Analysts expect Marble Comics to pay shareholders $1.00 per share annually for the next ﬁve years. After that, the dividend will be $1.50 annually forever. Given a discount rate of 10%, what is the value
Of the stock today?

Question

Quizplus · Accepted Answer

We can use the formula for calculating the present value of a growing perpetuity to find the value of the stock today: 
PV = (D/(r-g))
PV = Present value 
D = Dividend 
r = Discount rate 
g = Growth rate 
For the first five years, the dividend will be $1.00 per year, so the present value of this cash flow is: 
PV1-5 = [(1.00/1.1) + (1.00/1.1^2) + (1.00/1.1^3) + (1.00/1.1^4) + (1.00/1.1^5)]
PV1-5 = $4.02
After the first five years, the dividend will grow at a constant rate of $1.50 per year. The present value of this cash flow is: 
PV6-infinity = (1.50/(0.1-0.03))
PV6-infinity = $19.08
Therefore, the total present value of the cash flows is: 
PV = PV1-5 + PV6-infinity 
PV = $4.02 + $19.08 
PV = $23.10 
So, the value of the stock today is $23.10, rounded to the nearest cent. Therefore, the best choice is D.

Analysts Expect Marble Comics to Pay Shareholders $1