© 2007 Pearson Education Financial Analysis Supplement J.
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Transcript of © 2007 Pearson Education Financial Analysis Supplement J.
© 2007 Pearson Education
Financial Analysis
Supplement JSupplement J
© 2007 Pearson Education
Future Value of an Investment
F = PF = P(1 +(1 + r r))nn
wherewhere
FF == future value of the investment at the future value of the investment at the end ofend of n n periodsperiods
PP == amount invested at the beginning, amount invested at the beginning, called the principalcalled the principal
rr == periodic interest rateperiodic interest raterr == number of time periods for which the number of time periods for which the
interest compoundsinterest 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 Amount
wherewhere
FF == future value of the investment at the future value of the investment at the end ofend of n n periodsperiods
PP == amount invested at the beginning, amount invested at the beginning, called the principalcalled the principal
rr == periodic interest rate (discount rate)periodic interest rate (discount rate)rr == number of time periods for which the number of time periods for which the
interest compoundsinterest compounds
P P ==FF
(1 +(1 + r r))nn
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 P = = = = FFFF
(1 +(1 + r r))nn
11(1 +(1 + r r))nn
11(1 +(1 + r r))nn
= present value factor (or pf)= present value factor (or pf)
© 2007 Pearson Education
Present Value Factors (pf)
Present Value Factors for a Single PaymentNumber 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
© 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 P = + + …= + + …FF(1 +(1 + r r))nn
FF(1 +(1 + r r))n+1n+1
oror P = A P = A (af)(af)
where where PP = present value of an investment = present value of an investment AA = amount of the annuity received each year = amount of the annuity received each year af = present value factor for an annuity 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 AnnuityPresent Value Factors of an AnnuityNumber 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
© 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
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
© 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 D ==I I – S– S
nn
wherewhere
DD = annual depreciation= annual depreciationII = amount of investment= amount of investmentSS = salvage value= salvage valuenn = number of years of project’s life= number of years of project’s life
© 2007 Pearson Education
Modified Accelerated Cost Recovery System (MACRS)
3-year class:3-year class: tools and equipment used in researchtools and equipment used in research
5-year class:5-year class: autos, copiers, and computersautos, copiers, and computers
7-year class:7-year class: industrial equipment and office furnitureindustrial equipment and office furniture
10-year class:10-year class: longer-life equipmentlonger-life equipment
© 2007 Pearson Education
Modified Accelerated Cost Recovery System (MACRS)
3-year class:3-year class: tools and equipment used in researchtools and equipment used in research
5-year class:5-year class: autos, copiers, and computersautos, copiers, and computers
7-year class:7-year class: industrial equipment and office furnitureindustrial equipment and office furniture
10-year class:10-year class: longer-life equipmentlonger-life equipment
Class of InvestmentYear 3-Year 5-Year 7-Year 10-Year
1 33.33 20.00 14.29 10.002 44.45 32.00 24.49 18.003 14.81 19.20 17.49 14.404 7.41 11.52 12.49 11.525 11.52 8.93 9.226 5.76 8.93 7.377 8.93 6.558 4.45 6.559 6.55
10 6.5511 3.29
100.0% 100.0% 100.0% 100.0%
Modified ACRS Depreciation AllowancesModified ACRS Depreciation Allowances
© 2007 Pearson Education
Example J.1Calculating After-Tax Cash Flows
YEARYEARITEMITEM 20082008 20092009 20102010 2011 2011 20122012 20132013 20142014
Initial InformationInitial InformationAnnual demand (salads)Annual demand (salads) 11,00011,000 11,00011,000 11,00011,000 11,00011,000 11,00011,000InvestmentInvestment $16,000$16,000Interest (discount) rateInterest (discount) rate 0.140.14
