Calculating the Value of a Stock: Infinite Period Dividend Discount Model

Infinite Period Dividend Discount Model

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Question

You are going to hold a stock for an infinite amount of time. The current dividend is $1 per share and is expected to grow at 10% a year. Your long run required rate of return is 13%. Using the infinite period dividend discount model calculate the value of the stock.

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Explanations

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A. B. C. D.

C

g = .10 k = .13 Dividend = 1.10 x $1.00

V = 1.10/(.13 - .10) = $36.67

To calculate the value of the stock using the infinite period dividend discount model, we need to use the formula:

V0=D0×(1+g)r−gV_0 = \frac{D_0 \times (1+g)}{r - g}

Where:

  • V0V_0 is the value of the stock today,
  • D0D_0 is the current dividend per share,
  • gg is the expected growth rate of dividends, and
  • rr is the required rate of return.

Given:

  • D_0 = $1 (current dividend per share)
  • g=10%g = 10\% (expected growth rate of dividends)
  • r=13%r = 13\% (required rate of return)

Let's plug in the values into the formula and calculate the value of the stock:

V_0 = \frac{$1 \times (1 + 0.10)}{0.13 - 0.10}

Simplifying:

V_0 = \frac{$1.10}{0.03}

V_0 = $36.67

Therefore, the value of the stock using the infinite period dividend discount model is $36.67.

None of the provided answers (A, B, C, D) match the calculated value of $36.67, so the correct answer is "C. none of these answers."

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