# © 2007 Pearson Education Financial Analysis Supplement J.

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© 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 / 1.338 = \$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)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

© 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)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

© 2007 Pearson Education Present Value Factor (af) for Application J.3 Interest Rate (r) (n)0.06 0.08 0.10 0.12 0.14 10.9434 0.9259 0.9091 0.8929 0.8772 21.8334 1.7833 1.7355 1.6901 1.6467 3 2.6730 2.5771 2.4869 2.4018 2.3216 4 3.4651 3.3121 3.1699 3.0373 2.9137 54.2124 3.9927 3.7908 3.6048 3.4331

© 2007 Pearson Education Application J.3 P = A (af) A = \$500 for 5 years at 6% af = 4.2124 (from table) P = 500(4.2124) = \$2,106.20 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 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% Modified ACRS Depreciation Allowances Modified ACRS Depreciation Allowances

© 2007 Pearson Education Example J.1 Calculating After-Tax Cash FlowsYEAR ITEM200820092010 201120122013 2014 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 Local restaurant considering the addition of a salad bar:

© 2007 Pearson Education Example J.2 Calculating NPV 2009:\$6,380(0.8772)=\$5,597 2010:\$7,148(0.7695)=\$5,500 2011:\$6,329(0.6750)=\$4,272 2012:\$5,837(0.5921)=\$3,456 2013:\$5,837(0.5194)=\$3,032 2014:\$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)=\$5,597 2010:\$7,148(0.7695)=\$5,500 2011:\$6,329(0.6750)=\$4,272 2012:\$5,837(0.5921)=\$3,456 2013:\$5,837(0.5194)=\$3,032 2014:\$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 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(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: 446.40 Present value of Year 2 cash flow: 518.18 Present value of Year 3 cash flow: 640.62 Project NPV: \$ 55.20

© 2007 Pearson Education IRR for Project Application J.5

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

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