1. Rate of Return Analysis Chapter 7: Newnan, Eschenbach, and Lavelle Dr. Hurley’s AGB 555 Course

2. Internal Rate of Return This is the interest rate where net present worth is equal to zero or equivalent uniform annual worth are equal to zero It can also be considered the interest necessary to take the principal left on a loan to zero when the final payment on the debt is due In short, it is the rate that causes the benefits equal to the costs adjusted by discounting

3. Calculating the Rate of Return It can be calculated by finding the rate that makes the following true: Present worth of benefits minus the present worth of costs equal to zero The ratio of present worth of benefits to present worth of costs equal to one Present worth equal to zero Equivalent uniform annuity worth equal to zero Present worth of cost equal to present worth of benefits

4. Incremental Analysis When you have two alternatives, it may be of value to estimate the IRR based on the incremental returns between the two alternatives The book suggests that when ΔIRR≥MARR you should choose the higher cost alternative and when ΔIRR<MARR you should choose the lower cost alternative assuming that you are examining increments of investments Where MARR is the minimum attractive rate of return Where you are examining increments of borrowing, the choosing rule above is reversed You need to use caution when deciding what the higher cost option is; it may not be immediately clear

5. Modified Internal Rate of Return There are some investment opportunities that have multiple IRR’s because of changing signs of the net returns through the investment horizon Since this can cause ambiguity as to which return is the appropriate one, some people use the modified internal rate of return (MIRR) The MIRR calculates the interest rate that would cause the present worth of the expenses (PW e ) to equal the future worth (FW r ) of the receipts, i.e., PW e *(1+MIRR)^ n = FW r It should be noted that the PW of the expenses should be valued at the borrowing rate, while the PW of receipts is valued at the investment rate

6. Modified Internal Rate of Return Cont. Excel has a function that calculates the modified internal rate of return known as MIRR(values, finance_rate, reinvest_rate) In the MIRR function, values that are negative are considered costs and values that are positive are considered incomes