1. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Financial Analysis Supplement J

2. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Future Value of Money F = P(1 + r) n where F=future value of the investment at the end of n periods P=amount invested at the beginning, called the principal r=periodic interest rate r=number of time periods for which the interest compounds

3. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Present Value of a Future Amount where F=future value of the investment at the end of n periods P=amount invested at the beginning, called the principal r=periodic interest rate (discount rate) r=number of time periods for which the interest compounds P = F (1 + r) n

4. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Present Value Factors P = = F F (1 + r) n 1 1 = present value factor – pf See Table J.1

5. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Present Value Factors Table J.1Present Value Factors for a Single Payment Number of Interest Rate (r) Periods (n)0.010.02 0.03 0.04 0.05 0.06 0.080.100.12 0.14 10.99010.98040.97090.96150.95240.94340.92590.90910.89290.8772 20.98030.96120.94260.92460.90700.89000.85730.82640.79720.7695 30.97060.94230.91510.88900.86380.83960.79380.75130.71180.6750 40.96100.92380.88850.85480.82270.79210.73500.68300.63550.5921 50.95150.90570.86260.82190.78350.74730.68060.62090.56740.4194 60.94200.88800.83750.79030.74620.70500.63020.56450.50660.4556 70.93270.87060.81310.75990.71070.66510.58350.51320.45230.3996 80.92350.86350.78940.73070.67680.62740.54030.46650.40390.3506 90.91430.83680.76640.70260.64460.59190.50020.42410.36060.3075 100.90530.82030.74410.67560.61390.55840.46320.38550.32200.2697

6. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Annuities See Table J.2 P = + + … F (1 + r) n F (1 + r) n+1 P = A(af)

7. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Present Value Factors Table J.2Present Value Factors of an Annuity Number of Interest Rate (r) Periods (n)0.010.02 0.03 0.04 0.05 0.06 0.080.100.12 0.14 10.99010.98040.97090.96150.95240.94340.92590.90910.89290.8772 21.97041.94161.91351.88611.85941.83341.78331.73551.69011.6467 32.94102.88392.82862.77512.77322.67302.57712.48692.40182.3216 43.90203.80773.71713.62993.54603.46513.31213.16993.03732.9137 54.85344.71354.57974.45184.32954.21243.99273.79083.60483.4331 65.79555.60145.41725.24215.07574.91734.62294.35534.11143.8887 76.72826.47206.23036.00215.78645.58245.20644.86844.56384.2883 87.65177.32557.01976.73276.46326.20985.74665.33494.96764.6389 98.56608.16227.78617.43537.10786.80176.24695.75905.32824.9464 109.47138.98268.33028.11097.72177.36016.72016.14465.65025.2161

8. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Straight-Line Depreciation D = I – S n where D= annual depreciation I= amount of investment S= salvage value n= number of years of product life

9. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Modified Accelerated Cost Recovery System 3-year class:tools and equipment used in research 5-year class:autos, copiers, and computers 7-year class:industrial equipment and office furniture 10-year class:longer-life equipment

10. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Modified Accelerated Cost Recovery System 3-year class:tools and equipment used in research 5-year class:autos, copiers, and computers 7-year class:industrial equipment and office furniture 10-year class:longer-life equipment Class of Investment Year3-Year5-Year7-Year10-Year 133.3320.0014.2910.00 244.4532.0024.4918.00 314.8119.2017.4914.40 47.4111.5212.4911.52 511.528.939.22 65.768.937.37 78.936.55 84.456.55 96.55 106.55 11 3.29 100.0%100.0%100.0%100.0% Table J.3Modified ACRS Depreciation Allowances

11. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Calculating After-Tax Cash Flows Example J.1 YEAR ITEM2001200220032004200520062007 Initial Information Annual demand (salads)11,00011,00011,00011,00011,000 Investment$16,000 Interest (discount) rate0.14 Cash Flows Revenue$38,500$38,500$38,500$38,500$38,500 Expenses: Variable costs22,00022,00022,00022,00022,000 Expenses: Fixed costs8,0008,0008,0008,0008,000 Depreciation (D)3,2005,1203,0721,8431,843922 Pretax income$5,300$3,380$5,428$6,657$6,657– $922 Taxes (40%)2,1201,3522,1712,6632,663– 369 Net operating income (NOI)$3,180$2,208$3,257$3,994$3,994– $533 Total cash flow (NOI + D)$6,380$7,148$6,329$5,837$5,837$369

12. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Calculating NPV, IRR, and Payback Period Example J.2 2002:$6,380(0.8772)=$5,597 2003:$7,148(0.7695)=$5,500 2004:$6,329(0.6750)=$4,272 2005:$5,837(0.5921)=$3,456 2006:$5,837(0.5194)=$3,032 2007:$369(0.4556)=$168 NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) – $16,000 NPV = $6,024

13. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Calculating NPV, IRR, and Payback Period Example J.2 2002:$6,380(0.8772)=$5,597 2003:$7,148(0.7695)=$5,500 2004:$6,329(0.6750)=$4,272 2005:$5,837(0.5921)=$3,456 2006:$5,837(0.5194)=$3,032 2007:$369(0.4556)=$168 NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) – $16,000 NPV = $6,024 IRR by Trial and Error Discount RateNPV 14%$6,025 18%$4,092 22%$2,425 26%$977 30%– $199 28%$322

14. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Calculating After-Tax Cash Flows Example J.1 YEAR ITEM2001200220032004200520062007 Initial Information Annual demand (salads)11,00011,00011,00011,00011,000 Investment$16,000 Interest (discount) rate0.14 Cash Flows Revenue$38,500$38,500$38,500$38,500$38,500 Expenses: Variable costs22,00022,00022,00022,00022,000 Expenses: Fixed costs8,0008,0008,0008,0008,000 Depreciation (D)3,2005,1203,0721,8431,843922 Pretax income$5,300$3,380$5,428$6,657$6,657– $922 Taxes (40%)2,1201,3522,1712,6632,663– 369 Net operating income (NOI)$3,180$2,208$3,257$3,994$3,994– $533 Total cash flow (NOI + D)$6,380$7,148$6,329$5,837$5,837$369 Payback Period Add after-tax cash flows to get as close as possible to without exceeding the initial investment ($16,000) $6,380 + $7,148 = $13,528(2001 and 2002) $16,000 – $13,528 = $2,472(remainder for 2003) $2,472/$6,329 = 0.39(portion of 2003 required) Payback Period = 2.39 years Example J.2

15. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 2002:$6,380(0.8772)=$5,597 2003:$7,148(0.7695)=$5,500 2004:$6,329(0.6750)=$4,272 2005:$5,837(0.5921)=$3,456 2006:$5,837(0.5194)=$3,032 2007:$369(0.4556)=$168 NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) – $16,000 NPV = $6,024 Calculating NPV, IRR, and Payback Period Figure J.1