Engineering Economy

Question

The future worth in year 10 of an arithmetic gradient cash flow series for years 1 through 10 is $525,000. If the gradient increase each year, G, is $2500, determine the cash flow in year 1 at an interest rate of 6% per year.

Answer 1

Posting formulas here seems messy, so I will do a walk through with Excel. The future value is $575,000. So, you must find 10 cash flows and the year 0 (starting) present value.

Excel gives an easy formula for this: PV(rate, #periods, pmt, future value). If you plug in the following, you get your answer: PV(.06, 10, 0, 575000), or $321,077. You can also use this formula: 575000* (1.06)^-10.

I'm not even going to attempt a formula for cash flow, but you can think about it logically here. There is a starting cash flow value (what we are trying to solve) and each year we add $2500 to it. In total, our Year 0 PV + cash flows = 575,000.

Year Start CF

1 321077 14142.3

2 16642.3

3 19142.3

4 21642.3

5 24142.3

6 26642.3

7 29142.3

8 31642.3

9 34142.3

10 36642.3

Total 575000