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

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

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

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

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)

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)

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)

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

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

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 %100.0%100.0%100.0% Table J.3Modified ACRS Depreciation Allowances

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 ITEM 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, 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

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 :$6,380(0.8772)=$5, :$7,148(0.7695)=$5, :$6,329(0.6750)=$4, :$5,837(0.5921)=$3, :$5,837(0.5194)=$3, :$369(0.4556)=$168 NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) – $16,000 NPV = $6,024

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 :$6,380(0.8772)=$5, :$7,148(0.7695)=$5, :$6,329(0.6750)=$4, :$5,837(0.5921)=$3, :$5,837(0.5194)=$3, :$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

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 ITEM 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, 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

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 2002:$6,380(0.8772)=$5, :$7,148(0.7695)=$5, :$6,329(0.6750)=$4, :$5,837(0.5921)=$3, :$5,837(0.5194)=$3, :$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