Stock Return Breakdown With Scenarios

Problem:

A stock is selling today for $40 per share. At the end of the year, it pays a dividend of $2 per share and sells for $44. a. What is the total rate of return on the stock? b. What are the dividend yield and percentage capital gain? c. Now suppose the year-end stock price after the dividend is paid is $36. What are the dividend yield and percentage capital gain in this case?

To solve this, we need to calculate the total rate of return, dividend yield, and percentage capital gain. Let's work through each part.

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Part a: Total rate of return

The total rate of return ($R$) is given by:

$$R = \frac{\text{Dividend} + (\text{End Price} - \text{Initial Price})}{\text{Initial Price}}$$

Here:

• Initial Price = $40

• Dividend = $2

• End Price = $44

$$R = \frac{2 + (44 - 40)}{40} = \frac{2 + 4}{40} = \frac{6}{40} = 0.15 \text{ or } 15\%.$$

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Part b: Dividend yield and percentage capital gain

1. Dividend Yield ($DY$):
   The dividend yield is calculated as:

   $$DY = \frac{\text{Dividend}}{\text{Initial Price}}$$ $$DY = \frac{2}{40} = 0.05 \text{ or } 5\%.$$
   

2. Percentage Capital Gain ($CG$):
   The percentage capital gain is:

   $$CG = \frac{\text{End Price} - \text{Initial Price}}{\text{Initial Price}}$$ $$CG = \frac{44 - 40}{40} = \frac{4}{40} = 0.10 \text{ or } 10\%.$$
   

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Part c: Dividend yield and percentage capital gain (End Price = $36)

1. Dividend Yield ($DY$):
   The formula remains the same:

   $$DY = \frac{\text{Dividend}}{\text{Initial Price}}$$ $$DY = \frac{2}{40} = 0.05 \text{ or } 5\%.$$
   

2. Percentage Capital Gain ($CG$):
   In this case, the End Price is $36. The percentage capital gain is:

   $$CG = \frac{\text{End Price} - \text{Initial Price}}{\text{Initial Price}}$$ $$CG = \frac{36 - 40}{40} = \frac{-4}{40} = -0.10 \text{ or } -10\%.$$
   

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Summary of Results:

Scenario	Total Rate of Return	Dividend Yield	Percentage Capital Gain
End Price =$44	15%	5%	10%
End Price = $36 (after dividend)	—	5%	-10%

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