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You are considering the purchase of Zemen company common stock that paid dividend of Br. 2

yesterday. You expect the dividend to grow at the rate of 5% per year for the next 3 years, and, if you
buy the stock, you plan to hold it for 3 years and then sell it. Calculate the value of the common stock
if your required rate of return is 15%

1 answer

To calculate the value of Zemen company's common stock, we can use the Dividend Discount Model (DDM), specifically the Gordon Growth Model.

  1. Estimate Future Dividends: Given that the last dividend (D0) paid was Br. 2 and is expected to grow at a rate of 5% for the next 3 years, we can calculate the future dividends:

    • D1 = D0 × (1 + g) = 2 × (1 + 0.05) = 2 × 1.05 = Br. 2.10
    • D2 = D1 × (1 + g) = 2.10 × (1 + 0.05) = 2.10 × 1.05 = Br. 2.205
    • D3 = D2 × (1 + g) = 2.205 × (1 + 0.05) = 2.205 × 1.05 = Br. 2.31525

  2. Calculate Present Value of Future Dividends: We will discount each of these dividends back to the present value using the required rate of return of 15%:

    \[ PV(D1) = \frac{D1}{(1 + r)^1} = \frac{2.10}{(1 + 0.15)^1} = \frac{2.10}{1.15} \approx Br. 1.8261 \]

    \[ PV(D2) = \frac{D2}{(1 + r)^2} = \frac{2.205}{(1 + 0.15)^2} = \frac{2.205}{1.3225} \approx Br. 1.6681 \]

    \[ PV(D3) = \frac{D3}{(1 + r)^3} = \frac{2.31525}{(1 + 0.15)^3} = \frac{2.31525}{1.520875} \approx Br. 1.5238 \]

  3. Total Present Value of Dividends: Add the present values of the future dividends:

    \[ PV_{\text{Total}} = PV(D1) + PV(D2) + PV(D3) \approx 1.8261 + 1.6681 + 1.5238 \approx Br. 5.018 \]

  4. Calculate Price at the End of Year 3: At the end of Year 3, we will sell the stock. To find the selling price, we need the expected dividend in Year 4 (D4) and then calculate its present value using the Gordon Growth Model.

    \[ D4 = D3 \times (1 + g) = 2.31525 \times (1 + 0.05) = 2.31525 \times 1.05 \approx Br. 2.4310125 \]

    Now, using the Gordon Growth Model, we calculate the price at the end of Year 3:

    \[ P3 = \frac{D4}{(r - g)} = \frac{2.4310125}{(0.15 - 0.05)} = \frac{2.4310125}{0.10} \approx Br. 24.310125 \]

  5. Discount Selling Price Back to Present Value:

    \[ PV(P3) = \frac{P3}{(1 + r)^3} = \frac{24.310125}{1.520875} \approx Br. 15.982 \]

  6. Total Present Value of the Stock: Now, add the present value of the dividends and the present value of the selling price:

    \[ PV_{\text{Stock}} = PV_{\text{Total}} + PV(P3) \approx 5.018 + 15.982 \approx Br. 21.000 \]

Thus, the value of the common stock is approximately Br. 21.00.