Lectures in Engineering Economy
Prof. Corrado lo Storto
DIEG, Dept. of Economics and Engineering Management
School of Engineering, University of Naples Federico II
email: corrado.lostorto@unina.it
phone: 081-768.2932
Major issues
 Income tax definition (individual and corporate)
 Tax and net income
 Before-tax and after-tax analysis
 How to develop the format of after-tax cash flow statement?
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Income taxes
1. Since taxes are a cash outflow of a project, economic
analyses should reflect the after-tax cash flow of a project
in order to achieve a true reflection of the cash flow
patterns.
2. Tax laws are imposed for revenue generation. However, a
secondary purpose is that of social legislation. The laws
are very complex with many exceptions. However, this
lecture will focus on the fundamental concepts.
3. In a sense, the government shares in every profitable
venture through the taxation of a portion of the profits.
The contrary is also true if the individual or corporation has
other profit generating activities to offset the loss in a
venture.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Forms of business organization for tax purposes
Individual: Applicable to an employee, a sole proprietor
(individual engaging in business alone) or individual members
of partnerships; taxed at individual rates;
Partnership: Must file annual information return, each partner
is taxed on his share of partnership earnings - whether or not
distributed;
Corporation: Taxed at corporate tax rates unless the
corporation is treated like a partnership.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Forms of business organization for tax purposes
Earnings to a corporation are taxed twice:
• Once while in the corporation
• Once after distribution to shareholders as dividends
This occurs because dividends are usually not a tax deductible
expense for the corporation.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Taxation for individuals
Marginal percentage rates increase as taxable income increases.
Taxable income =
adjusted gross income
(revenue, earnings)
-
deductions for exemptions
-
itemized deductions in
excess of standard deduction
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Taxation for corporations
Tax rates:
approx. 35% currently (depends on Country)
Lower rates for taxable income
below $10,000,000 (approx., depends on Country)
Taxable income =
gross income (revenue)
- expenditures for operating
expenses
- tax depreciation and depletion
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Taxation for corporations
 A key point to remember is that capital expenditures (buildings,
machinery, etc.) are not deductible as operating expenses, but rather
are recovered through depreciation or depletion.
 A second key point to note is that depreciation when considered as a
tax deduction results in less taxes and therefore is a source of cash
flow to match the cash outflow when the investment is made.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example of computation of taxable income and
computation of income tax for a corporation
Gross Income (or revenue)
- Salaries
- Operating Costs
- Raw Materials
- Tax Depreciation
$ 3,000,000
$ 180,000
$ 200,000
$ 1,500,000
$ 620,000
Taxable Income
$
500,000
Taxes Payable @ 35%
$
175,000
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example of computation of taxable income and
computation of income tax for a corporation
As a practical matter, we normally assume a corporate tax rate of 35%
ignoring the smaller rates at lower levels of taxable income. We do this
because usually the firm for which the analysis is being done is large
enough to have many projects and since the lower rates may be used
on only once, the marginal rate for most corporations is 35%.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Capital gains and losses
If the selling price of a capital asset exceeds the book value, the excess
of selling price over book value is called a capital gain. If the selling
price is less than book value, the difference is a capital loss.
For a corporation, capital gains are taxed at ordinary corporate tax rates.
Corporate capital losses can be subtracted from any capital gains during
the tax year. The net remaining losses may be carried back or forward.
In general, capital losses cannot be used to offset ordinary operating
income.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Key Accounting Concepts Financial Accounting (Or Book)
Net Income - earnings after recognition of revenues less operating
expenses, book depreciation, and the book tax provision.
Revenues - value of product sales or services rendered.
Operating Expenses - salaries, product materials, rent, etc. Capital
expenditures and dividends are not operating expenses.
Book Depreciation - systematic allocation of original cost over the useful
life of the asset.
Book Tax Provision - tax rate times income before taxes.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Tax Accounting
Net Income - no such term in tax accounting.
Revenues - generally similar to book revenues. We assume no
difference.
Operating Expenses - generally similar to book definition. We
assume no difference.
Book Depreciation - no such term in tax accounting.
Tax Depreciation – i.e., MACRS allocation of tax basis in US.
Tax Basis - historical cost of asset less any accumulated tax
depreciation.
Taxable Income - revenues less operating expenses less tax
depreciation.
