IRR vs XIRR

I am using Excel 2013. I am attempting to use Excel to calculate an annual percentage rate for uneven timing of cash flows. I am attempting to use Excel for this because APRWIN does not accurately calculate the APR on transactions that contain uneven timing of cash flows. I have attached a simplified example. This example contains even timing and amounts of cash flows. The most accurate annual percentage rate for this example is 31.9702%. When I use IRR, I am able to match this rate exactly. When I use XIRR, I am unable to match the rate. This gives me no confidence that XIRR can accurately calculate uneven timing of cash flows if it can not calculate this simple test example. I can not use IRR for uneven timing of cash flows. What am I missing here?