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
t = periods
r = discount rate
FV = present value
The computation is as follows:
PV = 120.00 / (1+.35)^3 = $48.77
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from Finance 101: Principles of FinanceChapter 14 / Lesson 3