Julie's X-Ray Company paid $2.00 per share in common stock dividends last year. The company's policy is to allow its dividend to grow at 5 percent for 4 year and then the rate of growth changes to 3 percent per year from year 5 and on. What is the value of the stock if the required rate of return is 8 percent.
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To calculate the value of the stock, we can use the dividend discount model (DDM), which discounts the future dividends to the present value. The formula for the DDM is:
Value of Stock = Dividend / (Required Rate of Return - Dividend Growth Rate)
First, we need to calculate the annual dividends for the next 4 years, considering the 5% growth rate:
Year 1: $2.00
Year 2: $2.00 * (1 + 5%) = $2.10
Year 3: $2.10 * (1 + 5%) = $2.21
Year 4: $2.21 * (1 + 5%) = $2.32
From year 5 and onwards, the dividend growth rate changes to 3%. We can calculate the dividend for year 5 and beyond using the following formula:
Dividend Year n = Dividend Year n-1 * (1 + Growth Rate)
Year 5: $2.32 * (1 + 3%) = $2.39
Now, let's plug these values into the DDM formula:
Value of Stock = [$2.00 / (0.08 - 0.05)]
+ [$2.10 / (0.08 - 0.05)]
+ [$2.21 / (0.08 - 0.05)]
+ [$2.32 / (0.08 - 0.05)]
+ [$2.39 / (0.08 - 0.03)]
Value of Stock ≈ $2.00 / 0.03 + $2.10 / 0.03 + $2.21 / 0.03 + $2.32 / 0.03 + $2.39 / 0.05
Value of Stock ≈ $66.67 + $70 + $73.67 + $77.33 + $47.80
Value of Stock ≈ $335.47
Thus, the value of the stock is approximately $335.47 when the required rate of return is 8 percent.