Question

Synovec Corp. is experiencing rapid growth. Dividends are expected to grow at 28 percent per year during the next three years, 18 percent over the following year, and then 6 percent per year indefinitely. The required return on this stock is 12 percent, and the stock currently sells for $62 per share. What is the projected dividend for the coming year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Projected dividend           $

Answer 1

Let Dividend in the coming year be D.

For first 3 years, Dividend will grow by 28%. For next year 18% growth and after that 6% constant growth.

Required rate of return = 12% | Current Share price = $ 62

We will use multi-stage Dividend discount model for the calculation as there are different growth stages.

First Stage: Year 1 to Year 4

Dividend at Year 1 = D

Dividend at Year 2 = Dividend at Year 1 * Growth rate for first 3 years = D * (1+28%)

Dividend at Year 3 = Dividend at Year 2 * Growth rate for first 3 years = D * (1+28%)²

Dividend at Year 4 = Dividend at Year 3 * Growth rate for first 3 years = D * (1+28%)³

We will now form the Present Value expression of the First stage.

PV of first stage = Dividend at Year 1 / (1+R) + Dividend at Year 2 / (1+R)² + Dividend at Year 3 / (1+R)³ + Dividend at Year 4 / (1+R)⁴

PV of First stage = D / (1+12%) + D*(1+28%) / (1+12%)² + D*(1+28%)² / (1+12%)³ + D * (1+28%)³ / (1+12%)⁴

PV of First stage = D * (1 / 1.12 + 1.28 / 1.12² + 1.28² / 1.12³ + 1.28³ / 1.12⁴)

PV of First stage = D * (0.89286 + 1.02041 + 1.16618 + 1.33278)

PV of first stage = D * 4.41222

Second Stage: Next one year

Till 4th year, growth rate of 28% is to be used. For 5th year, we will use growth rate of 18% which will provide us the expeced dividend which can be used for calculating the Terminal value using 6% constant growth. In short, previous growth rate gives us the beginning dividend for the next stage.

Terminal value is the Price per share of the company at Year 5.

Dividend at Year 5 = D * (1+28%)³ * (1+18%)

At growth rate of 6%, we can calculate the Terminal value at Year 4.

Terminal Value at Year 4 = Dividend at Year 5 / (R - G)

Terminal Value at Year 4 = D * (1+28%)³ * (1+18%) / (12% - 6%)

Terminal Value at Year 4 = D * 41.244

Now we will calculate the Present Value of Terminal value at Year 0.

PV of Terminal value = Terminal Value / (1+R)⁴

PV of Terminal value = D * 41.244 / (1+12%)⁴

PV of Terminal value = D * 26.2113

Now we know the current price per share of $62 and we have calculated PV of each stage. Summing the stages, equalizing them with Share price and solving for D will provide us the projected dividend in the next year.

=> 62 = D * 4.41222 + D * 26.2113

=> 62 = D * 30.6235

=> D = 62 / 30.6235

Projected Dividend for the next year = $2.025 or $2.02

Hence, the projected dividend for the next year $2.02