Valuation of Common Stock

Calculating the Value of a Common Stock

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Question

An analyst uses a temporary supernormal growth model to value a common stock. The company paid a $2 dividend last year. The analyst expects dividends to grow at 15% each year for the next three years and then to resume a normal rate of 7% per year indefinitely. The analyst estimates that investors require a 12% return on the stock. The value of this common stock is closest to:

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A. B. C.

B

To value the common stock using the temporary supernormal growth model, we need to calculate the present value of all the future dividends and the expected price of the stock at the end of the three-year supernormal growth period. Here's the step-by-step calculation:

  1. Calculate the dividends for the next three years:

    • Year 1 dividend: $2 * (1 + 15%) = $2.30
    • Year 2 dividend: $2.30 * (1 + 15%) = $2.65
    • Year 3 dividend: $2.65 * (1 + 15%) = $3.04

  2. Calculate the present value of the dividends during the supernormal growth period (years 1-3):

    • Year 1 present value: $2.30 / (1 + 12%)^1 = $2.05
    • Year 2 present value: $2.65 / (1 + 12%)^2 = $2.16
    • Year 3 present value: $3.04 / (1 + 12%)^3 = $2.29

  3. Calculate the price of the stock at the end of the supernormal growth period:

    • Use the dividend discount model (DDM) formula to calculate the terminal value of the stock at the end of year 3: Terminal value = Year 4 dividend / (Required return - Dividend growth rate) Year 4 dividend = $3.04 * (1 + 7%) = $3.26 Terminal value = $3.26 / (12% - 7%) = $65.20

  4. Calculate the present value of the terminal value:

    • Present value of the terminal value = Terminal value / (1 + Required return)^3
    • Present value of the terminal value = $65.20 / (1 + 12%)^3 = $47.13

  5. Calculate the total present value of all dividends and the terminal value:

    • Total present value = Year 1 present value + Year 2 present value + Year 3 present value + Present value of the terminal value
    • Total present value = $2.05 + $2.16 + $2.29 + $47.13 = $53.63

The value of the common stock using the temporary supernormal growth model is closest to $53 (option B).

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