Current Taxes Payable - taxable income times tax rate.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
The Concept of Deferred Taxes
Deferred income taxes is a concept associated only with the book or
financial accounting.
It is not a tax accounting concept. Tax accounting computes an
income tax payable. It is payable for and within the current year.
Book accounting also computes a provision for income taxes as a
reduction of net income. Thus, the book provision for income taxes
is based upon book depreciation and will differ from current taxes
payable if book and tax depreciation are not equal.
The difference between current taxes payable and the book tax
provision is known as deferred taxes and thus is important in
tracking cash.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Comparison between tax and book account
Revenues
Operating Expenses
Depreciation
Taxable Income
Income Before Taxes
Current Taxes Payable (35%)
Book Provision (35%)
Net Income
Tax
$10,000
2,000
8,000
4,000
4,000
Book
$10,000
2,000
8,000
2,000
6,000
$ 1,400
2,100
$ 3,900
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Tax and book account, and the deferred tax
Thus, our book provision for income taxes is $2,100 while our current
taxes are $1,400. The difference of $700 is known as a deferred tax.
The meaning of a deferred tax is that it represents a tax on current
book year earnings that will be paid in a future year. The deferred tax
could alternatively be computed as the difference in tax and book
depreciation (4,000-2,000) times the tax rate (35%).
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Tax and book account, and the deferred tax
Assume the following depreciation schedules for book and tax purposes for
a $10,000 asset:
Year
1
2
3
4
5
6
7
8
9
10
Tax
Depreciation
Book
Depreciation
Difference
800
1,400
1,200
1,000
1,000
1,000
900
900
900
900
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
(200)
400
200
(100)
(100)
(100)
(100)
10,000
10,000
-0-
Tax
Rate
Deferred
Tax
Accumulated
Deferred Tax
35%
35%
35%
35%
35%
35%
35%
35%
35%
35%
(70)
140
70
(35)
(35)
(35)
(35)
(70)
70
140
140
140
140
115
70
35
-0-
-0-
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Tax depreciation trend
tax depreciation
1400
1200
1000
800
600
400
200
0
1
2
3
4
5
6
7
8
9
10
year
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
The deferred tax: Key Points
1.
The deferred tax in the first year is negative meaning that the
current taxes payable to the government are higher than the
book income tax provision.
2.
Over time the exact same amount will be taken for tax
depreciation as taken for book depreciation.
3.
Since the statement in 2. is correct, it follows that over time
the accumulated deferred tax will become zero.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Taxable Income and Income Taxes
Item
Gross Income
Expenses
Cost of goods sold (revenues)
Depreciation
Operating expenses
Taxable income
Income taxes
Net income
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Corporate Income Taxes
Facts:
Capital expenditure
(allowed depreciation)
$ 100,000
$ 58,000
Gross Sales revenue
$1,250,000
Expenses:
Cost of goods sold
Depreciation
Leasing warehouse
$ 840,000
$ 58,000
$ 20,000
Question: Taxable income?
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Corporate Income Taxes
Taxable income:
Gross income
- Expenses:
(cost of goods sold)
(depreciation)
(leasing expense)
Taxable income
• Income taxes:
First
$50,000 @ 15%
$25,000 @ 25%
$25,000 @ 34%
$232,000 @ 39%
Total taxes
$1,250,000
$840,000
$58,000
$20,000
$332,000
$
7,500
$
6,250
$
8,500
$ 90,480
$ 112,730
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Corporate Income Taxes
 Average tax rate:
Total taxes
=
Taxable income =
$112,730
$332,000
$112,730
$332,000
 33.95%
Average tax rate=
 Marginal tax rate:
Tax rate that is applied to the last dollar earned
39%
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Net Income Calculation
Item
Amount
Gross income (revenue)
$50,000
Expenses
Cost of goods sold
Depreciation
Operating expenses
20,000
4,000
6,000
Taxable income
20,000
Taxes (40%)
Net income
8,000
$12,000
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example of corporate taxation: the U.S. Corporate Tax Rate
(2005)
Tax rates are progressive: the more you earn, the more you pay
Tax rates increase in stair-step fashion
Taxable income
0-$50,000
$50,001-$75,000
$75,001-$100,000
$100,001-$335,000
$335,001-$10,000,000
$10,000,001-$15,000,000
$15,000,001-$18,333,333
$18,333,334 and Up
Tax rate
15%
25%
34%
39%
34%
35%
38%
35%
Tax computation
$0 + 0.15(D)
$7,500 + 0.25 (D)
$13,750 + 0.34(D)
$22,250 + 0.39 (D)
$113,900 + 0.34 (D)
$3,400,000 + 0.35 (D)
$5,150,000 + 0.38 (D)
$6,416,666 + 0.35 (D)
(D) denotes the taxable income in excess of the lower bound of each
tax bracket
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Capital Expenditure versus Depreciation Expenses
0
$28,000
0
1
2
3
4
5
6
7
8
Capital expenditure
(actual cash flow)
1
2
3
4
7
6
7
8
$1,250
$4,000
$3,500 $2,500 $2,500 $2,500
$4,900
$6,850
Allowed depreciation expenses (not cash flow)
(tax depreciation according to US MACRS)
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Cash Flow vs. Net Income
Net income:
Net income is an accounting means of
measuring a firm’s profitability based
on the matching concept. Costs become
expenses as they are matched against
revenue. The actual timing of cash inflows
and outflows are ignored.
