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

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

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.

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)

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

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

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

IRR Criterion - Relationship to PW fig 6.1 a 6.1 b

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

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

IRR Criterion -Accept/Reject for nonsimple figure 6.5

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

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

example 6.7 comments table through a and b

example 6.8, 6.9, and 6.10

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?

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)