Question

What is the present value of the following cash flow stream at a rate of 3.0% per year? Year 0: $0, Year 1: $75, Year 2: $225, Year 3: $0, Year 4: $300

Answer 1

Given the following information,

Year	Cashflows
0	0
1	75
2	225
3	0
4	300

Rate r = 3% = 0.03

We know that,

Net Present Value of the stream of cash flows is given by

NPV = CF0/(1+r)^0 + CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4

Where

CF0/(1+r)^0 = 0

CF1/(1+r)^1 = 75/(1+0.03)^1 = 75/1.03 = 72.82

CF2/(1+r)^2 = 225/(1+0.03)^2 = 225/1.03^2 = 225/1.0609 = 212.08

CF3/(1+r)^3 = 0

CF4/(1+r)^4 = 300/(1+0.03)^4 = 300/1.03^4 = 300/1.1255 = 266.55

NPV = 0 + 72.82 + 212.08 + 0 + 266.55

NPV = 551.45

Therefore, the present value of the given stream of cash flows is $551.45