Cash flow:
Considering the time value of money, it is better
to receive cash now than later, because cash
can be invested to earn more money. So,
cash flows are more relevant data to use in
project evaluation.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Why Do We Use Cash Flow in Project Evaluation?
Example: Both companies (A & B) have the same amount of
net income and cash sum over 2 years, but Company A returns
$1 million cash yearly, while Company B returns $2 million
at the end of 2nd year. Company A can invest $1 million in year
1, while Company B has nothing to invest during the same period.
Company A
Company B
Year 1
Net income
Cash flow
$1,000,000
1,000,000
$1,000,000
0
Year 2
Net income
Cash flow
1,000,000
1,000,000
1,000,000
2,000,000
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Cash Flow versus Net Income
Item
Income
Cash Flow
Gross income (revenue
$50,000
$50,000
Expenses
Cost of goods sold
Depreciation
Operating expenses
20,000
4,000
6,000
-20,000
Taxable income
20,000
Taxes (40%)
Net income
8,000
-6,000
-8,000
$12,000
Net cash flow
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
$16,000
Net income versus net cash flow
Net cash flows = Net income + non-cash expense (depreciation)
$50,000
$40,000
$30,000
$20,000
$10,000
Net
cash flow
Net income
$12,000
Depreciation
$4,000
Income taxes
$8,000
Operating expenses
Cost of goods sold
$6,000
Gross
revenue
$20,000
$0
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Just to remember…
=
=
Revenues
Operating Expenses
Depreciation (Book)
Income Before Taxes
Book Tax Provision
Net Income
Key Comment: Net income does not equate to cash flow from
operations as discussed later.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Just to remember…
=
x
=
Revenues
Operating Expenses
Tax Depreciation
Taxable Income
Tax Rate
Current Taxes Payable
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
After-Tax Economic Analyses
After-tax economic analyses (ATCFs) can be performed by using exctly the
same methods as before-tax analyses. The only difference is that ATCFs
are used in place of before-tax cash flows (BTCFs) by including expenses
(or savings) due to income taxes and then making equivalent worth
calculations using an after-tax MARR.
The income tax rates and governing regulations may be complex and
subject to changes, but once those rates and regulations have been
translated into their effect on ATCFs, the remainder of the after-tax
analysis is relatively straigthforward
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
After-Tax Economic Analyses
To formalize the procedure, the following notation is adopted:
Rk= revenues from the project; this is the positive cash flow from the
project during period k,
Ek= cash outflows during year k for deductible expenses and interest,
dk= sum of all noncash, or book, costs during year k, such as depreciation
and depletion,
t= effective income tax rate on ordinary income; t is assumed to remain
constant during the study period,
Tk= income taxes paid during year k
ATCFk=ATCF from the project during year k
K=0, 1, 2, …, N
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
After-Tax Economic Analyses
Because net income before-tax (NIBT) is
Rk – Ek - dk
The ordinary income tax liability when Rk>(Ek-dk) is computed as
Tk=-t(Rk-Ek-dk)
The net income after-tax (NIAT) is then simply taxable income (i.e., net
income before tax) minus the tax liability amount detemined
NIATk=(Rk-Ek-dk)-t(Rk-Ek-dk)
or
NIATk=(Rk-Ek-dk)(1-t)
The ATCF associated with a project equals the NIAT plus noncash items
such as depreciation
ATCFk=NIATk+dk=(Rk-Ek-dk)(1-t)+dk=(Rk-Ek)(1-t)+tdk
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
After-Tax Economic Analyses
In many economic analyses of engineering and business projects, ATCFs in
year k are computed in terms of BTCFs (i.e., year k before-tax cash flows)
BTCFk=Rk-Ek
Thus,
ATCFk=BTCFk+Tk
=(Rk-Ek)-t(Rk-Ek-dk)
=(1-t)(Rk-Ek)+tdk
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
After-Tax Economic Analyses
A Table useful to facilitate the computation of after-tax cash flows
year
(A)
Before-tax
Cash flow
(B)
Depreciation
(C )=(A)-(B)
Taxable income
(D)=-t(C )
Cash flow for
income taxes
(E)=(A)+(D)Afte
r-tax cash flow
k
Rk-Ek
dk
Rk-Ek-dk
-t(Rk-Ek-dk)
(1-t)(Rk-Ek)+tdk
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Project Cash Flow Analysis
How to develop the format of after-tax cash flow statement?
