Question

The appropriate discount rate for the following cash flows is 9 percent compounded quarterly.

Year	Cash Flow
1	$600
2	600
3	0
4	1,300

What is the present value of the cash flows?

Answer 1

Step 1 - Find the effective annual rate ;

EAR = [1+i/m]^m - 1

i - nominal rate = 9%

m - no. of compounding periods per year =4

EAR = (1+0.09/4)^4 - 1 = 1.0225^4 - 1

= 1.093083 - 1 = 0.093083 = 9.3083%

Step 2 - find the sum of present value of individual cash flows:

PV = FV/(1+r)^n

PV - Present value

FV - Future value

r - Interest rate

n - no. of periods

Present value of cash flows = 600/(1+0.093083)^1 + 600/(1+0.093083)^2 + 0/(1+0.093083)^3 + 1300/(1+0.093083)^4

= 548.9062 + 502.1633 + 0 + 910.6066 = 1961.6761

Present value of the given cash flows is $1961.68