Chapter 7: Rate of Return Analysis Engineering Economic Analysis Canadian Edition

7-2EECE 450 — Engineering Economics Chapter 7 … nIntroduces the internal rate of return (IRR) method of evaluating project cash flows. nRelates IRR to net present value (NPV) by plotting NPV versus the discount rate. nUses an incremental technique and IRR to evaluate mutually exclusive alternatives.

7-3EECE 450 — Engineering Economics Internal Rate of Return (IRR) nDefinition (borrower’s perspective): the interest rate on the balance of a loan such that the unpaid loan balance equals zero when the final payment has been made.

7-4EECE 450 — Engineering Economics Internal Rate of Return (IRR) … nDefinition (investor’s perspective): the interest rate earned on the unrecovered investment such that the unrecovered investment equals zero at the end of the life of the investment.

7-5EECE 450 — Engineering Economics Calculating Internal Rate of Return nAlternate definition: the IRR is the discount rate that forces the NPV to zero. nThe best approach to calculating the IRR is to use a “solver” like a preprogrammed financial calculator or the IRR() function of Excel ®. nIf NPV is plotted versus the discount rate, we see that the IRR is at the zero-crossing (next page).

7-6EECE 450 — Engineering Economics Calculating Internal Rate of Return …

7-7EECE 450 — Engineering Economics Rate of Return Analysis nThe rate of return is the most frequently used measure of merit in industry. nCompare the rate of return (usually called the Internal Rate of Return or IRR) to the minimum acceptable rate of return (MARR). nIf IRR > MARR, accept the investment. nIf IRR < MARR, do not accept the investment. nIf IRR = MARR, the investment is marginally acceptable.

7-8EECE 450 — Engineering Economics Rate of Return Analysis … nWhere two or more mutually exclusive alternatives with the same lifetime will provide the same utility, the IRR is calculated on the difference between/among the alternatives. nAnalyze the incremental project: subtract the cash flows of a project with a lower initial cost from the one that has the highest initial cost. nIf  IRR > MARR, accept the alternative with the higher initial cost; otherwise accept the lower cost initial cost alternative.

7-9EECE 450 — Engineering Economics Rate of Return Analysis …

7-10EECE 450 — Engineering Economics Analysis Period nThe analysis period must be considered and can be used as a way of ensuring the lifetimes are equal for incremental analysis. nRecall that there are three possible cases: Useful life of the alternative equals the analysis period Alternatives have useful lives different from the analysis period The analysis period is infinite, n = .

Chapter Appendix 7A: Difficulties in Solving for an Interest Rate Engineering Economic Analysis Canadian Edition

7-12EECE 450 — Engineering Economics Problems with the IRR nThe IRR has some drawbacks that force us to be cautious when we use it: The IRR technique can not distinguish between investing and borrowing; and the criterion for acceptance depends on which it is. Multiple IRR values can occur when there are two or more reversals in the signs of the cash flows. The IRR technique assumes that all cash flows are borrowed and reinvested at the IRR rate of return during the project (may not be realistic). nThe NPV technique always works properly. The Modified IRR fixes some of the problems.

7-13EECE 450 — Engineering Economics Problems with the IRR … nExample of multiple IRRs:

7-14EECE 450 — Engineering Economics Modified Internal Rate of Return nTwo of the problems with the IRR can be solved by calculating the Modified Internal Rate of Return (MIRR): Multiple IRR values Financing and reinvesting at the IRR rate of return nThe MIRR technique requires two external rates of return: e inv for investing e fin for financing

7-15EECE 450 — Engineering Economics Modified Internal Rate of Return … nFind the present value at the start of the project of all negative cash flows using e fin as the discount rate. nFind the future value at the end of the project of all positive cash flows using e inv as the discount rate. nFind the rate of return MIRR that balances these two values at both ends of the project. nNote: this is an approximate technique; it produces a reliable result that can be used appropriately in the analysis/decision.

7-16EECE 450 — Engineering Economics Modified Internal Rate of Return … nExample of MIRR technique applied to the previous multiple IRR example:

7-17EECE 450 — Engineering Economics Suggested Problems n7-31, 36, 38, 39, 46, 52, 54. n7A-9, 23, 26. Note the instructions at the start of the problems for this section in the text.