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Easy question but tricky wording.. (Stock price)

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  • Easy question but tricky wording.. (Stock price)

    I realize that this is a very easy topic, but easy questions on the exam can be deceiving.

    These are two questions that I have problem with because their answers doesn't seem to match... By the way, they are from BBP.

    A stock is going to pay its annual dividend of $5 later today. After today, the dividend is expected to increase by 3% each year forever. The annual effective interest rate is 10%. Calculate the price of this stock.

    Price of stock = PV(dividends) = 5 + 5 x (1.03) / (.10 - .03)
    I know there are other ways to think about the problem, but this is the first idea that I had and produce a correct answer of $78.57.

    Now, there is another problem involving constant growth dividend that troubled me.

    Company X paid a dividend earlier today of $5 per share. Its current stock price is $42.50. The stock has an expected required return of 14%. What is the company's expected growth rate of its equity assuming annual dividends?

    Ok. I figure same thing was going on. Price = div0 + div1 / (r - g) = 5 + 5 (1 + q) / (.14 - g). Solving for g, I get 0.5%, but the answer key says 2.0% and the following explanation.

    Price = div0 (1 + g) / (r - g) -> 42.50 = 5 (1+g) / (.14 - g).

    The only difference is that one says it's going to pay the div0 later today and the second one says that dividend was paid earlier today.

    So in the second problem, the stock price of $42.50 includes div0 already so stock price is equal to PV of all future dividends where as first one, it's $5 plus PV of all future dividends.

    It's easy question, but these things can bite you during exams... especially when you are short on time.

    Good luck on the exam.

  • #2
    That doesn't seem all that tricky to me. Why would someone buying a stock pay for a dividend that was already paid?