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 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, ,500(P/A,i,15) + 80,000(P/F,i,15) = 0
trial and error
PW(50%) = -1,250, ,500(P/A,i,15) + 80,000(P/F,i,15) = 209,842
PW(60%) = -1,250, ,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)