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Types of Cash Flow Elements in Project Analysis
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Cash Flows from Operating Activities
Approach 1
Income Statement Approach
Operating revenues
- Cost of goods sold
- Depreciation
- Operating expenses
- Interest expenses
Taxable income
- Income taxes
Net income
+ Depreciation
Approach 2
Direct Cash Flow Approach
Operating revenues
- Cost of goods sold
- Operating expenses
- Interest expenses
- Income taxes
Cash flow from operation
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
A Typical Format used for Presenting Cash Flow Statement
Cash flow statement
+ Net income
+Depreciation
Income statement
Revenues
Expenses
Cost of goods sold
Depreciation
Debt interest
Operating expenses
Taxable income
Income taxes
Net income
-Capital investment
+ Proceeds from sales of
depreciable assets
- Gains tax
- Investments in working
capital
+ Working capital recovery
+ Borrowed funds
-Repayment of principal
Operating
activities
+
Investing
activities
+
Financing
activities
Net cash flow
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: The Automated Machining Center Project (when
projects require only operating and investing activities)
 Project Nature: Installation of a new computer control system
 Financial Data:
– Investment: $125,000
– Project life: 5 years
– Working capital investment: $23,331
– Salvage value: $50,000
– Annual labor savings: $100,000
– Annual additional expenses:
• Labor: $20,000
• Material: $12,000
• Overhead: $8,000
– Depreciation Method: 7-year MACRS
– Income tax rate: 40%
– MARR: 15%
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: The Automated Machining Center Project (when
projects require working capital investments)
 Working capital means the amount carried in cash, accounts
receivable, and inventory that is available to meet day-to-day
operating needs.
 How to treat working capital investments: just like a capital
expenditure except that no depreciation is allowed.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Questions
 Develop the project’s cash flows over its project life.
 Is this project justifiable at a MARR of 15%?
 What is the internal rate of return of this project?
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
(a) Step 1: Depreciation Calculation
 Cost Base = $125,000
 Recovery Period = 7-year MACRS
N
MACRS Rate
Depreciation
Amount
Allowed Depreciation
Amount
1
14.29%
$17,863
$17,863
2
24.49%
$30,613
$30,613
3
17.49%
$21,863
$21,863
4
12.49%
$15,613
$15,613
5
8.93%
$11,150
$5,575
6
8.92%
$11,150
0
7
8.93%
$11,150
0
8
4.46%
$5,575
0
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
(a) Step 2: Gains (Losses) associated with Asset Disposal
 Salvage value = $50,000
 Book Value (year 5) = Cost Base – Total Depreciation
= $125,000 - $ 91,525
= $ 33,475
 Taxable gains = Salvage Value – Book Value
= $50,000 - $ 33,475
= $16,525
 Gains taxes = (Taxable Gains)(Tax Rate)
= $16,525 (0.40)
= $6,610
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Step 3 – Create an Income Statement
Income Statement
1
2
3
4
5
$100,000
$100,000
$100,000
$100,000
$100,000
Labor
20,000
20,000
20,000
20,000
20,000
Material
12,000
12,000
12,000
12,000
12,000
8,000
8,000
8,000
8,000
8,000
17,863
30,613
21,863
15,613
5,581
$42,137
$29,387
$38,137
$44,387
$54,419
16,855
11,755
15,255
17,755
21,768
$25,282
$17,632
$22,882
$26,632
$32,651
Revenues
0
Expenses:
Overhead
Depreciation
Taxable Income
Income Taxes (40%)
Net Income
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Step 4 – Develop a Cash Flow Statement
Cash Flow Statement
0
1
2
3
4
5
Operating Activities:
Net Income
$25,282
$17,632 $22,882 $26,632
