Question

2A. Firm ABC paid an annual dividend of $2.00 per share last year. Management just announced that future dividends will increase by 2 percent annually. What is the amount of the expected dividend in year 5? 

2B. Firm ABC is going to pay an annual dividend of $2.00 per share next year. Management just announced that future dividends will increase by 2 percent annually. What is the amount of the expected dividend in year 5? 

2C. Firm ABC is going to pay an annual dividend of $2.00 per share next year. Management just announced that future dividends will increase by 5 percent annually in the first two years and 2 percent annually afterwards. What is the amount of the expected dividend in year 5?

Answer 1

2 A. Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = Annual dividend = $2, r = rate of interest = 2%, n= time period = 5

now, putting theses values in the above equation, we get,

FV = $2 * (1 + 2%)5

FV = $2 * (1 + 0.02)5

FV = $2 * (1.02)5

FV = $2 * 1.1040808032

FV = $2.208161

So, expected dividend in year 5 is $2.208161.

2 B. Dividend will start growing from next year. So, time period (n) here will be 4 years.

where, FV = Future value, PV = Present value = Dividend next year = $2, r = rate of interest = 2%, n= time period = 4

now, putting theses values in the above equation, we get,

FV = $2 * (1 + 2%)4

FV = $2 * (1 + 0.02)4

FV = $2 * (1.02)4

FV = $2 * 1.08243216

FV = $2.16486432

So, expected dividend in year 5 is $2.16486432.

2 C. Annual dividends will grow by 5% for second and third year and it will grow by by 2% for fourth and fifth year. Now the formula will become as below:

FV = PV * (1 + r1%)n1 * (1 + r2%)n2

where, FV = Future value, PV = Present value = Dividend next year = $2, r1 = rate of interest for second and third year = 5%, r2 = rate of interest for fourth and fifth year = 2%, n1 = time period = 2 and n2 = time period = 2

now, putting theses values in the above equation, we get,

FV = $2 * (1 + 5%)2 * ( 1 + 2%)2

FV = $2 * (1 + 0.05)2 * (1 + 0.02)2

FV = $2 * (1.05)2 * (1.02)2

FV = $2 * 1.1025 * 1.0404

FV = $2.294082

So, expected dividend in year 5 is $2.294082

Answer 2

ANSWER :

2A.

Given :

D0 = 2 ($)

g = 2 % = 0.02

So,

D5 = D0 ( 1 + 0.02)^5 = 2 * 1.02^5 = 2.21 ($) (ANSWER)

2B.

Given :

D1 = 2 ($)

g = 2 % = 0.02

So,

D5 = D1 ( 1 + 0.02)^4 = 2 * 1.02^4 = 2.16 ($) (ANSWER)

2C.

Given :

D1 = 2 ($)

g = 5 % = 0.05 in the first 2 years and 2% thereafter.

So,

D5 = D1 ( 1 + 0.05)^2 * (1 + 0.02)^2  = 2 * 1.05^2 * 1.02^2 = 2.29 ($) (ANSWER)