Four different stocks, all of which have a required return of 20 percent and a most recent...

Question:

Four different stocks, all of which have a required return of 20 percent and a most recent dividend of $3.80 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and 5 percent per year, respectively. Stock Z is a growth stock that will increase its dividend by 20 percent for the next two years and then maintain a constant 15 percent growth rate thereafter.

What is the dividend yield for each of these four stocks? (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Dividend Yield
Stock W %
Stock X %
Stock Y %
Stock Z %

What is the expected capital gains yield for each of these four stocks? (Leave no cells blank - be certain to enter "0" wherever required. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Capital gains yield
Stock W %
Stock X %
Stock Y %
Stock Z %

Dividend Yield:

The dividend yield is a ratio which compares the annual dividend which is paid on the common stocks with the existing market price of the stock.

Dividend Yield = Dividend/Stock price

Answer and Explanation:

1.

For stock W:

{eq}Stock \ price \ = \ \dfrac{3.80\left ( 1 \ + \ 0.10 \right )}{\left ( 0.20 \ - \ 0.10 \right )} \\ Stock \ price \ = \ \dfrac{3.80 \ \times \ 1.10}{0.10} \\ Stock \ price \ = \ \$41.8 {/eq}


Dividend = 3.80 * (1 + 0.10)

Dividend = 3.80 * 1.10

Dividend = 4.18


{eq}Dividend \ Yield \ = \ \dfrac{Dividned}{Stock \ price} \\ Dividend \ Yield \ = \ \dfrac{4.18}{41.8} \\ Dividend \ Yield \ = \ 0.1 \ = \ 10\% {/eq}


For stock X:

{eq}Stock \ price \ = \ \dfrac{3.80}{0.20} \\ Stock \ price \ = \ \$19 {/eq}


{eq}Dividend \ Yield \ = \ \dfrac{Dividned}{Stock \ price} \\ Dividend \ Yield \ = \ \dfrac{3.80}{19} \\ Dividend \ Yield \ = \ 0.20 \ = \ 20\% {/eq}


For stock Y:

{eq}Stock \ price \ = \ \dfrac{3.80\left ( 1 \ - \ 0.05 \right )}{\left ( 0.20 \ + \ 0.05 \right )} \\ Stock \ price \ = \ \dfrac{3.80 \ \times \ 0.95}{0.25} \\ Stock \ price \ = \ \$14.44 {/eq}


Dividend = 3.80 * (1 - 0.05)

Dividend = 3.80 * 0.95

Dividend = 3.61


{eq}Dividend \ Yield \ = \ \dfrac{Dividned}{Stock \ price} \\ Dividend \ Yield \ = \ \dfrac{3.61}{14.44} \\ Dividend \ Yield \ = \ 0.25 \ = \ 25\% {/eq}


For stock Z:

{eq}Stock \ price (year \ 2) \ = \ \dfrac{3.80 \ \times \ (1 \ + \ 0.20)^2 \ \times \ (1 \ + \ 0.15)}{0.20 \ - \ 0.15} \\ Stock \ price (year \ 2) \ = \ \dfrac{3.80 \ \times \ 1.20^2 \ \times \ 1.15}{0.05} \\ Stock \ price (year \ 2) \ = \ \$125.86 {/eq}

The price of stock today is the present value of first three dividends, plus present value of year 3 stock prices.

Stock price = $95


Dividend = 3.80 * (1 + 0.20)

Dividend = 3.80 * 1.20

Dividend = 4.56


{eq}Dividend \ Yield \ = \ \dfrac{Dividned}{Stock \ price} \\ Dividend \ Yield \ = \ \dfrac{4.56}{95} \\ Dividend \ Yield \ = \ 0.048 \ = \ 4.8\% {/eq}


2.

For Stock W:

Capital gain yield = Total return - Dividend Yield

Capital gain yield = 20% - 10%

Capital gain yield = 10%


For Stock X:

Capital gain yield = Total return - Dividend Yield

Capital gain yield = 20% - 20%

Capital gain yield = 0


For Stock Y:

Capital gain yield = Total return - Dividend Yield

Capital gain yield = 20% - 25%

Capital gain yield = -5%


For Stock Z:

Capital gain yield = Total return - Dividend Yield

Capital gain yield = 20% - 4.8%

Capital gain yield = 15.2%


Learn more about this topic:

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What Is Dividend Yield? - Definition & Calculation

from Corporate Finance: Help & Review

Chapter 2 / Lesson 10
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