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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

Financial Analysis

Supplement J


Future value of an investment

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

Application J.1

Future Value of a $500 Investment in 5 Years

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


Present value of a future amount

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

Application J.2

Present Value of $500 Received in Five Years

500/1.338 =

$373.63


Present value factors

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 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

Present Value Factors (pf)


Present value factor pf for application j 2

Present Value Factor (pf) for Application J.2


Application j 2 using the pf factor

Application J.2 using the pfFactor


Annuities

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 af

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)


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

Present Value Factor (af) for Application J.3


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


Straight line depreciation

I – S

n

D =

where

D= annual depreciation

I= amount of investment

S= salvage value

n= number of years of project’s life

Straight-Line Depreciation


Modified accelerated cost recovery system macrs

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 accelerated cost recovery system macrs1

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


Example j 1 calculating after tax cash flows

YEAR

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

Example J.1Calculating After-Tax Cash Flows

Local restaurant considering the addition of a salad bar:


Example j 2 calculating npv

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


Example j 2 calculating irr

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


Example j 2 calculating payback period

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

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

$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


Om explorer financial analysis solver

OM ExplorerFinancial Analysis Solver

Salad Bar example:


Npv for project application j 4

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


Irr for project application j 5

IRR for ProjectApplication J.5


Payback period for project application j 6

Payback Period for ProjectApplication J.6


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