Question

Question 1 (Show calcultions) Not in tableform

On March 22, 2017, Woodlands paid annual dividend of R2.50 per share. Because Woodlands’ financial prospects are particularly bright, investors believe that the company will increase its dividend by 20 percent per year for the next four years. After that, Woodlands will increase the dividend at a modest annual rate of 4 percent. Investors require a 16 percent return on Woodlands stock, and Woodlands always make its dividend payment on March 22 each year.

Required: 1.1. What is the price of Woodlands stock on March 23, 2017? [2]

1.2. What is the price of Woodlands stock on March 23, 2018? [2]

1.3. Calculate the percentage change in price of Woodlands stock from March 23, 2017, to March 23, 2018. [2]

1.4. For an investor who bought Woodlands stock on March 23, 2017, received a dividend on March 22, 2018, and sold the stock on March 23, 2018, what was the total rate of return on the investment? How much of this return came from the dividend, and how much came from the capital gain? [4]

1.5. What is the price of Woodlands stock on March 23, 2021? [3]

1.6. What is the price of Woodlands stock on March 23, 2022? [3]

1.7. For an investor who bought Woodlands stock on March 23, 2021, received a dividend on March 22, 2022, and sold the stock on March 23, 2022, what was the total rate of return on the investment? How much of this return came from the dividend, and how much came the capital gains? Comment on the differences between your answers to this question and your answers in part (1.4). [4]

Answer 1

dividend paid on March 22, 2017 , d0 = 2.50

growth rate of dividends for 1st 4 years , g1 = 20% = 0.20

growth rate of dividends after 1st 4 years , g2 = 4% = 0.04

required return , r = 16% = 0.16

dividend paid on March 22, 2018 , d1 = d0*(1+g1) = 2.5*(1+0.20) = 3

dividend paid on March 22, 2019 , d2 = d1*(1+g1) = 3*(1+0.20) = 3.6

dividend paid on March 22, 2020 , d3 = d2*(1+g1) = 3.6*(1+0.20) = 4.32

dividend paid on March 22, 2021 , d4 = d3*(1+g1) = 4.32*(1+0.20) = 5.184

dividend paid on March 22, 2022 , d5 = d4*(1+g2) = 5.184*(1+0.04) = 5.39136

1.1)

price on March 23, 2017, p0 = {d1*[(1-((1+g1)/(1+r))⁴]/(r-g1)} + [d5/((r - g2)*(1+r)⁴)]

= {3*[(1-((1+0.20)/(1+0.16))⁴]/(0.16-0.20)} + [5.39136/((0.16 - 0.04)*(1+0.16)⁴)]

= {3*[(1-((1.20)/(1.16))⁴]/(0.16-0.20)} + [5.39136/((0.12)*(1.16)⁴)]

= 10.89231154 + 24.81333445 = 35.70564599 or 35.71 ( rounding off to 2 decimal places)

1.2)

price of Woodlands stock on March 23, 2018, p1 = {d2*[(1-((1+g1)/(1+r))³]/(r-g1)} + [d5/((r - g2)*(1+r)³)]

= {3.6*[(1-((1.20)/(1.16))³]/(0.16-0.20)} + [5.39136/((0.16 - 0.04)*(1.16)³)]

= 9.635081389 + 28.78346796 = 38.41854935 OR 38.42 ( rounding off to 2 decimal places)

1.3)

percentage change in price of Woodlands stock from March 23, 2017, to March 23, 2018, P =

[(price of Woodlands stock on March 23, 2018 - price of Woodlands stock on March 23, 2017)/(price of Woodlands stock on March 23, 2018)]*100

= [(38.41854935 - 35.70564599)/35.70564599]*100 = 7.597967% or 7.60% ( rounding off to 2 decimal places)

1.4)

total rate of return on the investment , R= [d1+(p1-p0)]/p0 = [3+(38.41854935 - 35.70564599)]/35.70564599

= 0.16 or 16%

return from capital gain = P = percentage change in price of Woodlands stock from March 23, 2017, to March 23, 2018 = 7.597967%

return from dividends = R-P = 16-7.597967 = 8.402033% or 8.40% ( rounding off to 2 decimal places)