Question

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.

Answer 1

Given that,

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%