Lectures in Engineering Economy

Lectures in Engineering Economy

Prof. Corrado lo StortoDIEG, Dept. of Economics and Engineering Management

School of Engineering, University of Naples Federico II

email: [email protected]

phone: 081-768.2932

Major issues

Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto

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?

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.


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.


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.


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


Taxation for corporations

Tax rates: approx. 35% currently (depends on Country)Lower rates for taxable incomebelow $10,000,000 (approx., depends on Country)

Taxable income = gross income (revenue) - expenditures for operating

expenses - tax depreciation and depletion


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.


Example of computation of taxable income and computation of income tax for a corporation

Gross Income (or revenue) $ 3,000,000- Salaries $ 180,000- Operating Costs $ 200,000- Raw Materials $ 1,500,000- Tax Depreciation $ 620,000

Taxable Income $ 500,000

Taxes Payable @ 35% $ 175,000


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%.


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.


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.


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.


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.


Comparison between tax and book account

Tax BookRevenues $10,000 $10,000Operating Expenses 2,000 2,000

8,000 8,000Depreciation 4,000 2,000Taxable Income 4,000 -Income Before Taxes 6,000Current Taxes Payable (35%) $ 1,400Book Provision (35%) 2,100Net Income $ 3,900


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%).


Tax and book account, and the deferred tax

Assume the following depreciation schedules for book and tax purposes for a $10,000 asset:

Tax Book Tax DeferredAccumulatedYear Depreciation Depreciation Difference Rate Tax Deferred Tax

1 800 1,000 (200) 35% (70) (70)

2 1,400 1,000 400 35% 140 70

3 1,200 1,000 200 35% 70 140

4 1,000 1,000 - 35% - 140

5 1,000 1,000 - 35% - 140

6 1,000 1,000 - 35% - 140

7 900 1,000 (100) 35% (35) 115

8 900 1,000 (100) 35% (35) 70

9 900 1,000 (100) 35% (35) 35

10 900 1,000 (100) 35% (35) -0-

10,000 10,000 -0- -0-


Tax depreciation trend

tax depreciation

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10

year


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.


Taxable Income and Income Taxes

Gross Income

Expenses

Cost of goods sold (revenues)

Depreciation

Operating expenses

Taxable income

Income taxes

Net income

Item


Example: Corporate Income Taxes

Facts:Capital expenditure $ 100,000(allowed depreciation) $ 58,000

Gross Sales revenue $1,250,000

Expenses:Cost of goods sold $ 840,000Depreciation $ 58,000Leasing warehouse $ 20,000

Question: Taxable income?



Taxable income:Gross income $1,250,000- Expenses:

(cost of goods sold) $840,000(depreciation) $58,000(leasing expense) $20,000

Taxable income $332,000

• Income taxes:First $50,000 @ 15% $

7,500$25,000 @ 25% $

6,250$25,000 @ 34% $

8,500$232,000 @ 39% $ 90,480

Total taxes $ 112,730Engineering Economy/income tax and after tax analysis/ 2005 /prof. corrado lo storto

Average tax rate:

Total taxes = $112,730Taxable income = $332,000

Marginal tax rate:

Tax rate that is applied to the last dollar earned 39%


33 95

$112,730Average tax rate=

$332,000

. %


Example: Net Income Calculation

Item Amount

Gross income (revenue) $50,000

Expenses Cost of goods sold Depreciation Operating expenses

20,0004,0006,000

Taxable income 20,000

Taxes (40%) 8,000

Net income $12,000


Example of corporate taxation: the U.S. Corporate Tax Rate (2005)

Taxable income0-$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 rate15%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

Tax rates are progressive: the more you earn, the more you payTax rates increase in stair-step fashion


Capital Expenditure versus Depreciation Expenses

01 2 3 4 5 6 7 8

0 87673 41 2

$4,000

$6,850$4,900

$3,500 $2,500 $2,500 $2,500$1,250

$28,000

Capital expenditure(actual cash flow)

Allowed depreciation expenses (not cash flow)

(tax depreciation according to US MACRS)


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.


Why Do We Use Cash Flow in Project Evaluation?

Example: Both companies (A & B) have the same amount ofnet income and cash sum over 2 years, but Company A returns $1 million cash yearly, while Company B returns $2 millionat the end of 2nd year. Company A can invest $1 million in year1, while Company B has nothing to invest during the same period.

