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

2. Chapter 7 …
Introduces the internal rate of return (IRR) method of evaluating project cash flows.
Relates IRR to net present value (NPV) by plotting NPV versus discount rate.
Uses an incremental technique and IRR to evaluate mutually exclusive alternatives.

3. Internal Rate of Return (IRR)
Definition (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.

4. Internal Rate of Return (IRR) …
Definition (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.

5. Calculating Rate of Return
Alternate definition: the IRR is the discount rate that forces the NPV to zero.
The best approach to calculating the IRR is to use a “solver” like a preprogrammed financial calculator or the IRR() function of Excel®.
If NPV is plotted versus the discount rate, we see that the IRR is at the zero-crossing (next page).

6. Calculating Rate of Return …

7. Rate of Return Analysis
The rate of return is the most frequently used measure of merit in industry.
Compare the rate of return (usually called the Internal Rate of Return or IRR) to the minimum acceptable rate of return (MARR).
If IRR > MARR, accept the investment.
If IRR < MARR, do not accept the investment.
If IRR = MARR, the investment is marginally acceptable.

8. Rate of Return Analysis …
Where two (or more) mutually exclusive alternatives will provide the same utility and they have the same lifetime, IRR is calculated on the difference(s) between the alternatives.
Form the incremental project by subtracting the cash flows of a project with a lower initial cost from the one that has the highest initial cost.
If IRR > MARR, accept the alternative with the higher initial cost; otherwise accept the lower cost initial cost alternative.

9. Rate of Return Analysis …

10. Analysis Period
The analysis period must be considered and can be used as a way of ensuring the lifetimes are equal for incremental analysis.
Recall 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 = .

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

12. Problems with the IRR
The 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).
The NPV technique always works properly. The Modified IRR fixes some of the problems.

13. Problems with the IRR …
Example of multiple IRRs:

14. Modified Internal Rate of Return
Two 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
The MIRR technique requires two external rates of return:
einv for investing
efin for financing

15. Modified Internal Rate of Return …
Find the total present value at the start of the project of all negative cash flows using efin as the discount rate.
Find the total value at the end of the project of all positive cash flows using einv as the discount rate.
Find the rate of return MIRR that balances these two values at both ends of the project.

16. Modified Internal Rate of Return …
Example of MIRR technique applied to the previous multiple IRR example:

17. Suggested Problems
7-31, 36, 38, 39, 46, 52, 54.
7A-9, 23, 26. Note the instructions at the start of the problems for this section in the text.