A stock is selling for $12.20 a share given a market return of 15.5 percent and a capital gains yield of 5.6 percent. What was the amount of the last annual dividend that was paid?
The correct answer and explanation is:
To determine the last annual dividend paid, we need to understand the relationship between the stock price, capital gains yield, and dividend yield. The formula for the total return of a stock can be broken into two parts: capital gains yield and dividend yield. The total return is the sum of these two components.
Formula: Total Return=Capital Gains Yield+Dividend Yield\text{Total Return} = \text{Capital Gains Yield} + \text{Dividend Yield}
We are given:
- Market return (Total Return) = 15.5% or 0.155
- Capital gains yield = 5.6% or 0.056
- Stock price = $12.20
First, we can calculate the dividend yield as follows: Dividend Yield=Total Return−Capital Gains Yield\text{Dividend Yield} = \text{Total Return} – \text{Capital Gains Yield} Dividend Yield=0.155−0.056=0.099 (or 9.9%)\text{Dividend Yield} = 0.155 – 0.056 = 0.099 \, (\text{or 9.9\%})
Now, the dividend yield is defined as the annual dividend divided by the stock price. Let DD represent the dividend paid. The formula for dividend yield is: Dividend Yield=DStock Price\text{Dividend Yield} = \frac{D}{\text{Stock Price}} 0.099=D12.200.099 = \frac{D}{12.20}
Now solve for DD: D=0.099×12.20=1.2078D = 0.099 \times 12.20 = 1.2078
So, the last annual dividend paid was approximately $1.21 per share.
Explanation:
The total return on a stock is influenced by both capital gains (the price appreciation of the stock) and the dividends paid to shareholders. The capital gains yield is the percentage increase in the stock price, while the dividend yield is the return from the dividends paid, expressed as a percentage of the stock price. By subtracting the capital gains yield from the total return, we can calculate the dividend yield. Then, using the stock price and the dividend yield, we can determine the dollar amount of the last dividend paid to the shareholders. In this case, it amounts to $1.21 per share.