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# Financial Analysis - PowerPoint PPT Presentation

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

Supplement J

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

Future Value of a \$500 Investment in 5 Years

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

(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.

Present Value of \$500 Received in Five Years

500/1.338 =

\$373.63

(1 + r)n

1

(1 + r)n

F

(1 + r)n

P = = F

= present value factor (or pf)

### Present Value Factors

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 pfFactor

(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

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)

(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

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

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

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

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

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

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 ExplorerFinancial Analysis Solver

Salad Bar example:

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 ProjectApplication J.5