Gareth owns 1 share of stock A and 1 share of stock B. In 1 year from today, the total value of his holdings is expected to be 175.63 dollars. Stock A is currently priced at 88.06 dollars, has an expected return of 10.62 percent, and is expected to pay a dividend of 4.38 dollars in 1 year from today. Stock B is currently priced at 82.11 dollars and is expected to pay a dividend of 6.11 dollars in 1 year from today. What is the expected return for stock B? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.
Gareth owns 1 share of stock A and 1 share of stock B
In one year, total value = $175.63
current price of stock A Pa = $88.06
Current price of stock B Pb = $82.11
expected dividend for stock A, Da = $4.38
expected dividend for stock b, Db = $6.11
Expected return of stock A ra = 10.62%
So, price of stock A at year 1, is PA1 = (Pa*(1+ra) - Da) = (88.06*1.1062 - 4.38 = $93.03
Similarly, price of stock B at year a is PB1 = (Pb*(1+rb) - Db) = (82.11*(1+rb) - 6.11)
So, equating total value, we get
93.03 + (82.11*(1+rb) - 6.11) = 175.63
=> rb = 8.04%
So, Expected return on stock B is 8.04%
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