Question

Roger purchased a stock for $16 a share. The stock paid a $1 annual dividend and increased in price by $2 a year for the following three years. What is the arithmetic average annual capital gain? The arithmetic average annual total return?

Answer 1

11.20%, 16.80%

Step-by-step explanation:

Purchase Price
`P_(0)` = $16

Year 1 end closing price
`P_(1)`= $18

Capital Gain Yield for the first year =
`(P_(1)\ -\ P_(0) )/(P_(0) )` =
`(18\ -\ 16)/(16)` = 12.5%

Capital Gain Yield for the second year =
`(20\ -\ 18)/(18)` = 11.11%

Capital gain yield for the third year =
`(22\ -\ 20)/(20)` = 10%

Average annual capital gain yield =
`(12.5\ +\ 11.11+\ 10)/(3)` = 11.20% approx

Dividend yield for first year =
`(D_(1) )/(P_(0) )` =
`(1)/(16)` = 6.25%

Dividend yield for the second year =
`(D_(2) )/(P_(1) )` =
`(1)/(18)` = 5.55%

Dividend yield for the third year =
`(D_(3) )/(P_(2) )` =
`(1)/(20)` = 5%

Average Annual Yield =
`(12.5\ +\ 6.25\ +\ 11.11\ +\ 5.55\ +\ 10\ +\ 5 )/(3)` =
`(50.41)/(3)` = 16.80%