Question

You buy a share of The Ludwig Corporation stock for $20.70. You expect it to pay dividends of $1.01, $1.14, and $1.2867 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of $30.50 at the end of 3 years.

1. Calculate the growth rate in dividends. Round your answer to two decimal places.
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2. Calculate the expected dividend yield. Round your answer to two decimal places.
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3. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return. What is this stock's expected total rate of return (assume market is in equilibrium with the required rate of return equal to the expected return)? Do not round intermediate calculations. Round your answer to two decimal places.
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Answer 1

a]

ending value = beginning value * (1 + growth rate)^{number of years}

Dividend in Year 3 = Dividend in Year 1 * (1 + growth rate)^{number of years}

$1.2867 = $1.01 * (1 + growth rate)²

growth rate = ($1.2867 / $1.01)^1/2 - 1

growth rate = 12.87%

b]

expected dividend yield = Dividend in Year 1 / current stock price

expected dividend yield = $1.01 / $20.70

expected dividend yield = 4.88%

c]

expected total rate of return = expected dividend yield + growth rate

expected total rate of return = 12.87% + 4.88%

expected total rate of return = 17.75%