MIE Class #5 Manufacturing & Engineering Economics Concerns and Questions Concerns and Questions Quick Recap of Previous ClassQuick Recap of Previous Class Today’s Focus: Today’s Focus: – Chap 3 Comparing Alternatives with Different Useful Lives – Chap 4 Rate of Return Methods Hmwk #3 Due in 1 Week: Hmwk #3 Due in 1 Week: – Chap 2 - 3, 4, 5, 6, 11, 12, 15, 16, 24, 30, 37 16, 24, 30, 37

Concerns and Questions?

Quick Recap of Previous Class b Effective Interest b Comparison of Alternatives b Procedure b Defining Investment Alternatives b Useful Life versus Study Period

Useful Life versus Study Period b Comparison must be over the same study period for ALL alternatives! b Useful Lives = Study Period b Useful Lives are Different Among Alters.  UL < SP  UL > SP

Same Study Period Required!! b Use either:  Repeatability Assumption  Cotermination Assumption

Example AB Capital Investment -$3,500 -$5,000 Annual Revenues 1,900 2,500 Annual Expenses ,020 Useful Life 4 6 Market Value 0 0

Several In-class Examples

The Effect of Compounding  Benjamin Franklin, according to the American Bankers Association, left $5,000 to the residents of Boston in 1791, with the understanding that it should be allowed to accumulate for a hundred years. By 1891 the $5,000 had grown to $322,000. A school was built, and $92,000 was set aside for a second hundred years of growth. In 1960, this second century fund had reached $1,400,000. As Franklin put it, in anticipation: "Money makes money and the money that money makes makes more money."  Question: What average interest rate per year was earned from 1791 to 1891?

The “Ben Franklin” Problem Solution Given: P=$5,000 N=100 F = $322,000 Find: i'% F = P(F|P, i'%, 100) $322,000 = $5000(F|P, i'%, 100) therefore, (F|P, i'%, 100) = 64.4 From tables, (F|P, 4%, 100) = (F|P, 5%, 100) = F = P(1+i') N therefore, 322 = 5(1+i') = (1+i') 100 or (1+i') = so that i' = 4.25%

Chapter 4 - Rate of Return Methods  Compare against minimum standard of desirability - minimum attractive rate of return (MARR)  Internal Rate of Return (IRR) Method Solves for the interest rate that equates the equivalent worth of a project's cash outflows (expenditures) to the equivalent worth of cash inflows (receipts or savings).

IRR is Like a “Break-Even” Problem b Find i' such that FW(neg, i') = FW(pos, i') b FW = 0 = FW(pos, i') - FW(neg, i') b Can use any one of the EW methods for IRR: b PW(i' %) = 0 b AW(i' %) = 0 b FW(i' %) = 0  Why?

Can Solve for i' by:  Trial and error  Linear interpolation  An equation solver  Computer program  You will need to know how to interpolate in this course!

Evaluating Project with IRR  Compare IRR to MARR to determine whether or not the project is acceptable with respect to profitability.  IRR = i'  MARRacceptable  IRR = i' < MARRunacceptable (reject)

 Difficulties with the IRR Method  The IRR Method assumes that recovered funds are reinvested at the IRR rather than the MARR  Possible multiple IRRs  Why should you learn the RR Methods?  The majority of companies favor the RR methods for evaluating investment projects

Example Problem Using IRR Cost/Revenue Estimates Initial Investment:$50,000 Annual Revenues:$20,000 Annual Operating Costs:$2,500 Salvage EOY 5:$10,000 Study Period: 5 years MARR20%

Solution using IRR method Find i'% such that the PW(i'%) = 0 0=-50,000+17,500(P|A, i'%,5)+10,000(P|F, i'%,5) PW(20%) = tells us that i' > 20% PW(25%) = > 0, tells us that i'% > 25% PW(30%) = -4, < 0, tells us that i'% < 30% 25% < i' < 30% Use linear interpolation to estimate i'% or Use “short-cut” to draw a conclusion

Linear Interpolation example i%PW i' i' =  25.3% > MARR, accept

Comparing Mutually Exclusive Alternatives (MEAs) with RR Methods  Fundamental Purpose of Capital Investment: Obtain at least the MARR for every dollar invested.Obtain at least the MARR for every dollar invested.  Basic Rule: Spend the least amount of capital possible unless the extra capital can be justified by the extra savings or benefits.Spend the least amount of capital possible unless the extra capital can be justified by the extra savings or benefits. (i.e., any increment of capital spent above the minimum must be able to pay its own way)

Why not select the investment opportunity that maximizes IRR? See example below ABB-A(  ) Investment -$100 -$10,000- $9,900 Lump-Sum $1,000$15,000$14,000 Receipt Next Year IRR900% 50%41.4% If MARR = 20%, would you rather have A or B if comparable risk is involved?

Comparing MEAs - using the IRR method cont'd. If MARR = 20%, PW A = $733 and PW B = $2,500 If MARR = 20%, PW A = $733 and PW B = $2,500 * Never simply maximize the IRR. * Never simply maximize the IRR. * Never compare the IRR to anything except * Never compare the IRR to anything except the MARR. the MARR. IRR A->B : IRR A->B : PW A->B = 0 = -9, ,000(P|F, i'%, 1) PW A->B = 0 = -9, ,000(P|F, i'%, 1) 9,900/14,000 = (P|F, i'%, 1) i' = 41.4% > MARR

Rate of Return Methods for Comparing Alternatives MUST use an Incremental Approach! Step 1. Rank order alternatives from least to greatest initial investment. Step 2. Compare current feasible alternative with next challenger in the list Step 3. Compute RR (IRR or ERR) and compare with MARR. If RR < Marr choose the least initial investment alternative. If RR  MARR choose the greater initial investment alternative Step 4. Remove rejected alternative from list. Continue with next comparison

Example Problem: Given three MEAs and MARR = 15% Investment (FC) -28, , ,500 Net Cash Flow/yr 5,500 3,300 4,800 Salvage Value 1, Useful Life 10 yrs10 yrs 10 yrs Study Period 10 yrs10 yrs 10 yrs Use the IRR procedure to choose the best alternative.

Example Problem Cont. Step 1. DN -> 2 -> 3 -> 1 Step 2. Compare DN -> 2  cash flows  cash flows  Investment-16, = -16,000  Annual Receipts 3, = 3,300  Salvage Value = 0 Compute  IRR DN->2 PW(  i') = 0 = -16, ,300(P|A,  i'%, 10)  i' DN->2  15.9%

Step 3. Since  i' > MARR, keep alt. 2 (higher FC) as current best alternative. Drop DN from further consideration. Step 4. Next comparison: 2 -> 3  Investment-23,500 - (-16,000) = - 7,500  Annual Receipts4, ,300 = 1,500  Salvage Value = 500 Computing  IRR 2->3 PW(  i') = 0 0= -7, ,500(P|A,  i'%, 10) + 500(P|F,  i'%, 10)

 i' 2->3  15.5% Since  i' > MARR, keep Alt. 3 (higher FC) as current best alternative. Drop Alt. 2 from further consideration. Next comparison: 3 -> 1  cash flows  Investment-28,000 - (-23,500) = - 4,500  Annual Receipts5, ,800 = 700  Salvage Value 1, = 1,000 Compute  IRR 3->1 PW(  i') = 0 0= -4, (P|A,  i'%, 10) + 1,000(P|F,  i'%, 10)  i' 3->1  10.9%

Since  i' < MARR, keep alt. 3 (lower FC) as current best alternative. Drop alt. 1 from further consideration. Step 5. All alternatives have been considered. Recommend alternative 3 for investment.

Graphical Interpretation of Example