Company A Company B

Year 1 Net incomeCash flow

$1,000,000 1,000,000

$1,000,0000

Year 2 Net incomeCash flow

1,000,000 1,000,000

1,000,0002,000,000


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

20,0004,0006,000

-20,000

-6,000

Taxable income 20,000

Taxes (40%) 8,000 -8,000

Net income $12,000

Net cash flow $16,000


Net income versus net cash flow

$0

$50,000

$40,000

$30,000

$20,000

$10,000

$8,000

$6,000

$20,000

Net income

Depreciation

Income taxes

Operating expenses

Cost of goods sold

Netcash flow

Grossrevenue

$4,000

$12,000

Net cash flows = Net income + non-cash expense (depreciation)


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.


Just to remember…

Revenues- Operating Expenses- Tax Depreciation= Taxable Incomex Tax Rate= Current Taxes Payable


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



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



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)

orNIATk=(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



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



year (A)Before-taxCash flow

(B)Depreciatio

n

(C )=(A)-(B)Taxable income

(D)=-t(C )Cash flow for income taxes

(E)=(A)+(D)After-tax

cash flow

k Rk-Ek dk Rk-Ek-dk -t(Rk-Ek-dk) (1-t)(Rk-Ek)+tdk

A Table useful to facilitate the computation of after-tax cash flows


Project Cash Flow Analysis

How to develop the format of after-tax cash flow statement?


Types of Cash Flow Elements in Project Analysis


Cash Flows from Operating Activities

Approach 1Income Statement

Approach

Approach 2Direct Cash Flow Approach

Operating revenues - Cost of goods sold - Depreciation - Operating expenses - Interest expensesTaxable income - Income taxes

Net income+ Depreciation

Operating revenues - Cost of goods sold

- Operating expenses - Interest expenses

- Income taxes

Cash flow from operation


A Typical Format used for Presenting Cash Flow Statement

Income statement Revenues Expenses Cost of goods sold Depreciation Debt interest Operating expenses

Taxable incomeIncome taxesNet income

Cash flow statement

+ Net income+Depreciation

-Capital investment+ Proceeds from sales of depreciable assets- Gains tax- Investments in working capital+ Working capital recovery

+ Borrowed funds-Repayment of principal Net cash flow

Operatingactivities

Investing activities

Financingactivities

+

+


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%


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.


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?


(a) Step 1: Depreciation Calculation

Cost Base = $125,000

Recovery Period = 7-year MACRS

NMACRS 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


(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


Step 3 – Create an Income Statement

Income Statement 0 1 2 3 4 5

Revenues $100,000

$100,000

$100,000

$100,000

$100,000

Expenses:

Labor 20,000 20,000 20,000 20,000 20,000

Material 12,000 12,000 12,000 12,000 12,000

Overhead 8,000 8,000 8,000 8,000 8,000

Depreciation 17,863 30,613 21,863 15,613 5,581

Taxable Income $42,137 $29,387 $38,137 $44,387 $54,419

Income Taxes (40%)

16,855 11,755 15,255 17,755 21,768

Net Income $25,282 $17,632 $22,882 $26,632 $32,651


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 ($125,000)

Working capital ($23,331) $23,331

Salvage $50,000

Gains Tax ($6,613)

Net Cash Flow ($148,331)

$43,145

$48,245

$44,745

$42,245

$104,950


An Excel Worksheet


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

$50,000*23,331

$16,525

$6,613 $43,387$23,331Information required to

calculate the income taxes

*Salvage value Note thatH = C-D-E-F-GI = 0.4 * HJ= B+C-D-E-F-I

k


Cash Flow Diagram including Working Capital

0 1 2 3 4 5

$23,331Years

$23,331

Working capital recovery cycles

01 2 3 4 5

$43,145$48,245 $44,745

$42,245$81,619

Working capitalrecovery

$23,331

$125,000 Investment in physical assets

$23,331 Investment inworking capital

$23,331

$23,331


• Is this investment justifiable at a MARR of 15%?

• PW(15%) = -$148,331 + +$43,145(P/F, 15%, 1) + . . . . + $104,950 (P/F, 15%, 5)

= $31,420 > 0

Yes, Accept the Project !

Question (b):

0

1 2 3 4 5

$148,331

$43,145

$48,245$44,745$42,245

$104,950

Years


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%


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 Investmen

t(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


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.


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

BeginningBalance

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


Loan Repayment Schedule (Example)

Additionalentries related

to debt financing


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

Regular Business

ProjectCombined Operation

Taxable incomeIncome taxes (35%)

$100M

$35M

(10M)

?

$90M

$31.5M

Tax Savings = $35M - $31.5M

= $3.5M

Or (10M)(0.35) = -$3.5M

Tax savings


Effects of Inflation on Project Cash Flows

Item Effects of Inflation

Depreciation expense

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




Salvage value

Inflated salvage value combined with book values based on historical costs results in higher taxable gains.




Loan repayments

Borrowers repay historical loan amounts with money of decreased purchasing power, reducing the debt-financing cost.