$32,651
Depreciation
$17,863 $30,613 $21,863 $15,613
$5,581
Investment Activities:
Investment
Working capital
($125,000)
($23,331)
$23,331
Salvage
$50,000
Gains Tax
($6,613)
Net Cash Flow
($148,331)
$43,145 $48,245
$44,745 $42,245
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
$104,950
An Excel Worksheet
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Net Cash Flow Table Generated by Traditional
Method Using Approach 2
A
B
C
D
E
F
G
H
I
J
Year
End
Investment &
Salvage Value
Revenue
Labor
Expenses
Materials
Overhead
Depreciation
Taxable
Income
Income
Taxes
Net Cash
Flow
0
-$125,000
-$23,331
-$125,000
1
$100,000
$20,000
$12,000
$8,000
$17,863
$42,137
$16,855
$43,145
2
$100,000
$20,000
$12,000
$8,000
$30,613
$29,387
$11,755
$48,245
3
$100,000
$20,000
$12,000
$8,000
$21,863
$38,137
$15,255
$44,745
4
$100,000
$20,000
$12,000
$8,000
$15,613
$44,387
$17,755
$42,245
5
$100,000
$20,000
$12,000
$8,000
$5,581
$54,419
$21,678
$38,232
$16,525
$6,613
$43,387
$23,331
$50,000*
23,331
*Salvage value
Note that
H = C-D-E-F-G
I = 0.4 * H
J= B+C-D-E-F-I
k
Information required to
calculate the income taxes
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Cash Flow Diagram including Working Capital
$23,331
$43,145
$48,245
1
2
0
$125,000 Investment in
physical assets
$23,331
$44,745
3
Working capital
recovery
$81,619
$42,245
4
5
$23,331
$23,331
Investment in
working capital
0
$23,331
1
$23,331
2
3
4
Years
Working capital recovery cycles
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
5
Question (b):
• Is this investment justifiable at
a MARR of 15%?
$104,950
• PW(15%) = -$148,331 +
+$43,145(P/F, 15%, 1) + . . .
. + $104,950 (P/F, 15%, 5)
= $31,420 > 0
$43,145
$48,245 $44,745
$42,245
0
1
2
3
 Yes, Accept the Project !
4
5
Years
$148,331
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Question (C): IRR
A
B
1
Period
Cash Flow
2
0
($148,331)
3
1
$43,145
4
2
$48,245
5
3
$44,745
6
4
$42,245
7
5
$104,950
=IRR(B2:B7,0.10)
IRR = 22.55%
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Rate of Return Analysis (IRR = 22.55%)
n=0
n =1
n=2
n=3
n=4
n=5
Beginning
Balance
-$148,331
-$138,635
-$121,652
-$104,339
-$85,622
Return on
Investment
(interest)
-$33,449
-$31,262
-$27,432
-$23,528
-$19,328
Payment
-$148,331
$43,145
$48,245
$44,745
$42,245
$104,950
Project
Balance
-$148,331
-$138,635
-$121,652
-$104,339
-$85,622
0
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
When Projects are Financed with Borrowed Funds
 Key issue: Interest payment is
a tax-deductible expense.
 What Needs to Be Done: Once
a loan repayment schedule is
known, separate the interest
payments from the annual
installments.
 What about Principal
Payments? As the amount of
borrowing is NOT viewed as
income to the borrower, the
repayments of principal are
NOT viewed as expenses
either– NO tax effect.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Loan Repayment Schedule (Example)
 Amount financed: $62,500, or 50% of total capital expenditure
 Financing rate: 10% per year
 Annual installment: $16,487 or, A = $62,500(A/P, 10%, 5)
End of
Year
Beginning
Balance
Interest
Payment
Principal
Payment
Ending
Balance
1
$62,500
$6,250
$10,237
$52,263
2
$52,263
$5,226
$11,261
$41,002
3
$41,002
$4,100
$12,387
$28,615
4
$28,615
$2,861
$13,626
$14,989
5
$14,989
$1,499
$14,988
0
$16,487
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Loan Repayment Schedule (Example)
Additional
entries related
to debt financing
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
When Projects Results in Negative Taxable Income
Negative taxable income
(project loss) means you can
reduce your taxable income
from regular business
operation by the amount of
loss, which results in a tax
savings.
