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QuestionFawlty Foods paid a \$1.40 dividend, closing price \$21, required return 12%. Find growth rate, dividend yield, and capital gains yield.

Studdy Solution

STEP 1

Assumptions1. The annual dividend per share is 1.40.Theclosingpriceofthestockis1.40. The closing price of the stock is 213. The market's required return or capitalization rate is12%
4. Dividends are expected to grow at a constant rate forever

STEP 2

We will use the Gordon Growth Model to calculate the implied growth rate in dividends. The Gordon Growth Model is given by=r−g = \frac{}{r - g}Where- is the price of the stock- D is the dividend per share- r is the required return or capitalization rate- g is the growth rate of dividends

STEP 3

Rearrange the Gordon Growth Model equation to solve for the growth rate (g).
g=r−g = r - \frac{}{}

STEP 4

Now, plug in the given values for the dividend per share (), the required return (r), and the price of the stock () to calculate the growth rate (g).
g=12%−$1.40$21g =12\% - \frac{\$1.40}{\$21}

STEP 5

Convert the percentage to a decimal value.
12%=0.1212\% =0.12g=0.12−$1.40$21g =0.12 - \frac{\$1.40}{\$21}

STEP 6

Calculate the growth rate.
g=0.12−$1.40$21=0.06g =0.12 - \frac{\$1.40}{\$21} =0.06So, the implied growth rate in dividends is6%.

STEP 7

The dividend yield is calculated as the annual dividend per share divided by the price per share.
Dividend yield=Dividend\, yield = \frac{}{}

STEP 8

Plug in the given values for the dividend per share () and the price per share () to calculate the dividend yield.
Dividend yield=$1.40$21Dividend\, yield = \frac{\$1.40}{\$21}

STEP 9

Calculate the dividend yield.
Dividend yield=$.40$21=.067Dividend\, yield = \frac{\$.40}{\$21} =.067So, the expected dividend yield is6.7%.

STEP 10

The capital gains yield is the difference between the required return and the dividend yield. It can be calculated asCapital gains yield=r−Dividend yieldCapital\, gains\, yield = r - Dividend\, yield

STEP 11

Plug in the given values for the required return (r) and the dividend yield to calculate the capital gains yield.
Capital gains yield=0.−0.067Capital\, gains\, yield =0. -0.067

STEP 12

Calculate the capital gains yield.
Capital gains yield=0.12−0.067=0.053Capital\, gains\, yield =0.12 -0.067 =0.053So, the expected capital gains yield is5.%.
a. The implied growth rate in dividends is6%. b. The expected dividend yield is6.7%. c. The expected capital gains yield is5.%.

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