Transcript IENG 302 Lecture 19: Final Review and Example Exam Questions

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
Pn = F (1 + f ) –n
– or –
– or –
Fn = P (F/P, f, n)
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
CONSTANT
$
1980
2009
$785 / QTR
Tuition & Fees
$785 / QTR
Tuition & Fees
$C = $A (1+ f )– n
$A = $C (1+ f )n
ACTUAL
$
1980
2009
$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
13
14
15
16
5.90
* Year to switch to straight line depreciation
Values shown are percentages
5.91
5.90
5.91
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
$0 to $50,000
$50,001 to $75,000
$75,001 to $100,000
$100,001 to $335,000
$335,001 to $10,000,000
$10,000,001 to $15,000,000
$15,000,001 to $18,333,333
$18,333,334 and up
Tax Rate
15%
25%
34%
39%
34%
35%
38%
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