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QuestionSally bought 100 shares of Kelsey Drums stock at a 16% return. Now, with a 12% return, find her capital gain or loss.

Studdy Solution

STEP 1

Assumptions1. The dividend per share per year is $5.00. The dividend is expected to remain constant for the foreseeable future3. Sally purchased100 shares of Kelsey class A common10 years ago4. The required rate of return for the stock was16% when Sally purchased the shares5. The current required rate of return for the stock is12%
6. The value of a zero-growth stock is calculated as the annual dividend divided by the required rate of return

STEP 2

First, we need to find the purchase price of the stock10 years ago. We can do this by dividing the annual dividend by the required rate of return at that time.
Purchase price=Annual dividendRequired rate of returnPurchase\, price = \frac{Annual\, dividend}{Required\, rate\, of\, return}

STEP 3

Now, plug in the given values for the annual dividend and required rate of return to calculate the purchase price.
Purchase price=$5.0016%Purchase\, price = \frac{\$5.00}{16\%}

STEP 4

Convert the percentage to a decimal value.
16%=0.1616\% =0.16Purchase price=$.000.16Purchase\, price = \frac{\$.00}{0.16}

STEP 5

Calculate the purchase price per share.
Purchase price=$5.000.16=$31.25Purchase\, price = \frac{\$5.00}{0.16} = \$31.25

STEP 6

Now that we have the purchase price per share, we can find the total purchase price for the100 shares.
Total purchase price=Purchase price per share×Number of sharesTotal\, purchase\, price = Purchase\, price\, per\, share \times Number\, of\, shares

STEP 7

Plug in the values for the purchase price per share and the number of shares to calculate the total purchase price.
Total purchase price=$31.25×100Total\, purchase\, price = \$31.25 \times100

STEP 8

Calculate the total purchase price.
Total purchase price=$31.25×100=$3,125Total\, purchase\, price = \$31.25 \times100 = \$3,125

STEP 9

Now, we need to find the current price of the stock. We can do this by dividing the annual dividend by the current required rate of return.
Current price=Annual dividendCurrent required rate of returnCurrent\, price = \frac{Annual\, dividend}{Current\, required\, rate\, of\, return}

STEP 10

Now, plug in the given values for the annual dividend and current required rate of return to calculate the current price.
Current price=$5.0012%Current\, price = \frac{\$5.00}{12\%}

STEP 11

Convert the percentage to a decimal value.
%=0.\% =0.Current price=$5.000.Current\, price = \frac{\$5.00}{0.}

STEP 12

Calculate the current price per share.
Current price=$5.000.12=$41.67Current\, price = \frac{\$5.00}{0.12} = \$41.67

STEP 13

Now that we have the current price per share, we can find the total current price for the100 shares.
Total current price=Current price per share×Number of sharesTotal\, current\, price = Current\, price\, per\, share \times Number\, of\, shares

STEP 14

Plug in the values for the current price per share and the number of shares to calculate the total current price.
Total current price=$41.67×100Total\, current\, price = \$41.67 \times100

STEP 15

Calculate the total current price.
Total current price=$41.67×100=$4,167Total\, current\, price = \$41.67 \times100 = \$4,167

STEP 16

Now that we have the total purchase price and the total current price, we can calculate the capital gain or loss by subtracting the total purchase price from the total current price.
Capital gain or loss=Total current price−Total purchase priceCapital\, gain\, or\, loss = Total\, current\, price - Total\, purchase\, price

STEP 17

Plug in the values for the total current price and the total purchase price to calculate the capital gain or loss.
Capital gain or loss=$4,167−$3,125Capital\, gain\, or\, loss = \$4,167 - \$3,125

STEP 18

Calculate the capital gain or loss.
Capital gain or loss=$4,167−$3,125=$,042Capital\, gain\, or\, loss = \$4,167 - \$3,125 = \$,042ally will have a capital gain of $,042 on her shares.

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