A broker offers to sell you shares of Bay Area Healthcare which just paid a divi
ID: 2676379 • Letter: A
Question
A broker offers to sell you shares of Bay Area Healthcare which just paid a dividend of $2 per share. The dividend is expected to grow at a constant rate of 4% per year. The stock's required rate of return is 12%.a. what is the expected dollar dividend over the next three years?
b. what is the current value of the stock and the expected stock price at the end of each of the next three years?
c. what is the expected dividend yield and caital gains yield for each of the next three years?
d. what is the expected total return for each of the next three years?
e. how does the expected total return compare with the required rate of return on the stock? does this make sense? explain your answer.
Explanation / Answer
Dividend just paid (D0) = $2 per share
Expected dividend growth rate (G) = 4% per year
Stock’s required rate of return (R) = 12%
(A) What is the expected dollar dividend over the next three years:
Expected dollar dividend for the first year = [$2 * (1+0.04)]
= [$2 * 1.04]
= $2.08
Expected dollar dividend for the second year = [$2.10 * (1+0.04)]
= [$2.10 * 1.04]
= $2.204
Expected dollar dividend for the third year = [$2.205 * (1+0.04)]
= [$2.205 * 1.04]
= $2.314
(B) What is the current value of stock and the expected stock price at the end of the three years?
Expected stock price at the end of the 1st year (P1) = [D2 / (R + g)]
= [$2.205 / (0.12 + 0.04)]
= [$2.205 / 0.14]
= $15.75
Expected stock price at the end of the 2nd year (P2) = [D3 / (R + g)]
= [$2.315 / (0.12 + 0.04)]
= [$2.315 / 0.16]
= $14.468
Expected stock price at the end of the 3rd year (P3) = [D4 / (R + g)]
Expected Dividend for the 4th year (D4) = [$2.314 (1.04)]
Expected Dividend for the 4th year (D4) = [$2.406]
Expected Stock price at the end of the 3rd year (P3) = [D4 / (R + g)]
Expected Stock price at the end of the 3rd year (P3) = [$2.406 / (0.12 + 0.04)]
Expected Stock price at the end of the 3rd year (P3) = [$2.406 / 0.16]
Expected Stock price at the end of the 3rd year (P3) = $15.03
(C) What is the expected dividend yield and capital gains yield for each of the next 3 years?
Dividend yield = [Current year dividend payment / Current year stock value per share]
Expected dividend yield for the 1st year = [$2.10 / $12.97]
Expected dividend yield for the 1st year = 0.1619 (or) 16.19%
Expected dividend yield for the 2nd year = [$2.205 / $13.62]
Expected dividend yield for the 2nd year = 0.16189 (or) 16.19%
Expected dividend yield for the 3rd year = [$2.315 / $14.30]
Expected dividend yield for the 3rd year = 0.16188 (or) 16.19%
Capital gains yield = [(Ending Price – Beginning Price) / Beginning Price]
Capital gains yield for the first year = [($2.10 - $2) / $2]
Capital gains yield for the first year = 0.05 (or) 5%
Capital gains yield for the second year = [($2.205 - $2.10) / $2.10]
Capital gains yield for the second year = 0.04 (or) 4%
Capital gains yield for the third year = [($2.315 - $2.205) / $2.205]
Capital gains yield for the third year = 0.040 (or) 4%
(D) What is the expected total return for each of the 3 years:
Expected total return = [Dividend yield + Capital gains yield]
Expected total return for the first year = [$16.19% + 4%]
Expected total return for the first year = 21.19%
Expected total return for the second year = [0.16189 + 0.04]
Expected total return for the second year = 0.21189 (or) 21.2%
Expected total return for the third year = [0.16188 + 0.049]
Expected total return for the third year = 0.21088 (or) 21.08%
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