© 2007 Pearson Education Financial Analysis Supplement J

© 2007 Pearson Education Future Value of an Investment 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 The value of an investment at the end of the period over which interest is compounded.

© 2007 Pearson Education Application J.1 Future Value of a $500 Investment in 5 Years 500(1 +.06) 5 = 500(1.338) = $669.11

© 2007 Pearson Education Present Value of a Future Amountwhere 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 The amount that must be invested now to accumulate to a certain amount in the future at a specific interest rate.

© 2007 Pearson Education Application J.2 Present Value of $500 Received in Five Years 500 / = $373.63

© 2007 Pearson Education Present Value Factors P = = F F (1 + r) n 1 1 = present value factor (or pf)

© 2007 Pearson Education Present Value Factors (pf) Present Value Factors for a Single Payment Number of Interest Rate (r) Periods (n)

© 2007 Pearson Education Present Value Factor (pf) for Application J.2

© 2007 Pearson Education Application J.2 using the pf Factor

© 2007 Pearson Education Annuities P = + + … F (1 + r) n F (1 + r) n+1 or P = A (af) where P = present value of an investment A = amount of the annuity received each year af = present value factor for an annuity A = amount of the annuity received each year af = present value factor for an annuity A series of payments on a fixed amount for a specified number of years.

© 2007 Pearson Education Present Value Factors (af) Present Value Factors of an Annuity Present Value Factors of an Annuity Number of Interest Rate (r) Periods (n)

© 2007 Pearson Education Present Value Factor (af) for Application J.3 Interest Rate (r) (n)

© 2007 Pearson Education Application J.3 P = A (af) A = $500 for 5 years at 6% af = (from table) P = 500(4.2124) = $2, Present Value of a $500 Annuity for 5 Years

© 2007 Pearson Education Straight-Line Depreciation D = I – S n where D= annual depreciation I= amount of investment S= salvage value n= number of years of project’s life

© 2007 Pearson Education Modified Accelerated Cost Recovery System (MACRS) 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

© 2007 Pearson Education Modified Accelerated Cost Recovery System (MACRS) 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% Modified ACRS Depreciation Allowances Modified ACRS Depreciation Allowances

© 2007 Pearson Education Example J.1 Calculating After-Tax Cash FlowsYEAR 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 Local restaurant considering the addition of a salad bar:

© 2007 Pearson Education Example J.2 Calculating NPV 2009:$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

© 2007 Pearson Education Example J.2 Calculating IRR 2009:$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

© 2007 Pearson Education Example J.2 Calculating Payback PeriodYEAR 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(2009 and 2010) $16,000 – $13,528 = $2,472(remainder for 2010) $2,472/$6,329 = 0.39(portion of 2010 required) Payback Period = 2.39 years

© 2007 Pearson Education OM Explorer Financial Analysis Solver Salad Bar example:

© 2007 Pearson Education NPV for Project Application J.4 Year 1: $500 Year 2: $650 Year 3: $900 The discount rate is 12%, and the initial investment is $1,550, so the project’s NPV is: Present value of investment (Year 0): ($1,550.00) Present value of Year 1 cash flow: Present value of Year 2 cash flow: Present value of Year 3 cash flow: Project NPV: $ 55.20

© 2007 Pearson Education IRR for Project Application J.5

© 2007 Pearson Education Payback Period for Project Application J.6