IEN255 Chapter 6 - Rate of Return Analysis

1. IEN255 Chapter 6 - Rate of Return Analysis • Yet another measure of investment worth • Many consider rate of return more intuitive (15% vs NPW of $10,000) • Agenda • concepts • calculation • development of an internal rate of return criterion • comparison of mutually exclusive alternatives based on rate of return

2. Return on Investment (def #1) • Definition 1 - interest rate earned on the unpaid balance of an amortized loan • Bank lends $10,000 - you pay $4021 at end of each year for 3 years • $10,000 = $4021(P/A,i,3) • solve for i, i = 10% • so, the three annual payments repay the loan and provide a return of 10% on the outstanding balance

3. Return on Investment (def #2) • the breakeven interest rate, i*, which equates PW of outflows to inflows • i* = rate of interest that PW, FW, and AE all equal 0.

4. Return on Investment (def #3) • invested capital • interest rate charged on the unrecovered project balance of the investment (so the unrecovered balance equals zero.) • Frequently referred to as IRR (internal rate of return) • kind of a payback period with time value of money (can payback costs and provide the firm with a return of i)

5. How to do it (simple vs nonsimple) • simple - only one sign change in net cash flow • nonsimple - more than one sign change • table in example 6.1 • fig 6.1

6. How to do it (methods of finding i*) • direct solution - only for very simple simple problems • trial and error • computer solutions

7. methods of finding i* - trial and error • just example 6.3

8. IRR Criterion - Relationship to PW • fig 6.1 a 6.1 b

9. Good or bad? • If IRR > MARR, accept • If IRR = MARR, indifferent • If IRR < MARR, reject • single project only!!!!! not comparing alternatives

10. IRR Criterion - Accept/Reject for Simple • Example 6.5 • draw the cash flow diagram • determine sign change (simple) • set up with factors • PW(i) = -1,250,000 + 731,500(P/A,i,15) + 80,000(P/F,i,15) = 0 • trial and error • PW(50%) = -1,250,000 + 731,500(P/A,i,15) + 80,000(P/F,i,15) = 209,842 • PW(60%) = -1,250,000 + 731,500(P/A,i,15) + 80,000(P/F,i,15) = -31,822 • i=58.71% • accept IRR > MARR

11. IRR Criterion -Accept/Reject for nonsimple • figure 6.5

12. Mutually Exclusive Alternatives • Flaws! • cannot rank projects using IRR • IRR is relative, NPW, FW, and AE are absolute! • to compare, need to do IRR incrementally! • table on page 317

13. Good or bad? to compare, a new rule • If IRRB-A > MARR, select B • If IRRB-A = MARR, indifferent, select either one • If IRRB-A < MARR, select A • B is the more costly investment option • don’t forget “do nothing” alternative

14. example 6.7 • comments • table through a and b

15. example 6.8, 6.9, and 6.10

16. Incremental Borrowing Approach • If BRRB-A < MARR, select B • If BRRB-A = MARR, indifferent, select either one • If BRRB-A > MARR, select A • B is the least costly investment option • is it cheaper than our own money?

17. IEN255 Summer’99 Chapter 6 HW#3 • Homework Assignment: Chapter 6 #’s 6.1; 6.5; 6.7a,c; 6.11; 6.20; 6.28 • Due with chapter 7 homework (likely Tues July 13)