Calculation of Working Capital in Capital Budget Analysis

I know working capital is deducted at time zero and added back in the final time period when performing capital budget analysis. However, I was given a problem where the ending balance of current assets in a 6 year project is as follows:

Time 0: $0

Year 1: $2000

Year 2: $2000

Year 3: $2000

Year 4: $2000

Year 5: $2000

Year 6: $0

Over the same time period, the ending balance of current liabilities is as follows:

Time 0: $0

Year 1: $1000

Year 2: $1000

Year 3: $1000

Year 4: $1000

Year 5: $1000

Year 6: $0

Does this mean that the $1000/year in working capital ($2000-$1000) is discounted back to time 0 in order to calculate the deduction in the initial outlay? In this case, the cost of capital is 10%, so present value would be $3790.79.

Would I be correct in deducting the $3790.79 in year 0 and adding it back in year 6?