a) What is the price Mr. A is willing to pay for a stock that pays a dividend of $5 per share...

Question:

a) What is the price Mr. A is willing to pay for a stock that pays a dividend of $5 per share annually and will be sold at $50 after two years according to the Generalized Valuation Model? Mr. A's required rate of return is 8%.

b) Explain why Ms. B is willing to pay a higher price for the same stock.

c) What is the value of the above stock according to the Gordon Growth model if the dividend growth is 3%?

Gordon Growth Model:

The Gordon Growth model is a simple stock valuation model that represents a special case of the more general discounted dividend model. The Gordon model assumes that dividends grow at a constant rate indefinitely.

Answer and Explanation:

a) The price Mr.A will be willing to pay is the discounted present value of cash flows from the stock, which include $5 dividend for the next two years, plus the resale value of $50 at the end of 2 years. At a discount rate of 8%, the present value is:

  • {eq}\dfrac{5}{(1 + 8\%)} + \dfrac{5 + 50}{(1 + 8\%)^2} = 51.78 {/eq}

Thus, the price Mr. A is willing to pay is $51.78.

b) Ms. B will be willing to pay a higher price if her required rate of return is lower.

c) According to the Gordon Growth model, the price of a stock is given by:

  • price per share = next dividend / (required return - dividend growth rate)
  • price per share = 5 / (8% - 3%)
  • price per share = $100

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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