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Kiffer SARL just paid a dividend of €0.85 on its stock.They expect dividends to grow at a rate of 8% in the next three years and 5% per year thereafter.Given a required rate of return of 15%, what is the current value of the company's common stock?€8.28€9.64€10.41€11.24€12.41

Question

Kiffer SARL just paid a dividend of €0.85 on its stock.They expect dividends to grow at a rate of 8% in the next three years and 5% per year thereafter.Given a required rate of return of 15%, what is the current value of the company's common stock?€8.28€9.64€10.41€11.24€12.41

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Solution

To calculate the current value of the company's common stock, we need to calculate the present value of the dividends for the next three years and the present value of the dividends from the fourth year onwards.

Step 1: Calculate the dividends for the next three years:

  • Year 1: €0.85 * 1.08 = €0.918
  • Year 2: €0.918 * 1.08 = €0.99144
  • Year 3: €0.99144 * 1.08 = €1.070752

Step 2: Calculate the present value of these dividends:

  • Year 1: €0.918 / (1.15^1) = €0.79826
  • Year 2: €0.99144 / (1.15^2) = €0.74960
  • Year 3: €1.070752 / (1.15^3) = €0.68783

Step 3: Calculate the dividend for the fourth year:

  • Year 4: €1.070752 * 1.05 = €1.1242896

Step 4: Calculate the present value of the dividends from the fourth year onwards. This is a perpetuity, so we use the formula for the present value of a perpetuity: D / (r - g), where D is the dividend, r is the required rate of return, and g is the growth rate.

  • PV = €1.1242896 / (0.15 - 0.05) = €11.242896

Step 5: Calculate the present value of this perpetuity discounted back three years:

  • PV = €11.242896 / (1.15^3) = €7.217

Step 6: Add up all the present values to get the current value of the stock:

  • Current value = €0.79826 + €0.74960 + €0.68783 + €7.217 = €9.45

So, the closest answer is €9.64.

This problem has been solved

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