Value Investing Principles

Determine Stock Value: Dividend Discount Model

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Question

What is the value of a stock that paid a $10 per share dividend this year, and is expected to pay a dividend 20% higher in a year's time, the stock is expected to be selling for $40 per share at the end of the year. The appropriate discount rate is 10% per year?

Answers

Explanations

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A. B. C. D.

Explanation

Value = $52/1.10=$47.27

To calculate the value of the stock, we can use the dividend discount model (DDM) which considers the present value of future dividends. The formula for the DDM is as follows:

Stock Value=D1(1+r)1+D2(1+r)2+…+Dn(1+r)n\text{Stock Value} = \frac{{D_1}}{{(1+r)^1}} + \frac{{D_2}}{{(1+r)^2}} + \ldots + \frac{{D_n}}{{(1+r)^n}}

Where:

  • D1D_1 represents the dividend to be received at the end of the first year.
  • D2D_2 represents the dividend to be received at the end of the second year.
  • rr is the discount rate.

In this case, we have the following information:

  • The current dividend (at the end of this year) is $10 per share.
  • The dividend expected in one year is 20% higher than the current dividend, so D2=1.2×D1D_2 = 1.2 \times D_1 (dividend next year is 20% higher).
  • The expected selling price of the stock at the end of the year is $40 per share.

Now, let's calculate the value of the stock using the dividend discount model:

Stock Value=$10(1+0.1)1+$10×1.2(1+0.1)2+$40(1+0.1)2\text{Stock Value} = \frac{{\$10}}{{(1+0.1)^1}} + \frac{{\$10 \times 1.2}}{{(1+0.1)^2}} + \frac{{\$40}}{{(1+0.1)^2}}

Simplifying this expression:

Stock Value=$101.1+$10×1.21.12+$401.12\text{Stock Value} = \frac{{\$10}}{{1.1}} + \frac{{\$10 \times 1.2}}{{1.1^2}} + \frac{{\$40}}{{1.1^2}}

Calculating the values:

Stock Value=$9.09+$9.92+$30.58\text{Stock Value} = \$9.09 + \$9.92 + \$30.58 Stock Value=$49.59\text{Stock Value} = \$49.59

Therefore, the value of the stock is approximately $49.59.

None of the provided answer choices match the calculated value of the stock. Therefore, the correct answer is A. Not able to compute with the above data.

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