Concept explainers
To determine: The dividend yield for each four stocks.
Introduction:
Dividend is a sum of money paid to the shareholders of the company. It is distributed among the investors from a portion of company’s earnings. This can be issued or paid as shares of stock or cash payment.
Dividend yield is a ratio that specifies how much a company pays as dividends every year compared with its share price. It is considered as the return on investment for a stock.
Answer to Problem 31QP
The dividend yield of Stock W is 9%.
The dividend yield of Stock X is 16.99%.
The dividend yield of Stock Y is 22%.
The dividend yield of Stock Z is 4.68%.
Explanation of Solution
Given information:
Four different stocks have a required rate of return of 17% and the recent dividend is $2.40 per share. The Stock Z has a growth rate of 12%.
The constant growth rate in dividends of Stock W is 8%.
The constant growth rate in dividends of Stock X is 0%.
The constant growth rate in dividends of Stock Y is −5%.
The constant growth rate in dividends of Stock Z is 20%.
Steps to determine the dividend yields and capital gains for each of the stocks:
- Firstly, determine the stock price for each stock. It is because all the stocks have a required return of 17%, which is the sum of dividend yield and capital gains yield.
- After determining the stock price of each stock, use the stock price and dividend to compute the dividend yield of the four stocks.
- Finally, determine the capital gains yield for the each stock by subtracting the dividend yield from the total return.
Formulae:
The formula to calculate the price of stock:
Where,
Po refers to the present value of a share of stock,
Do refers to the current year dividend paid,
R refers to the discount rate,
g refers to the constant growth of dividends.
The formula to calculate the dividend yield:
Where,
D1 refers to the next period dividend per share,
Po refers to the present value of a share of stock.
Compute the stock price of Stock W:
Hence, the stock price of the Stock W is $28.80.
Compute the dividend yield of the Stock W:
Hence, the dividend yield of the Stock W is 0.09 or 9%.
Compute the stock price of Stock X:
Hence, the stock price of the Stock X is $14.12.
Compute the dividend yield of the Stock X:
Hence, the dividend yield of the Stock X is 0.1699 or 16.99%.
Compute the stock price of Stock Y:
Hence, the stock price of the Stock Y is $10.36.
Compute the dividend yield of the Stock Y:
Hence, the dividend yield of the Stock Y is 0.22 or 22%.
Compute the stock price in Year 2 of Stock Z:
Note: The stock starts at constant growth rate in the Year 3. As a result, now determine the price of stock in Year 2.
Hence, the stock price in Year 2 of Stock Z is $77.41.
Compute the current stock price of Stock Z:
Hence, the stock price of the Stock Z is $61.54.
Compute the dividend yield of the Stock Z:
Hence, the dividend yield of the Stock Z is 0.0468 or 4.68%.
To determine: The capital gains yield of four stocks.
Introduction:
Capital gains yield is a ratio that indicates the rise in the price of a common stock.
Answer to Problem 31QP
The capital gains yield of Stock W is 8%.
The capital gains yield of Stock X is 0.01%.
The capital gains yield of Stock Y is −5%.
The capital gains yield of Stock Z is 12.32%.
Explanation of Solution
Given information:
Four different stocks have a required rate of return of 17%. The computed dividend yield of each of the four stocks is as follows:
- The dividend yield of Stock W is 9%.
- The dividend yield of Stock X is 16.99%.
- The dividend yield of Stock Y is 22%.
- The dividend yield of Stock Z is 4.68%.
The formula to calculate the capital gains yield:
Compute the capital gains yield of Stock W:
Hence, the capital gains yield of stock W is 0.08 or 8%.
Compute the capital gains yield of Stock X:
Hence, the capital gains yield of stock X is 0.0001 or 0.01%.
Compute the capital gains yield of Stock Y:
Hence, the capital gains yield of stock Y is −0.05 or −5%.
Compute the capital gains yield of Stock Z:
Hence, the capital gains yield of stock Z is 0.1232 or 12.32%.
Interpretation regarding the relationship among the various returns of each stock:
The entire four stocks have a required rate of return of 17%. However, this return is distributed in different ways between the capital gains and current income. As per the analysis, a higher growth stock has an appreciable capital gains yield but a relatively smaller current income yield. Moreover, a negative growth stock provides a higher current income even when the price decreases over time.
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Chapter 7 Solutions
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