Dismal.Com is a producer of depressing Internet products. The company is currently not paying...

Question:

Dismal.Com is a producer of depressing Internet products. The company is currently not paying dividends, but its chief financial officer thinks that starting in 3 years it can pay a dividend of $15 per share, and that this dividend will grow by 20% per year. Assuming that the cost of equity of Dismal.Com is 35%, value a share based on the discounted dividends.

Dividend Discount Model:

This problem entails use of the constant growth dividend discount model (DDM), a widely used method for valuing a stock. The DDM, which is also referred to as the Gordon Growth Model, assumes the fair value of a stock is the sum of all future dividends, discounted to the present day using an appropriate cost of equity.

Answer and Explanation:

The answer is $48.77.

The formula for the DDM is illustrated below.

We are given the following information, which will hold three years from now:

D0 = $15.00

g = 20.0%

r = 35.0%

To solve for P0, we first must determine D1, the dividend expected in the fourth year. It's computed as follows:

D1 = D0(1+g)

D1 = $15.00(1.20) = $18.00

Now, we can plug the known information into the DDM to solve for P0. The computation is below.

P0 = $18.00 / (.35-.20)

P0 = $120.00

However, remember, $120.00 is the value of the stock anticipated in 3 years. To find the present value, we must discount this amount back 3 years at the 35.0% cost of equity. This can be accomplished using the present value formula and computation below.

PV = FV / (1+r)^t

Where,

t = periods

r = discount rate

FV = present value

The computation is as follows:

PV = 120.00 / (1+.35)^3 = $48.77


Learn more about this topic:

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The Dividend Growth Model

from Finance 101: Principles of Finance

Chapter 14 / Lesson 3
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