Winter Green Decors announced today that it will begin paying annual dividends. The ﬁrst dividend will be paid next year in the amount of $.40 a share. The following dividends will be $.60, $.85, and
$1.00 a share annually for the following 3 years, respectively. After that, dividends are projected to
Increase by 2% per year. How much are you willing to pay to buy one share of this stock today if
Your desired rate of return is 10%?

Question

Quizplus · Accepted Answer

To calculate the present value of all future cash flows (dividends), we can use the dividend discount model:

PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + ... + Dn/(1+r)^n

Where:
PV = Present Value
D1, D2, D3...Dn = Dividends for each year
r = Desired rate of return

Using the information given:

D1 = $0.40
D2 = $0.60
D3 = $0.85
D4 = $1.00

Next, we need to calculate the present value of the dividends from Year 5 and beyond, which are projected to increase by 2% per year. We can use the formula:

Dn = Dn-1 x (1+g)

Where:
Dn = Dividend in Year n
Dn-1 = Dividend in Year n-1
g = Growth rate

In this case: 
D5 = $1.00 x (1+0.02) = $1.02
D6 = $1.02 x (1+0.02) = $1.04
D7 = $1.04 x (1+0.02) = $1.06
and so on.

We can then calculate the present value of these future dividends using the formula for perpetuity:

PV = Dn / (r-g)

Where: 
PV = Present value 
Dn = Dividend in year n (in this case, D5, D6, D7...)
r = Desired rate of return 
g = Growth rate (2% in this case)

Summing up all the present values of dividends, we get:

PV = $0.40/(1+0.10) + $0.60/(1+0.10)^2 + $0.85/(1+0.10)^3 + $1.00/(1+0.10)^4 + ($1.02/(0.10-0.02))/(1+0.10)^4 + ($1.04/(0.10-0.02))/(1+0.10)^5 + ($1.06/(0.10-0.02))/(1+0.10)^6 + ...

Calculating this using a financial calculator or spreadsheet software, we get:

PV = $10.89

Therefore, the best choice is B) $10.89.

Winter Green Decors Announced Today That It Will Begin Paying