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

Answer:

11.20%, 16.80%

Explanation:

Purchase Price $P_{0}$ = $16

Year 1 end closing price $P_{1}$= $18

Capital Gain Yield for the first year =  $\frac{P_{1}\ -\ P_{0} }{P_{0} }$   = $\frac{18\ -\ 16}{16}$  = 12.5%

Capital Gain Yield for the second year = $\frac{20\ -\ 18}{18}$ = 11.11%

Capital gain yield for the third year = $\frac{22\ -\ 20}{20}$ = 10%

Average annual capital gain yield = $\frac{12.5\ +\ 11.11+\ 10}{3}$ =  11.20% approx

Dividend yield for first year = $\frac{D_{1} }{P_{0} }$  = $\frac{1}{16}$ = 6.25%

Dividend yield for the second year = $\frac{D_{2} }{P_{1} }$ = $\frac{1}{18}$ = 5.55%

Dividend yield for the third year = $\frac{D_{3} }{P_{2} }$ = $\frac{1}{20}$ = 5%

Average Annual Yield = $\frac{12.5\ +\ 6.25\ +\ 11.11\ +\ 5.55\ +\ 10\ +\ 5 }{3}$ =  $\frac{50.41}{3}$ = 16.80%