## Irr2088

In this case, the net present value rule ranks the second investment higher, while the IRR rule ranks first investment as the better project. The differences arise because the NPV rule assumes that intermediate cash flows get invested at the hurdle rate, which is 15%. The IRR rule assumes that intermediate cash flows get reinvested at the IRR of that project. While both projects are impacted by this assumption, it has a much greater effect for project A, which has higher cash flows earlier on. The reinvestment assumption is made clearer if the expected end balance is estimated under each rule. End Balance for ATM1 with IRR of 21.41% = \$10,000,000*1.21414 = \$21,730,887 End Balance for ATM2 with IRR of 20.88% = \$10,000,000*1.20884 = \$21,353,673 To arrive at these end balances, however, the cash flows in years 1, 2, and 3 will have to be reinvested at the IRR. If they are reinvested at a lower rate, the end balance on these projects will be lower than the values stated above, and the actual return earned will be lower than the IRR even though the cash flows on the project came in as anticipated.

The reinvestment rate assumption made by the IRR rule creates more serious

Modified Internal Rate of Return (MIRR):

This is the internal rate of return, computed on the assumption that intermediate cashflows are reinvested at the hurdle rate.

consequences the longer the term of the project and the higher the IRR, since it implicitly assumes that the firm has and will continue to have, a fountain of projects yielding returns similar to that earned by the project under consideration.

A Solution to the Reinvestment Rate Problem: The Modified Internal Rate of Return One solution that has been suggested for the reinvestment rate assumption is to assume that intermediate cash flows get reinvested at the hurdle rate - the cost of equity if the cash flows are to equity investors and the cost of capital if they are to the firm - and to calculate the internal rate of return from the initial investment and the terminal value. This approach yields what is called the modified internal rate of return (MIRR), as illustrated in Figure 5.11.

Figure 5.11: IRR versus Modified Internal Rate of Return Cash Flow \$ 300 \$ 400 \$ 500

Investment <\$ 1000>

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