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 – F n = P (F/P, f, n) P n = F (1 + f ) –n – or – P n = 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. Actual Dollars f = Average Inflation Rate $785 / QTR Tuition & Fees ACTUAL $ $785 / QTR Tuition & Fees $785 (1+ f ) 29 / QTR Tuition & Fees CONSTANT $ $A = $C (1+ f ) n $C = $A (1+ f ) – n

Incorporating Inflation Inflation can be accounted for as an additional component on top of the MARR or interest rate: d = i + f + if (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)

DepreciationDepreciation 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 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 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 Method D n = ( I – S ) N B n = I – D n (n) Where: I = Cost Basis; Initial Price plus installation expenses. S = Salvage Value D n = Depreciation in Year n B n = Book Value remaining in Year n N = estimated years of useful life n = the year currently under consideration

Declining Balance Method  = (Multiplier) = % reduction each year D n =  I (1–  ) n–1 B n = I (1–  ) n Typical multipliers are 150% and 200%. 200% is also called Double Declining Balance (DDB). 1N1N

Sum of Years Digits Method SOYD = … + N = N(N+1) 2 D n = ( N – n + 1 ) ( I – S ) SOYD B n = B n–1 – D n

Units of Production Method D n = Service Units Consumed During Year n ( I – S ) Total Service Units n B n = I –  Service Units Consumed During Year n ( I – S ) Total Service Units

MACRSMACRS MACRS is a simpler, more rapid depreciation method. MACRS has been required for tax purposes since 1981 / MACRS book value is the legal standard for valuing equipment for tax purposes.

MACRS Depreciation Schedule Class: Year200% DB 150% DB * * * *5.90* * Year to switch to straight line depreciation Values shown are percentages

MACRSMACRS D n = ( Year n MACRS Class Table Value )( I ) n B n = ( 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 D n value lower, and … Selling year book value is ½ D n value higher!

Marginal 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 Rates 2009 Federal Corporate Tax Schedule Taxable IncomeTax Rate $0 to $50,00015% $50,001 to $75,00025% $75,001 to $100,00034% $100,001 to $335,00039% $335,001 to $10,000,00034% $10,000,001 to $15,000,00035% $15,000,001 to $18,333,33338% $18,333,334 and up35%

After Tax Analysis 1.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 Asset 1. 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 D n lower,  and the book value is ½ D n 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 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