So I have this problem and don't understand why the solution is as stated below.

A four-year investment project calls for an investment in working capital equal to 20% of next period’s sales. Estimated sales for the project in year one through four is: 200, 150, 120, 180, respectively.

What is the net present value of the working capital investment if the discount rate is 10%?

The cash flow is as follows

Code:

Period: 0 1 2 3 4
Sales: 0 200 150 120 180
WC 40 30 24 36 0
change in WC: -40 10 6 -12 36

$\displaystyle PV = -40 + \frac{10}{1.10} + \frac{6}{1.10^2} - \frac{12}{1.10^3} + \frac{36}{1.10^4} \approx -10.38$

Why do I need to calculate the "change in working capital" (last line in the cash flow) to get the correct answer?

The way I read the problem, I thought I only had to calculate the present value of the working capital (ie: 2nd line).