Handling Project Loss
Taxable
income
Income
taxes (35%)
Regular
Business
Project
Combined
Operation
$100M
(10M)
$90M
$35M
?
$31.5M
Tax savings
Tax Savings = $35M - $31.5M
= $3.5M
Or (10M)(0.35) = -$3.5M
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Effects of Inflation on Project Cash Flows
Item
Depreciation expense
Effects of Inflation
Depreciation expense is charged to
taxable income in money of declining
values; taxable income is overstated,
resulting in higher taxes
Note: Depreciation expenses are based on historical costs and
always expressed in actual money
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Effects of Inflation on Project Cash Flows
Item
Salvage value
Effects of Inflation
Inflated salvage value combined with
book values based on historical costs
results in higher taxable gains.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Effects of Inflation on Project Cash Flows
Item
Loan repayments
Effects of Inflation
Borrowers repay historical loan
amounts with money of decreased
purchasing power, reducing the debtfinancing cost.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Effects of Inflation on Project Cash Flows
Item
Working capital
requirement
Effects of Inflation
Known as working capital drain, the
cost of working capital increases in an
inflationary environment.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Effects of Inflation on Project Cash Flows
Item
Rate of Return and
NPW
Effects of Inflation
Unless revenues are sufficiently
increased to keep pace with inflation,
tax effects and/or a working capital
drain result in lower rate of return or
lower NPW.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Effects of Inflation on Project Cash Flows
A
1
7
8
9
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
B
C
D
E
F
G
H
Example 9.3 Cash Flow Statement for the Automated Machining Center Project
Income Statement
Inflation Rate
1
2
3
4
5
5%
$ 105,000
$ 110,250
$ 115,763
$ 121,551
$ 127,628
5%
5%
5%
21,000
12,600
8,400
17,863
22,050
13,230
8,820
30,613
23,153
13,892
9,261
21,863
24,310
14,586
9,724
15,613
25,526
15,315
10,210
5,581
Taxable Income
Income Taxes (40%)
$ 45,137
18,055
$ 35,537
14,215
$ 47,595
19,038
$ 57,317
22,927
$ 70,996
28,398
Net Income
$ 27,082
$ 21,322
$ 28,557
$ 34,390
$ 42,598
27,082
17,863
21,322
30,613
28,557
21,863
34,390
15,613
42,598
5,581
(1,351)
63,814
(12,139)
28,361
Revenues
Expenses:
Labor
Material
Overhead
Depreciation
0
Cash Flow Statement
Operating Activities:
Net Income
Depreciation
Investment Activities:
Investment
Salvage
Gains Tax
Working Capital
Net Cash Flow
(in actual dollars)
(125,000)
5%
5%
(23,331)
(1,167)
$ (148,331) $ 43,778
(1,225)
$ 50,710
(1,287)
$ 49,133
$ 48,652
$ 128,215
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example: Applying Specific Inflation Rates
Example 9.4 Cash Flow Statement for AMC Project under Inflation (Multiple Price Indices)
Income Statement
Inflation Rate
Revenues
Expenses:
Labor
Material
Overhead
Depreciation
0
6%
1
2
3
4
5
$106,000 $112,360 $119,102 $ 126,248 $ 133,823
5%
4%
5%
21,000
12,480
8,400
17,863
22,050
12,979
8,820
30,613
23,153
13,498
9,261
21,863
24,310
14,038
9,724
15,613
25,526
14,600
10,210
5,581
Taxable Income
Income Taxes (40%)
$ 46,257 $ 37,898 $ 51,327 $ 62,562 $ 77,906
18,503
15,159
20,531
25,025
31,162
Net Income
$ 27,754 $ 22,739 $ 30,796 $ 37,537 $ 46,744
Cash Flow Statement
Operating Activities:
Net Income
Depreciation
Investment Activities:
Investment
Salvage
Gains Tax
Working Capital
Net Cash Flow
(in actual dollars)
27,754
17,863
22,739
30,613
30,796
21,863
37,537
15,613
46,744
5,581
(1,351)
57,964
(9,799)
28,361
(125,000)
3%
5%
(23,331)
(1,167)
(1,225)
(1,287)
$ (148,331) $ 44,450 $ 52,127 $ 51,372 $ 51,799 $ 128,851
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Rate of Return Analysis under Inflation
_
f  10%
 Principle:True (real) rate of
return should be based on
constant money.
