Question

An arithmetic cash flow gradient series equals $400 in year 1, $500 in year 2, and amounts increasing by $100 per year through year 10. At i = 9% per year, determine the present worth of the cash flow series in year 0. The present worth of the cash flow series in year 0 is $ .?

Answer 1

Present Value = Future Value / ( 1 + r / 100) ^ n

Here, rate of interest (r) = 9% , n = number of years

Present worth of cash flow = First year value / (1+0.09)^1 + Second Year Value / (1+0.09)^2 ...till Tenth Year Value/(1+0.09)^10

First Year Value = 400 / (1.09) ^ 1 = 366.97

Second Year = 500 / (1.09) ^ 2 = 420.84

In a similar manner, we will calculate all the values till 10th cash flow as shown in the below table:

So, from the table we can see, that Present Value of cash flow is $5004.34.