Inflation / DeflationInflation / DeflationInflation / DeflationInflation / Deflation
• Inflation is an increase over time in the price of a good or service with a constant value – denoted ( f )• Fn = P (1 + f )n – or – Fn = P (F/P, f, n)• Pn = F (1 + f ) –n – or – Pn = F (P/F, f, n)
• Deflation is a decrease over time in the price of a good or service of constant value.• Average inflation rate ( f ) is replaced by ( – f
) in the above equations
Constant Dollars vs. Constant Dollars vs. Actual DollarsActual Dollars
Constant Dollars vs. Constant Dollars vs. Actual DollarsActual Dollars
f = Average Inflation Rate
$785 / QTR Tuition & Fees
$785 / QTR Tuition & Fees
1980 2009
ACTUAL
$ $785 / QTR Tuition & Fees
$785 (1+ f )29 / QTR Tuition & Fees
1980 2009
CONSTANT
$
$A = $C (1+ f )n $C = $A (1+ f )– n
Incorporating InflationIncorporating InflationIncorporating InflationIncorporating Inflation
• Inflation can be accounted for as an additional component on top of the MARR or interest rate:
• d = i + f + i•f (d replaces i in tables/equations)
where:• i is the effective interest
rate• f is the constant inflation
rate
• Example: NPW = P + A (P/A, d, n) + F (P/F, d, n)
DepreciationDepreciationDepreciationDepreciation
•Depreciable Life – the period of time over which the asset is usable.
•Matching Concept – A fraction of the cost of the asset is chargeable as an expense in each of the accounting periods in which the asset provides service to the firm.
•Depreciation is NOT a real cash flow!
Cost BasisCost BasisCost BasisCost Basis
Cost Basis – the total cost claimed as an expense over an asset’s life. Includes:• Actual Cost• All other incidental
expenses: Freight Site Preparation Installation
These are the costs req’d to put the asset into service!
Cost BasisCost BasisCost BasisCost Basis• If the asset is purchased by trading
in a similar asset, the difference between the book value and trade in allowance must be considered in determining the cost basis of the new asset.
• If the trade-in allowance exceeds the book value, the difference (unrecognized gain) needs to be subtracted from the cost basis of the new asset.
• If the book value exceeds the trade-in allowance, the difference (unrecognized loss) needs to be added to the cost basis of the new asset.
Straight Line MethodStraight Line MethodStraight Line MethodStraight Line MethodDn = ( I – S )
N
Bn = I – Dn (n)Where:I = Cost Basis; Initial Price plus
installation expenses.S = Salvage ValueDn = Depreciation in Year nBn = Book Value remaining in Year n
N = estimated years of useful lifen = the year currently under
consideration
Declining Balance Declining Balance MethodMethod
Declining Balance Declining Balance MethodMethod = (Multiplier)
= % reduction each year
Dn = I (1–)n–1
Bn = I (1–)n
Typical multipliers are 150% and 200%.
200% is also called Double Declining Balance (DDB).
1
N
Sum of Years Digits Sum of Years Digits MethodMethod
Sum of Years Digits Sum of Years Digits MethodMethod
SOYD = 1 + 2 + 3 + … + N
= N(N+1) 2
Dn = ( N – n + 1 ) ( I – S ) SOYD
Bn = Bn–1 – Dn
Units of Production Units of Production MethodMethod
Units of Production Units of Production MethodMethod
Dn = Service Units Consumed During Year n ( I – S ) Total Service Units
n
Bn = I – Service Units Consumed During Year n ( I – S )
Total Service Units
MACRSMACRSMACRSMACRS
• MACRS is a simpler, more rapid depreciation method.
• MACRS has been required for tax purposes since 1981 / 1986.
• MACRS book value is the legal standard for valuing equipment for tax purposes.
MACRS Depreciation MACRS Depreciation ScheduleSchedule
MACRS Depreciation MACRS Depreciation ScheduleScheduleClass: 3 5 7 10 15
Year 200% DB 200% DB 200% DB 200% DB 150% DB
1 33.33 20.00 14.29 10.00 5.00
2 44.45 32.00 24.49 18.00 9.50
3 14.81* 19.20 17.49 14.40 8.55
4 7.41 11.52* 12.49 11.52 7.70
5 11.52 8.93* 9.22 6.93
6 7.54 8.92 7.37 6.23
7 8.93 6.55* 5.90*
8 4.46 6.55 5.90
9 6.56 5.91
10 6.55 5.90
11 3.28 5.91
12 5.90
13 5.91
14 5.90
15 5.91
16 2.95
* Year to switch to straight line depreciation
Values shown are percentages
MACRSMACRSMACRSMACRS
Dn = (Year n MACRS Class Table Value)( I )
n
Bn = ( I )[1 – ( Year n MACRS Class Table Values )] j=1
NOTE: If selling an asset BEFORE the final year of depreciation:• Selling year depreciation is ½ Dn value lower, and …• Selling year book value is ½ Dn value higher!
Marginal Tax RatesMarginal Tax RatesMarginal Tax RatesMarginal Tax Rates
• Tax rates for corporations and individuals vary depending on the amount of taxable income.
• Different tax rates apply to incremental income.
• Assume project will keep us in the same marginal tax bracket.
• Terms:Federal Tax Rate (FTR)Federal Taxable Income
Federal Taxes = ( FTR ) (Federal Taxable Income)
Marginal Tax RatesMarginal Tax RatesMarginal Tax RatesMarginal Tax Rates2009 Federal Corporate Tax
ScheduleTaxable Income Tax Rate
$0 to $50,000 15%
$50,001 to $75,000 25%
$75,001 to $100,000 34%
$100,001 to $335,000 39%
$335,001 to $10,000,000 34%
$10,000,001 to $15,000,000 35%
$15,000,001 to $18,333,333 38%
$18,333,334 and up 35%
After Tax AnalysisAfter Tax AnalysisAfter Tax AnalysisAfter Tax Analysis1. Determine Taxable Income:
( + ) Income( - ) Expenses (COGS and O & M)( - ) Interest Paid( - ) Depreciation
2. Determine Taxes• Use the marginal tax rate
3. Determine After Tax Cash Flow:( + ) Income( - ) Expenses( - ) Loan Payments( - ) Taxes
Sale of AssetSale of AssetSale of AssetSale of Asset1. If selling an asset before the final year
of tax depreciation, you may only claim ½ of the depreciation for that year: so the depreciation is ½ Dn lower, and the book value is ½ Dn higher
2. End of year taxable income from sale: = Sale Price – Book Value*
* Subtract depreciation, if not already accounted for in that year
3. Tax cash flow from sale of the asset:
= (Taxable income from sale) (Marginal Tax Rate)
4. After tax cash flow: = Sale Price – Tax cash flow from sale
of the asset
Project ProfitabilityProject ProfitabilityProject ProfitabilityProject Profitability
1. NPW of ATCF > 0
2. EAW of ATCF > 0
3. Rate of Return > MARR
Need to know MARR, Inflation Rates, Interest Rate, …
Need estimates of amounts & timing of cash flows, …
Need to know marginal tax rates, depreciation methods