Question

n ordinary share pays dividend every year at a constant growth rate of g p.a. forever. The share has just paid a dividend of $3. Jacky buys the share today for $40 at a rate of return of 12% p.a. for the next 12 months.

Which of the following can be used to calculate the return on income for Jacky if he plans to sell the share in 12 months immediately after he receives the dividend (only one correct answer)?

3/40

3*1.12/40

3*(1+g)/40+g

None of the options give the correct answer.

3*(1+g)/40

3*(1+g)/40+0.12

Calculate the annual growth rate g for this share. (Round your answer to a percentage of 2 decimals without the “%” symbol. E.g. if you answer is 0.12345, you should input “12.35”.)

3/40

3*1.12/40

3*(1+g)/40+g

None of the options give the correct answer.

3*(1+g)/40

3*(1+g)/40+0.12

Calculate the annual growth rate g for this share. (Round your answer to a percentage of 2 decimals without the “%” symbol. E.g. if you answer is 0.12345, you should input “12.35”.)

Answer

Answer 1

Answer is 3*(1+g)/40.

return on income is the dividend to be received by Jacky.

return on income = dividend to be received/purchase price of stock

dividend to be received will be dividend just paid*(1+constant growth rate) because dividend just paid will grow by constant growth rate next year.

return on investment will also include the capital gain which is the difference between selling price and purchase price of the stock. return on investment = (capital gain + dividend received)/purchase price of stock

rate of return = [dividend just paid*(1+constant growth rate)/price of stock] + constant growth rate

0.12 = [3*(1+g)/$40] + g

0.12 - g = (3 + 3g)/$40

$40*(0.12 - g) = (3 + 3g)

4.8 - 40g = 3 + 3g

4.8 - 3 = 3g + 40g

1.8 = 43g

g = 1.8/43 = 0.0419 or 4.19%

the annual growth rate g for this share is 4.19.