Engineering Economy

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

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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

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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.

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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)

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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

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How to do it (methods of finding i*)

direct solution - only for very simple simple problems

trial and error

computer solutions

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

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IRR Criterion - Relationship to PW

fig 6.1 a 6.1 b

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Good or bad?

If IRR > MARR, accept

If IRR = MARR, indifferent

If IRR < MARR, reject

single project only!!!!! not comparing alternatives

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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

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IRR Criterion -Accept/Reject for nonsimple

figure 6.5

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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

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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

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example 6.7

comments

table through a and b

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example 6.8, 6.9, and 6.10

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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?

Engineering Economy

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)