Working capital requirement

Known as working capital drain, the cost of working capital increases in an inflationary environment.




Rate of Return and NPW

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.



178

91112131415161718192021222324

252627282930313233343536

A B C D E F G H

Example 9.3 Cash Flow Statement for the Automated Machining Center Project

Income StatementInflation Rate 0 1 2 3 4 5

Revenues 5% 105,000$ 110,250$ 115,763$ 121,551$ 127,628$ Expenses: Labor 5% 21,000 22,050 23,153 24,310 25,526 Material 5% 12,600 13,230 13,892 14,586 15,315 Overhead 5% 8,400 8,820 9,261 9,724 10,210 Depreciation 17,863 30,613 21,863 15,613 5,581

Taxable Income 45,137$ 35,537$ 47,595$ 57,317$ 70,996$ Income Taxes (40%) 18,055 14,215 19,038 22,927 28,398

Net Income 27,082$ 21,322$ 28,557$ 34,390$ 42,598$

Cash Flow Statement

Operating Activities: Net Income 27,082 21,322 28,557 34,390 42,598 Depreciation 17,863 30,613 21,863 15,613 5,581 Investment Activities: Investment (125,000) Salvage 5% 63,814 Gains Tax (12,139) Working Capital 5% (23,331) (1,167) (1,225) (1,287) (1,351) 28,361

Net Cash Flow (148,331)$ 43,778$ 50,710$ 49,133$ 48,652$ 128,215$ (in actual dollars)


Example: Applying Specific Inflation Rates

Example 9.4 Cash Flow Statement for AMC Project under Inflation (Multiple Price Indices)

Income StatementInflation Rate 0 1 2 3 4 5

Revenues 6% 106,000$ 112,360$ 119,102$ 126,248$ 133,823$ Expenses: Labor 5% 21,000 22,050 23,153 24,310 25,526 Material 4% 12,480 12,979 13,498 14,038 14,600 Overhead 5% 8,400 8,820 9,261 9,724 10,210 Depreciation 17,863 30,613 21,863 15,613 5,581

Taxable Income 46,257$ 37,898$ 51,327$ 62,562$ 77,906$ Income Taxes (40%) 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 27,754 22,739 30,796 37,537 46,744 Depreciation 17,863 30,613 21,863 15,613 5,581 Investment Activities: Investment (125,000) Salvage 3% 57,964 Gains Tax (9,799) Working Capital 5% (23,331) (1,167) (1,225) (1,287) (1,351) 28,361

Net Cash Flow (148,331)$ 44,450$ 52,127$ 51,372$ 51,799$ 128,851$ (in actual dollars)


Rate of Return Analysis under Inflation

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:

nNet cash flows in

actual dollars

Net cash flows in constant dollars

01234

-$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%

ii

f'

.

..40%

_

1

11

1 0 3134

1 0 101

19

f_

10%


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.


Example

Input OutputTax Rate(%) = 40 PW(i) = $37,761

MARR(%) = 15 IRR(%) = 33.74%

0 1 2 3 4 5 6Income Statement

Revenues (savings) $38,780 $38,780 $38,780 $38,780 $38,780 $38,780Expenses: Depreciation 9,817 16,825 12,016 8,581 6,135 3,064

Taxable Income $28,963 $21,955 $26,764 $30,199 $32,645 $35,716Income Taxes (40%) 11,585 8,782 10,706 12,080 13,058 14,286

Net Income $17,378 $13,173 $16,059 $18,120 $19,587 $21,430

Cash Flow StatementOperating Activities: Net Income 17,378$ 13,173$ 16,059$ 18,120$ 19,587$ 21,430$ Depreciation 9,817$ 16,825$ 12,016$ 8,581$ 6,135$ 3,064$ Investment Activities: Investment (68,701)$ Salvage 3,500$ Gains Tax 3,505$

Net Cash Flow ($68,701) $27,195 $29,998 $28,074 $26,700 $25,722 $31,499


Calculating the after-tax Cost of Debt

d s d s m b d b mi (c / c )k (1 t ) (c / c )k (1 t )

s

b

s

b

m

where C the amount of the term loan,

C the amount of bond financing,

k the before-tax interest rate on the term loan,

k the before-tax interest rate on the bond,

t the firm's marginal tax rate,

d s b

and

C C C


Practice Problem

Alpha Corporation needs to raise $10 million and has decided to finance $4 million by securing a term loan and issuing 20‑year $1,000 par bonds for the following condition. (The remaining 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?

Source AmountFractio

nInterest rate

Term Loan

Bond

$1.33M

$2.67M

0.333

0.667

12%

10.74%

di = 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.


Summary

Because it employs accelerated methods of depreciation and shorter-than-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.


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.


Documents

Lectures in Engineering Economy