Cash FlowsCash FlowsRevenueRevenue $38,500$38,500 $38,500$38,500 $38,500$38,500 $38,500$38,500 $38,500$38,500Expenses: Variable costsExpenses: Variable costs 22,00022,000 22,00022,000 22,00022,000 22,00022,000 22,00022,000Expenses: Fixed costsExpenses: Fixed costs 8,0008,000 8,0008,000 8,0008,000 8,0008,000 8,0008,000Depreciation (D)Depreciation (D) 3,2003,200 5,1205,120 3,0723,072 1,8431,843 1,8431,843 922922
Pretax incomePretax income $5,300$5,300 $3,380$3,380 $5,428$5,428 $6,657$6,657 $6,657$6,657 – $922– $922Taxes (40%)Taxes (40%) 2,1202,120 1,3521,352 2,1712,171 2,6632,663 2,6632,663 – 369– 369
Net operating income (NOI)Net operating income (NOI) $3,180$3,180 $2,208$2,208 $3,257$3,257 $3,994$3,994 $3,994$3,994 – $533– $533
Total cash flow (NOI + D)Total cash flow (NOI + D) $6,380$6,380 $7,148$7,148 $6,329$6,329 $5,837$5,837 $5,837$5,837 $369$369
Local restaurant considering the addition of a salad bar:
© 2007 Pearson Education
Example J.2 Calculating NPV
2009:2009: $$ 6,380(0.8772)6,380(0.8772) == $$ 5,5975,5972010:2010: $$ 7,148(0.7695)7,148(0.7695) == $$ 5,5005,5002011:2011: $$ 6,329(0.6750)6,329(0.6750) == $$ 4,2724,2722012:2012: $$ 5,837(0.5921)5,837(0.5921) == $$ 3,4563,4562013:2013: $$ 5,837(0.5194)5,837(0.5194) == $$ 3,0323,0322014:2014: $$ 369(0.4556)369(0.4556) == $$ 168168
NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) –– $16,000 $16,000NPV = $6,024NPV = $6,024
© 2007 Pearson Education
Example J.2 Calculating IRR
2009:2009: $$ 6,380(0.8772)6,380(0.8772) == $$ 5,5975,5972010:2010: $$ 7,148(0.7695)7,148(0.7695) == $$ 5,5005,5002011:2011: $$ 6,329(0.6750)6,329(0.6750) == $$ 4,2724,2722012:2012: $$ 5,837(0.5921)5,837(0.5921) == $$ 3,4563,4562013:2013: $$ 5,837(0.5194)5,837(0.5194) == $$ 3,0323,0322014:2014: $$ 369(0.4556)369(0.4556) == $$ 168168
NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) NPV = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) –– $16,000 $16,000NPV = $6,024NPV = $6,024
IRR by Trial and Error
Discount Rate NPV
14% $ 6,02518% $ 4,09222% $ 2,42526% $ 97730% – $ 199
28% $ 322
© 2007 Pearson Education
Example J.2 Calculating Payback Period
YEARYEARITEMITEM 20012001 20022002 20032003 20042004 20052005 20062006 20072007
Initial InformationInitial InformationAnnual demand (salads)Annual demand (salads) 11,00011,000 11,00011,000 11,00011,000 11,00011,000 11,00011,000InvestmentInvestment $16,000$16,000Interest (discount) rateInterest (discount) rate 0.140.14
Cash FlowsCash FlowsRevenueRevenue $38,500$38,500 $38,500$38,500 $38,500$38,500 $38,500$38,500 $38,500$38,500Expenses: Variable costsExpenses: Variable costs 22,00022,000 22,00022,000 22,00022,000 22,00022,000 22,00022,000Expenses: Fixed costsExpenses: Fixed costs 8,0008,000 8,0008,000 8,0008,000 8,0008,000 8,0008,000Depreciation (D)Depreciation (D) 3,2003,200 5,1205,120 3,0723,072 1,8431,843 1,8431,843 922922
Pretax incomePretax income $5,300$5,300 $3,380$3,380 $5,428$5,428 $6,657$6,657 $6,657$6,657 – $922– $922Taxes (40%)Taxes (40%) 2,1202,120 1,3521,352 2,1712,171 2,6632,663 2,6632,663 – 369– 369
Net operating income (NOI)Net operating income (NOI) $3,180$3,180 $2,208$2,208 $3,257$3,257 $3,994$3,994 $3,994$3,994 – $533– $533
Total cash flow (NOI + D)Total cash flow (NOI + D) $6,380$6,380 $7,148$7,148 $6,329$6,329 $5,837$5,837 $5,837$5,837 $369$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 ProjectApplication J.4
Year 1: $500Year 2: $650Year 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 ProjectApplication J.5
Discount Rate
NPV
10% $500 (0.9091) + $650 (0.8264) + $900 (0.7513) = $117.88
12% $500 (0.8929) + $650 (0.7972) + $900 (0.7188)
= $ 55.20
14% $500 (0.8772) + $650 (0.7695) + $900 (0.6750) = ($ 3.72)
© 2007 Pearson Education
Payback Period for ProjectApplication J.6
Payback for year 1 = $500
Payback for years 1 and 2 = $500 + $650 = $1,150
Proportion of year 3 = ($1,550 $1,150) / $900 = 0.44 year
Payback periods for project = 2.44 years