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Stock Valuation with Dividend Growth Model

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Question

A stock paid a $5 per share dividend this year. The company's dividends are expected to grow at 5% per year, forever. What is the value of the stock if the appropriate discount rate is 8% per year?

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Explanations

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A. B. C. D.

C

Value = $5.25/(0.08-0.05) = $175.00

To calculate the value of the stock using the dividend discount model (DDM), we need to determine the present value of all future dividends.

The formula for the present value of a perpetuity (a stream of cash flows that continues indefinitely) is:

PV = D / r

Where: PV = Present value D = Dividend payment r = Discount rate

In this case, the dividend payment (D) is $5 per share, and the discount rate (r) is 8% per year.

First, we need to find the value of the first dividend payment (D1) by applying the growth rate of 5%:

D1 = D * (1 + g) = $5 * (1 + 0.05) = $5 * 1.05 = $5.25

Now, we can calculate the present value of all future dividends (PV) using the perpetuity formula:

PV = D1 / r = $5.25 / 0.08 = $65.625

Therefore, the value of the stock is $65.625 per share. However, this value is not listed among the provided answer choices.

Since none of the answer choices match the calculated value, the correct answer would be D. Not able to compute with the above data.

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