Chapter 7 - Rate of Return Analysis Click here for Streaming Audio To Accompany Presentation (optional)EGR 403 - The Big PictureThree Major Methods of Economic AnalysisInternal Rate of Return (IRR)Calculating Rate of ReturnCalculating IRR - Example 7-1Calculating IRR - Example 7-2Calculating IRR - Example 7-2 (cont’d)Calculating IRR - Example 7-3Calculating IRR - Example 7-3 (Cont’d)Slide 11Calculating IRR for a Bond - Example 7-4aExample 7-4a EXCEL SolutionRate Of Return (ROR) AnalysisCalculating RORThe Minimum Attractive Rate of Return (MARR)ROR on Alternatives With Equivalent BenefitsExample 7-5 (Cont’d)Slide 19Analysis PeriodChapter 7 - Rate of Return Analysis Click here for Streaming Audio To Accompany Presentation (optional)EGR 403 Capital Allocation TheoryDr. Phillip R. RosenkrantzIndustrial & Manufacturing Engineering DepartmentCal Poly PomonaEGR 403 - Cal Poly Pomona - SA9 2EGR 403 - The Big Picture•Framework: Accounting & Breakeven Analysis•“Time-value of money” concepts - Ch. 3, 4•Analysis methods–Ch. 5 - Present Worth–Ch. 6 - Annual Worth–Ch. 7, 8 - Rate of Return (incremental analysis)–Ch. 9 - Benefit Cost Ratio & other techniques•Refining the analysis–Ch. 10, 11 - Depreciation & Taxes–Ch. 12 - Replacement AnalysisEGR 403 - Cal Poly Pomona - SA9 3Three Major Methods of Economic Analysis•PW - Present Worth•AW - Annual Worth•IRR - Internal Rate of ReturnIf P = A(P/A, i, n)Then (P/A, i, n) = P/ASolve for (P/A, i, n) and look up interest in Compound Interest TablesEGR 403 - Cal Poly Pomona - SA9 4Internal Rate of Return (IRR)•The interest rate paid on the unpaid balance of a loan such that the payment schedule makes the unpaid loan balance equal to zero when the final payment is made. Ex: P = $5000, i = 10%, n = 5Year Principal Prin. Paid Int Paid Payment1 5000.00 818.99 500.00 1318.992 4181.01 900.89 418.10 1318.993 3280.13 990.97 328.01 1318.994 2289.15 1090.07 228.92 1318.995 1199.08 1199.08 119.91 1318.996 0.00 0.00EGR 403 - Cal Poly Pomona - SA9 5Calculating Rate of Return•The IRR is the interest rate at which the benefits equal the costs. IRR = i*PW Benefit - PW Cost = 0PW Benefit/PW Cost = 1NPW = 0EUAB - EUAC = 0PW Benefit = PW CostEGR 403 - Cal Poly Pomona - SA9 6Calculating IRR - Example 7-1•PWB/PWC = 1•2000(P/A, i, 5)/8200 = 1•(P/A, i, 5) = 8200/2000 = 4.1•From Table, IRR = 7%3.9938%4.1007%4.2126%(P/A,i,5)Interest rateFrom Compound Interest TablesEGR 403 - Cal Poly Pomona - SA9 7Calculating IRR - Example 7-2Sometimes we have more than one factor in our equation. When that happens we cannot solve for just one factor.If we use: EUAB - EUAC = 0100 + 75(A/G, i, 4) - 700(A/P, i, 4) = 0EGR 403 - Cal Poly Pomona - SA9 8Calculating IRR - Example 7-2 (cont’d)•No direct method for calculating. Use trial and error and iterate to get answer.•Try i = 5%:100 + 75(A/G, 5%, 4) - 700(A/P, 5%, 4) = + 11+ 11 is too high. The interest rate was too low•Try i = 8%100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = - 6- 6 is too low. The interest rate was too high•Try i = 7%100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = 0Therefore IRR = 7%EGR 403 - Cal Poly Pomona - SA9 9Calculating IRR - Example 7-3• Example 7-3 shows a series of cash flows that does not match any of our known patterns. We must use trial and error. • Using NPW = 0, suppose we start with i = 10% . NPW = + 10.16, which is too high. • Using i = 15%, NPW = - 4.02. IRR is between 10% & 15%• The iterations may be graphed and the true IRR will be indicated at the point where the NPW curve = 0.Yr CF0 - 1001 + 202 + 203 + 304 + 405 + 40EGR 403 - Cal Poly Pomona - SA9 10Calculating IRR - Example 7-3 (Cont’d)•We can use linear interpolation to find estimate the point where the curve crosses 0.•IRR = i* = 10% + (15%-10%)[10.16/(10.16 + 4.02)] = 13.5%•This is a linear interpolation of a non-linear function so the answer is slightly inaccurate, but good enough for decision making here (after all, the guesswork in our future cash flows introduces uncertainty in the analysis).EGR 403 - Cal Poly Pomona - SA9 11Calculating IRR - Example 7-3 (Cont’d)-100203020404013.47%• To get an exact answer, we can use the IRR function in EXCEL• Select the IRR function from the fx icon. • Block the column on the spreadsheet that has the cash flows for all years.• The function returns the IRR. =IRR(A1:A6)The IRR function in EXCEL allows you to evaluate the return of investments very easilyEGR 403 - Cal Poly Pomona - SA9 12Calculating IRR for a Bond - Example 7-4aBond Costs and Benefits:Purchase price = $1000Dividends = $40 every six monthsSold after one year for $950Calculation of Periodic interest rate & IRR:m = 2 compounding periods/year1000 = 40(P/A, i, 2) + 950(P/F, i, 2)By trial and error and interpolation i* 1.5%IRR Nominal rate = 2 x 0.015 = 0.03 (3%)IRR Effective rate = (1 + 0.015)2 - 1 = 0.0302 (3.02%)EGR 403 - Cal Poly Pomona - SA9 13Example 7-4a EXCEL SolutionPeriod Buy/sell Dividend Total0 -1000 -10001 40 402 950 40 9901.52% periodic3.04% nominal3.06% effective• Use IRR function to find periodic IRR (i)• Find nominal using r = i * m• Use EFFECT function to find effective interest rateEGR 403 - Cal Poly Pomona - SA9 14Rate Of Return (ROR) Analysis•Most frequently used measure of merit in industry.•More accurately called Internal Rate of Return (IRR).EGR 403 - Cal Poly Pomona - SA9 15Calculating ROR•Where two mutually exclusive alternatives will provide the same benefit, ROR is performed using an incremental rate of return (ROR) on the difference between the alternatives.•You cannot simply choose the higher IRR alternative.Choose lower-cost alternativeROR MARRChoose higher-cost alternativeROR MARRDecisionTwo-alternative situationEGR 403 - Cal Poly Pomona - SA9 16The Minimum Attractive Rate of Return (MARR)•The MARR is a minimum return the company will accept on the money it invests•The MARR is usually calculated by financial analysts in the company and provided to those who evaluate projects•It is the same as the interest rate used for Present Worth and Annual Worth analysis.EGR 403 - Cal Poly Pomona - SA9 17ROR on Alternatives With Equivalent BenefitsYearCash flow - alternative A (Leaseco)Cash flow - alternative B (Saleco)Cash flow - alternative B - A0 -$1,000.00 -$2,783.00 -$1,783.001 $200.00 $1,200.00 $1,000.002 $200.00 $1,200.00 $1,000.003 $1,200.00 $1,200.00 $0.004 $1,200.00 $1,200.00
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