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The Co. just paid a dividend of $1 per share. Analysts expect its dividend to grow at 25 percent per year for the next three years and then 5 percent per year thereafter. If the required rate of return on the stock is 18 percent, what is the current value of the stock?

Question

The Co. just paid a dividend of $1 per share. Analysts expect its dividend to grow at 25 percent per year for the next three years and then 5 percent per year thereafter. If the required rate of return on the stock is 18 percent, what is the current value of the stock?

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Solution

To calculate the current value of the 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: 11.25=1 * 1.25 = 1.25
  • Year 2: 1.251.25=1.25 * 1.25 = 1.56
  • Year 3: 1.561.25=1.56 * 1.25 = 1.95

Step 2: Calculate the present value of these dividends.

  • Year 1: 1.25/(1+0.18)=1.25 / (1 + 0.18) = 1.06
  • Year 2: 1.56/(1+0.18)2=1.56 / (1 + 0.18)^2 = 1.12
  • Year 3: 1.95/(1+0.18)3=1.95 / (1 + 0.18)^3 = 1.18

Step 3: Calculate the dividend for the fourth year and onwards.

  • Year 4 onwards: 1.951.05=1.95 * 1.05 = 2.05

Step 4: Calculate the present value of these dividends.

  • Year 4 onwards: 2.05/(0.180.05)=2.05 / (0.18 - 0.05) = 15.77

Step 5: Discount this value back to the present.

  • Present value of Year 4 onwards: 15.77/(1+0.18)3=15.77 / (1 + 0.18)^3 = 9.54

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

  • Current value = 1.06+1.06 + 1.12 + 1.18+1.18 + 9.54 = $13.90

So, the current value of the stock is $13.90.

This problem has been solved

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