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Assume that the risk-free rate of interest is 2% and the expected rate of return on the market is 8%. A share of stock sells for $50 today. It will pay a dividend of $3 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year?

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Answer: $51.60

Explanation:

The Gordon growth model can be used to calculate this however both the required return and the growth rate will need to be solved for.

Required return using CAPM;

= Risk free rate + beta * ( market return - risk free rate)

= 2% + 1.2 * ( 8% - 2%)

= 9.2%

Current price is $50. Using Gordon growth model, growth is;

Price = Next dividend / ( Required return - growth rate)

50 = 3 / ( 9.2% - g)

( 9.2% - g) * 50 = 3

( 9.2% - g) = 3/50

g = 9.2% - 3/50

g = 3.2%

Stock price at end of year using Gordon growth model;

= (3 * ( 1 + 3.2%)) / ( 9.2% - 3.2%)

= $51.60

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