Inflation / Deflation Inflation is an increase over time in the price of a good or service with a constant value – denoted ( f ) F n = P (1 + f ) n – or.

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