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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) 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10 0.12 0.14

1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9259 0.9091 0.8929 0.8772

2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8573 0.8264 0.7972 0.7695

3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.7938 0.7513 0.7118 0.6750

4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7350 0.6830 0.6355 0.5921

5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.6806 0.6209 0.5674 0.4194

6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6302 0.5645 0.5066 0.4556

7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.5835 0.5132 0.4523 0.3996

8 0.9235 0.8635 0.7894 0.7307 0.6768 0.6274 0.5403 0.4665 0.4039 0.3506

9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5002 0.4241 0.3606 0.3075

10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.4632 0.3855 0.3220 0.2697

Present Value Factors (pf)



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) 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10 0.12 0.14

1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9259 0.9091 0.8929 0.8772

2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.7833 1.7355 1.6901 1.6467

3 2.9410 2.8839 2.8286 2.7751 2.7732 2.6730 2.5771 2.4869 2.4018 2.3216

4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3121 3.1699 3.0373 2.9137

5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 3.9927 3.7908 3.6048 3.4331

6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.6229 4.3553 4.1114 3.8887

7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.2064 4.8684 4.5638 4.2883

8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.7466 5.3349 4.9676 4.6389

9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.2469 5.7590 5.3282 4.9464

10 9.4713 8.9826 8.3302 8.1109 7.7217 7.3601 6.7201 6.1446 5.6502 5.2161

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

1 0.9434 0.9259 0.9091 0.8929 0.8772

2 1.8334 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

5 4.2124 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

Year 3-Year 5-Year 7-Year 10-Year

1 33.33 20.00 14.29 10.00

2 44.45 32.00 24.49 18.00

3 14.81 19.20 17.49 14.40

4 7.41 11.52 12.49 11.52

5 11.52 8.93 9.22

6 5.76 8.93 7.37

7 8.93 6.55

8 4.45 6.55

9 6.55

10 6.55

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

ITEM 2008 2009 2010 2011 2012 2013 2014

Initial Information

Annual demand (salads) 11,000 11,000 11,000 11,000 11,000

Investment $16,000

Interest (discount) rate 0.14

Cash Flows

Revenue $38,500 $38,500 $38,500 $38,500 $38,500

Expenses: Variable costs 22,000 22,000 22,000 22,000 22,000

Expenses: Fixed costs 8,000 8,000 8,000 8,000 8,000

Depreciation (D) 3,200 5,120 3,072 1,843 1,843 922

Pretax income $5,300 $3,380 $5,428 $6,657 $6,657 – $922

Taxes (40%) 2,120 1,352 2,171 2,663 2,663 – 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 Rate NPV

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

ITEM 2001 2002 2003 2004 2005 2006 2007

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

Initial Information

Annual demand (salads) 11,000 11,000 11,000 11,000 11,000

Investment $16,000

Interest (discount) rate 0.14

Cash Flows

Revenue $38,500 $38,500 $38,500 $38,500 $38,500

Expenses: Variable costs 22,000 22,000 22,000 22,000 22,000

Expenses: Fixed costs 8,000 8,000 8,000 8,000 8,000

Depreciation (D) 3,200 5,120 3,072 1,843 1,843 922

Pretax income $5,300 $3,380 $5,428 $6,657 $6,657 – $922

Taxes (40%) 2,120 1,352 2,171 2,663 2,663 – 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



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