So let's summarize what we've discussed. The IRR is a great basis on which to appraise investments. However, it does have some shortcomings. Notably, if we have investments of different lengths, it fails to factor in a separate reinvestment rate. Furthermore, it struggles when we have cash flows changing in direction multiple times. To address these issues, we turn to the modified internal rate of return, which is essentially the compound annual growth rate formula. It turns an investment into a zero coupon bond. The more predominant and reliable investment appraisal technique is net present value or NPV. It's great where we have investments of different sizes and different lengths and doesn't get tied up if we have multiple changes in cashflow directions. Finally, each of these techniques we've been discussing uses a discount rate, sometimes referred to as a cost of financing. This is essentially a hurdle rate, a minimum required rate of return that the investment being appraised is required to meet.