Engineering Economic Analysis Chapter 7 Rate of Return Analysis Donald G. Newnan San Jose State University Ted G. Eschenbach University of Alaska Anchorage Jerome P. Lavelle North Carolina State University Neal A. Lewis University of New Haven Copyright Oxford University Press 2017

Chapter Outline Internal Rate of Return Calculating Rate of Return Interest Rates When There Are Fees or Discounts Loans & Investments Incremental Analysis Analysis Period XIRR Copyright Oxford University Press 2017

Learning Objectives Evaluate cash flows with internal rate of return Plot PW vs. interest rate to find IRR Use incremental rate of return to evaluate alternatives Develop & use spreadsheet in solving rate of returns Copyright Oxford University Press 2017

Vignette: Barcodes Give a Number; RFID Codes Tell a Story! Radio Frequency Identification (RFID) revolutionizes operations RFID tag costs are dropping significantly RFID tags can track & trace goods from manufacturing to consumers Real cost & benefit to track items is? Copyright Oxford University Press 2014 Copyright Oxford University Press 2017

Vignette: Barcodes Give a Number; RFID Codes Tell a Story! A clothing manufacturer may use RFID tags on new season’s line. What costs & benefits should be considered? How would costs & benefits differ for those already using RFID vs. those who aren’t yet? How do military costs & benefits differ from commercial companies? Can RFID tags invade privacy? What are the ethical & social costs for a retail company? “Kill“ technologies allow consumers to disable RFID tags after purchase. How might this affect consumer attitudes & company costs? Copyright Oxford University Press 2017

Rate of Return Analysis Rate of return is most frequently used measure Major advantages Single figure of merit that is readily understood Calculating rate of return independent from minimum attractive rate of return (MARR) Copyright Oxford University Press 2017

Internal Rate of Return Interest rate at which PW = 0 = EUAW On a loan it is interest rate paid on unpaid balance so balance = 0 after final payment On an investment it is interest rate earned on the un- recovered investment so un-recovered investment = 0 after last cash flow Copyright Oxford University Press 2017

Rate of Return in Investment $5000 investment in 5 yrs at rate of return of 8% Yr Cash Flow Unrecovered Investment at Beginning of Year 8% Return on Unrecovered Investment Investment Repayment at End of Year Unrecovered Investment at End of Year −$5000 $5000 1 $1252 $400 $ 852 $4148 2 $331 $ 921 $3227 3 $258 $ 994 $2233 4 $178 $1074 $1159 5 $ 93 $ 0 Subtotal $1260 Copyright Oxford University Press 2017

Calculating rate of return Internal rate of return is interest rate where: NPV = 0 PV of benefits = PV of costs Annual benefits = annual costs All of the above None of the above E All of the above Copyright Oxford University Press 2017

Calculating rate of return Internal rate of return is interest rate where: NPV = 0 PV of benefits = PV of costs Annual benefits = annual costs All of the above None of the above E All of the above Copyright Oxford University Press 2017

Example 7-1 Rate of Return Calculation Engineer invests $5000 annually at year-end for 40 years. For $1 million at retirement, what interest must be earned? Look in compound interest tables for rate where true. The interest is 7%. Copyright Oxford University Press 2017

Firm invests $75,000 to save $9000/year in energy costs for 15 years. What is project’s rate of return? 8.44% 10.08% 12.38% 14.65% None of the above Copyright Oxford University Press 2017

Firm invests $75,000 to save $9000/year in energy costs for 15 years. What is project’s rate of return? 8.44% 10.08% 12.38% 14.65% None of the above =RATE(15,9000,−75000) Copyright Oxford University Press 2017

What is project’s rate of return? -3.68% 8.22% 8.75% 11.38% A small restaurant costs $350,000. Expected profits equal $22,000/year for 6 years when value is $400,000. What is project’s rate of return? -3.68% 8.22% 8.75% 11.38% None of the above Copyright Oxford University Press 2017

What is project’s rate of return? -3.68% 8.22% 8.75% 11.38% A small restaurant costs $350,000. Expected profits equal $22,000/year for 6 years when value is $400,000. What is project’s rate of return? -3.68% 8.22% 8.75% 11.38% None of the above =RATE(6,22000,−350000,400000) Copyright Oxford University Press 2017

Example 7-2 Rate of Return Calculation Year Cash Flow −$700 1 +100 2 +175 3 +250 4 +325 175 100 250 325 4 1 2 3 700   Copyright Oxford University Press 2017

Example 7-2 Rate of Return Calculation Year Cash Flow −$700 1 +100 2 +175 3 +250 4 +325 175 100 250 325 4 1 2 3 700 Copyright Oxford University Press 2017

Example 7-3 Rate of Return Calculation Year Cash Flow +$300,000 1 −45,000 2 3 4 5 −45,000 − 170,000 This can be solved in one step with the annuity function Copyright Oxford University Press 2017

Example 7-3 Rate of Return Calculation Year Cash Flow +$300,000 1 −45,000 2 3 4 5 −45,000 − 170,000 At i = 7%, PW = -$5717. At i = 8%, PW = $4629. Interpolating, Copyright Oxford University Press 2017

