12. In a recent period Joshua Inc. reported earnings per share (EPS) of $4 and following its
policy just paid a dividend based on a payout ratio of 50%. The company’s share price
and dividends have grown at an average of 5% per year, and there is no reason to
expect that this will change in the future. You want to buy Joshua stock and have
determined that the market expected return for this type of stocks is 16%. If Joshua
stock was trading at $18.45 on the market, you would likely
A) not buy the stock because the fair value is $ 17.27
B) not buy the stock because the fair value is $18.18
C) buy the stock because the fair value is $19.09
D) buy the stock because the fair value is $36.36
E) buy the stock because the fair value is $66.67
Answer C
We answer this question using the dividend discount model where the fair value of
the stock can be calculated as P
0 = D
1 / (r – g), where the growth rate g = 5%.
The current dividend D
0 is 50% of EPS or $2.00 therefore the expected dividend
D
1 = D
0 (1 + g) = $2.00 (1 + 0.05) = $2.10.
The fair value of the stock P
0 = $2.10 / (0.16 – 0.05) = $19.09.
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