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Financial Analysis. Supplement J. 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. Future Value of an Investment.

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Financial Analysis

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Financial Analysis

Supplement J

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

Future Value of an Investment

The value of an investment at the end of the period over which interest is compounded.

F = P(1 + r)n

Application J.1

Future Value of a \$500 Investment in 5 Years

500(1 + .06)5 = 500(1.338) = \$669.11

F

(1 + r)n

P =

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

Present Value of a Future Amount

The amount that must be invested now to accumulate to a certain amount in the future at a specific interest rate.

Application J.2

Present Value of \$500 Received in Five Years

500/1.338 =

\$373.63

1

(1 + r)n

1

(1 + r)n

F

(1 + r)n

P = = F

= present value factor (or pf)

Present Value Factors

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

F

(1 + r)n

F

(1 + r)n+1

P = + + …

Annuities

A series of payments on a fixed amount for a specified number of years.

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

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

Present Value Factors (af)

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

Present Value Factor (af) for Application J.3

Application J.3

Present Value of a \$500 Annuity for 5 Years

P = A (af)

A = \$500 for 5 years at 6%

af = 4.2124 (from table)

P = 500(4.2124) = \$2,106.20

I – S

n

D =

where

D= annual depreciation

I= amount of investment

S= salvage value

n= number of years of project’s life

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

Modified ACRS Depreciation Allowances

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 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

YEAR

ITEM200820092010 201120122013 2014

Initial Information

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

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

IRR by Trial and Error

Discount RateNPV

14%\$6,025

18%\$4,092

22%\$2,425

26%\$977

30%– \$199

28%\$322

Example J.2Calculating 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

Payback Period

YEAR

ITEM2001200220032004200520062007

Add after-tax cash flows to get as close as possible to without exceeding the initial investment (\$16,000)

Initial Information

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

\$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

Example J.2Calculating Payback Period

NPV for ProjectApplication 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