Example 7-4 Rate of Return Calculation Maria borrowed $9000 yearly for 4 years. No interest was charged until graduation, then rate = 5%. Maria makes 5 equal annual payments of? Rate of return for Maria’s loan = ? 9000 4 1 2 3 5 8 6 7 9 A   Copyright Oxford University Press 2017

Example 7-4 Spreadsheet solution Copyright Oxford University Press 2017

Example 7-4 Rate of Return on Student Loan Yr Amount Owed at Start of Year Interest at 2.66% Cash Flow at End of Year Amount Owed at End of Year $9,000.00 1 $239.17 $18,239.17 2 $484.69 $27,723.86 3 $736.74 $37,460.59 4 $995.48 $38,456.07 5 $1,021.93 -$8,315.09 $31,162.91 6 $828.13 $23,675.95 7 $629.17 $15,990.02 8 $424.92 $8,099.85 9 $215.25 $0.00 Copyright Oxford University Press 2017

Example 7-4 Rate of Return on Student Loan $(6,000) $- $6,000 $12,000 $18,000 0% 5% 10% 15% 20% Interest Rate Net Present Worth Copyright Oxford University Press 2017

Plot of NPW versus Interest Rate for Borrowed Money Year Cash Flow +P 1 -A 2 3 4 : NPW  + i IRR Copyright Oxford University Press 2017

Plot of NPW versus Interest Rate for Invested Money Year Cash Flow -P 1 +A 2 3 4 : NPW  + i IRR Copyright Oxford University Press 2017

Example 7-5 Corporate bond initially sold for $1000. Issuer will pay $40 interest every 6 months & repay $1000 face value after 10 years. After 1 year, bond was sold for $950. (a) What rate of return did original buyer receive? 950   40 1 2 1000 Copyright Oxford University Press 2017

(b) What rate of return for new buyer if bond kept for remaining 9-year life? Example 7-5 1000 40 4 1 2 3 17 18 4 1 2 3 17 18 1 2 3 4 17 18 950   Copyright Oxford University Press 2017

Example 7-5, Spreadsheet Solution Copyright Oxford University Press 2017

=EFFECT() IRR = 1.66%/month APR = nominal rate = 19.9% IRR = effective annual rate = (1 + .0166)12 – 1 = 21.8% Or, =EFFECT(nominal_rate,npery) =EFFECT(19.9%,12) = 0.218 = 21.8% The reverse is =NOMINAL(effect_rate,npery) Copyright Oxford University Press 2017

Example 7-6, Fees or Discounts If issuing firm paid a 1% fee to sell bond, what effective interest rate did firm pay on bond? Example 7-6, Fees or Discounts   Copyright Oxford University Press 2017

Example 7-7 Two options to acquire a property priced at $300,000: Finance through the seller with 20% down & the balance due in 5 annual payments at 12% Pay cash with 10% discount What is the IRR for the loan offered by the seller?   Copyright Oxford University Press 2017

Example 7-8 Two options for parking permit: Buy annual parking permit on August 15th at $180; or Buy semester permits on August & January 15th at $130 each What is the IRR for annual permit? Copyright Oxford University Press 2017

Example 7-9 Pay for liability insurance: $10,000/quarter or $35,000/year What is rate of return for paying annually?   Copyright Oxford University Press 2017

Example 7-10 Buy or lease options (for 2 years): Buy for $40,000 with salvage value of $6000; or Lease at $2500/month What is IRR of lease? Copyright Oxford University Press 2017

Incremental Analysis With 2 or more alternatives, rate of return analysis must determine incremental rate of return, ΔIRR, on difference between alternatives Incremental cash flow = higher initial-cost alternative minus lower initial-cost alternative If ΔIRR≥MARR, choose higher-cost alternative If ΔIRR<MARR, choose lower-cost alternative Copyright Oxford University Press 2017

Example 7-11 Incremental ROR Two mutually exclusive alternatives (MARR=6%): Incremental Year Alt.1 Alt.2 Alt.2-Alt.1 −$1000 −$2000 1 + 1500 + 2800 + 1300 IRR 50% 40% ΔIRR=30% Copyright Oxford University Press 2017

Example 7-13 A cost-saving device has no salvage value after 5 years. Two options: Device A: Costs $10,000 & saves $3000 annually Device B: Costs $13,500 & saves $3000 the 1st year & increases $500 annually   Copyright Oxford University Press 2017

Example 7-14 Machine X Machine Y Initial Cost $200 $700 Uniform annual benefit 95 120 Salvage value 50 150 Useful life, in years 6 12 Copyright Oxford University Press 2017

Example 7-15, Goal Seek Pump A Pump B Initial Cost $7000 $5000 End-of-useful-life salvage value 1500 1000 Useful life, in years 12 6 Copyright Oxford University Press 2017

Example 7-16, XIRR A 401(k) is invested in stocks. On September 13, 2016 $1500 was deposited & another $2200 on June 7, 2017. If account worth $3840 on August 7, 2017, what annual rate of return has been earned? Copyright Oxford University Press 2017