# IENG 302 Lecture 19: Final Review and Example Exam Questions by 32Gp64yR

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```									       Inflation / 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.
Actual Dollars
1980                                       2009
CONSTANT
\$                    \$785 / QTR                    \$785 / QTR
Tuition & Fees                Tuition & Fees

\$A = \$C (1+ f )n                                                     \$C = \$A (1+ f )– n

1980                                       2009
ACTUAL
\$                    \$785 / QTR
Tuition & Fees
\$785 (1+ f )29 / QTR
Tuition & Fees

f = Average Inflation Rate
Incorporating 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)
Depreciation
• 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
Dn = ( I – S )
N

Bn = I – Dn (n)
Where:
I = Cost Basis; Initial Price plus installation
expenses.
S = Salvage Value
Dn = Depreciation in Year n
Bn = Book Value remaining in Year n
N = estimated years of useful life
n = the year currently under consideration
Declining Balance Method
=     1
(Multiplier)
N

= % 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).
Sum of Years Digits Method

SOYD = 1 + 2 + 3 + … + N
= N(N+1)
2

Dn = ( N – n + 1 ) ( I – S )
SOYD

Bn = Bn–1 – Dn
Units of Production Method

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
MACRS
• 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 Schedule
Class:      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
* Year to switch to straight line depreciation
14                                                       5.90
15      Values shown are percentages                     5.91
16                                                       2.95
MACRS

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 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 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 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 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 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

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