 If the rate of return is
computed based on actual
money, the real rate of return
can be calculated as:
i' 
1 i
_
Net cash flows
in constant
dollars
n
Net cash flows
in actual dollars
0
1
2
3
4
-$30,000
$13,570
$15,860
$13,358
$13,626
-$30,000
$12,336
$13,108
$10,036
$9,307
IRR
31.34%
19.40%
1
1 f
1  0.3134

1
1  0.10
 19.40%
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Decision Criterion
 If you use 31.34% as your IRR, you should use a market interest
rate (or inflation-adjusted MARR) to make an accept and reject
decision.
 If you use 19.40% as your IRR, you should use an inflation-free
interest rate (inflation-free MARR) to make an accept and reject
decision.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Example
Input
Tax Rate(%) =
MARR(%) =
Output
PW(i) =
IRR(%) =
40
15
0
1
2
3
$37,761
33.74%
4
5
6
Income Statement
Revenues (savings)
Expenses:
Depreciation
$38,780
$38,780
$38,780
$38,780
$38,780
$38,780
9,817
16,825
12,016
8,581
6,135
3,064
Taxable Income
Income Taxes (40%)
$28,963
11,585
$21,955
8,782
$26,764
10,706
$30,199
12,080
$32,645
13,058
$35,716
14,286
Net Income
$17,378
$13,173
$16,059
$18,120
$19,587
$21,430
Cash Flow Statement
Operating Activities:
Net Income
Depreciation
Investment Activities:
Investment
Salvage
Gains Tax
Net Cash Flow
$
$
$
17,378 $
9,817 $
13,173 $
16,825 $
16,059 $
12,016 $
18,120 $
8,581 $
19,587 $
6,135 $
21,430
3,064
$
$
3,500
3,505
(68,701)
($68,701)
$27,195
$29,998
$28,074
$26,700
$25,722
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
$31,499
Calculating the after-tax Cost of Debt
id  (c s / c d )k s (1  tm )  (cb / c d )k b (1  tm )
where C s  the amount of the term loan,
Cb  the amount of bond financing,
k s  the before-tax interest rate on the term loan,
k b  the before-tax interest rate on the bond,
t m  the firm's marginal tax rate, and
C d  C s  Cb
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Practice Problem
 Alpha Corporation needs to
Interest
Source
Amount
Fraction
raise $10 million and has
rate
decided to finance $4 million
$1.33M
0.333
12%
by securing a term loan and
Term
Loan
issuing 20-year $1,000 par
bonds for the following
condition. (The remaining
Bond
$2.67M
0.667
10.74%
funds would be raised through
equity financing.)
 Alpha’s marginal tax rate is
38%, and it is expected to
remain constant in the future.
What is the after-tax cost of
debt?
id = 0.3330.121  0.38 + 0.667 0.1074 1  0.38
= 6.92%.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Summary
 Accounting depreciation can be broken into two categories:
1. Book depreciation—the method of depreciation used for financial
reports and pricing products;
2. Tax depreciation—the method of depreciation used for calculating
taxable income and income taxes; it is governed by tax legislation.
 The four components of information required to calculate
depreciation are:
(a) cost basis, (b) salvage value, (c) depreciable life , and (4)
depreciation method.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Summary
 Because it employs accelerated methods of depreciation and shorterthan-actual depreciable lives, the MACRS (Modified Accelerated Cost
Recovery System) gives taxpayers a break: It allows them to take
earlier and faster advantage of the tax-deferring benefits of
depreciation.
 The total amount of taxes to pay remains unchanged regardless of
depreciation methods adopted. It only changes the timing of the
payment.
 Many firms select straight-line depreciation for book depreciation
because of its relative ease of calculation.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto
Summary
 Explicit consideration of taxes is a necessary aspect of any complete
economic study of an investment project.
 Once we understand that depreciation has a significant influence on
the income and cash position of a firm, we will be able to appreciate
fully the importance of utilizing depreciation as a means to maximize
the value both of engineering projects and of the organization as a
whole.
Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto