = growth rate after the eighth year.

Step 3: Sum the present values of dividends from steps 1 and 2 to get the total present value of dividends.

Step 4: Calculate the stock price by adding the present value of dividends to the present value of the terminal value:

Stock Price = PV(div) + PV(terminal)

Using the given information:

D1 = $1.70 (dividend in year 1)

r = 15% (required return)

g = 5% (growth rate after the eighth year)

By plugging in the values into the formulas, the price of the stock today is $17.42.

Answer 2

Dn = Do x (1+g)^n

D1 = 1.70 x (1+0.20)^1 = 2.04

D2 = 1.70 x (1+0.20)^2 = 2.448

Year Dividend

1 2.040

2 2.448

3 2.938

4 3.525

5 4.230

6 5.076

7 6.091

8 7.310

Price at the end of 8th year = D8 x (1+g)/(Ke- g)

Price at the end of 8th year = 7.310 x (1+0.05)/ (0.15-0.05)

Price at the end of 8th year = $76.755

Year Cash flows PV Factor 15% Present Value

1 2.040 0.8696 1.77

2 . 2.448 0.7561 1.85

3 2.938 0.6575 1.93

4 3.525 0.5718 2.02

5 . 4.230 0.4972 2.10

6 5.076 0.4323 2.19

7 6.091 0.3759 2.29

8 84.065 0.3269 27.48

Total 41.64

Hence, the price of the stock today is $41.64