Investors require a 7% rate of return on Levine Company's stock (i.e., r_{s} = 7%).
What is its value if the previous dividend was D_{0} = $2.00 and investors expect dividends to grow at a constant annual rate of (1) -7%, (2) 0%, (3) 4%, or (4) 6%? Do not round intermediate calculations. Round your answers to the nearest cent.
(1) $
(2) $
(3) $
(4) $
a.
P_{0} = D_{0} ( 1 + g) / (K_{e} -g)
P_{0} = Price of stock at year 0
D_{0} = Dividend at year 0 = $2
g = growth rate
K_{e} = Required rate of return = 7%
1. $2 ( 1- 0.07) /( 0.07 + 0.07) = $13.29
2. $2 /( 0.07) = $28.57
3. $2 ( 1+ 0.04) /( 0.07 - 0.04) = $69.33
4. $2 ( 1+ 0.06) /( 0.07 - 0.06) = $212
b. 1. P_{0} = 2(1.15) / (0.15 - 0.15) = Undefined
2. P_{0} = 2(1.20) / (0.15 - 0.20) = -$48 , which is a nonsense
IV . These results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate.
c. No,
IV It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. Such a stock, in theory, would become so large that it would eventually overtake the whole economy.
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