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Fundamentals of Engineering Economics © 2004 by Chan S. Park
1
Chapter 5Project Cash Flow Analysis
Cost ClassificationsIncome Tax Rate to
Use in Project Analysis
Incremental Project Cash Flows
Impacts of Inflation on Project Cash Flows
Cost of Capital
Fundamentals of Engineering Economics © 2004 by Chan S. Park
2
Engineering Economic Decisions
• Evaluation of a Fixed Asset– Equipment– Buildings
• Valuation of Fixed Assets– Based on usable after-tax cash flows the asset
produces
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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General Cost Terms• Manufacturing Costs
Direct materialsDirect laborMfg. Overhead
• Non-manufacturing CostsOverheadMarketingAdministrative
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Classifying Costs for Financial Statements
• Matching Concept: The costs incurred to generate particular revenue should be recognized as expenses in the same period that the revenue is recognized.
• Period costs: Those costs that are matched against revenues on a time period basis
• Product costs:Those costs that are matched against revenues on a product basis.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Cost Classification for Predicting Cost Behavior
• Volume index• Cost Behaviors
Fixed costsVariable costsMixed costs
• Average unit costs
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Volume Index
• Def: The unit measure used to define “volume”
• Examples:– Automobile – “miles”
driven– Generating plant –
“kWh” produced– Stamping machine –
“parts” stamped
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Fixed Costs
• Def: The costs of providing a company’s basic operating capacity
• Cost behavior: Remain constant over the relevant range
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Variable Costs
• Def: Costs that vary depending on the level of production or sales
• Cost behavior: Increase or decrease proportionally according to the level of volume
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Average Unit Cost
• Def: activity cost per unit basis
• Cost Behaviors:– Fixed cost per unit
varies with changes in volume.
– Variable cost per unit of volume is a constant.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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What Income Tax Rate Should be Used in Project Analysis?
Regular Business
Project
RevenuesExpenses
$200,000$130,000
$40,000$20,000
Taxable IncomeIncome Taxes
$70,000$12,500
$20,000
?
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Incremental Income Tax Rate
Before Undertaking
Project
After Undertaking
Project
The Effect of Project
Gross revenue $200,000 $240,000 $40,000Expenses 130,000 150,000 20,000Taxable income $70,000 $90,000 $20,000Income taxes $12,500 $18,850 $6,350
Average tax rate 17.86% 20.94% 31.75%
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Before After Incremental
Taxable income $70,000 $90,000 $20,000
Income taxes 12,500 18,850 6,350
Average tax rate 17.86% 20.94%
Incremental tax rate 31.75%
$0
$20,000 $40,000 $60,000 $80,000 $100,000
Regular income from operation
$20,000 incrementaltaxable income due to
undertaking project
Marginal tax rate15% 25% 34%
$5,000at 25%
$15,000at 34%
0.25($5,000/$20,000) + 0.34($15,000/$20,000) = 31.75%
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Elements of Investment Decision
• Identification of Investment Opportunities• Generation of Cash Flows• Measures of Investment Worth• Project Selection• Project Implementation• Project-Control/Post-Audit
Our focus in this chapter is to
develop the format of after-tax cash flow statements.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Types of Cash Flow Elements in Project Analysis
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Approach 1Income Statement Approach
Approach 2Direct Cash Flow Approach
Operating revenues Cost of goods sold Depreciation Operating expenses Interest expensesTaxable income Income taxesNet income+ Depreciation
Operating revenues - Cost of goods sold
- Operating expenses - Interest expenses
- Income taxesCash flow from operation
Cash Flows from Operating Activities
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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A Typical Format used for Presenting Cash Flow Statement
Income statement Revenues Expenses Cost of goods sold Depreciation Debt interest Operating expensesTaxable 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
+
+
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Example 9.1 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%
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Questions
• (a) Develop the project’s cash flows over its project life.
• (b) Is this project justifiable at a MARR of 15%?
• (c) What is the internal rate of return of this project?
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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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.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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• (a) Step 1: Depreciation Calculation– Cost Base = $125,000– Recovery Period = 7-year MACRS
NMACRS
RateDepreciation
AmountAllowed Depreciation
Amount
1 14.29% $17,863 $17,8632 24.49% $30,613 $30,6133 17.49% $21,863 $21,8634 12.49% $15,613 $15,6135 8.93% $11,150 $5,5756 8.92% $11,150 07 8.93% $11,150 08 4.46% $5,575 0
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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(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
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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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
Example 9.1 - Income Statement
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Example 9.1- 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
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Example 9.1 - Net Cash Flow Table Generated by Traditional Method Using Approach 2
A B C D E F G H I JYear 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 $43,38723,331
Information required tocalculate the income taxes
*Salvage value Note thatH = C-D-E-F-GI = 0.4 * HJ= B+C-D-E-F-I
k
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Cash Flow Diagram including Working Capital
0 1 2 3 4 5
$23,331Years
$23,331
Working capital recovery cycles
0 1 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 in
working capital
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Question (b):
• 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 !
01 2 3 4 5
$148,331
$43,145
$48,245 $44,745 $42,245
$104,950
Years
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Question (C): IRR
A B1 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%
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Rate of Return Analysis (IRR = 22.55%)
n = 0 n =1 n = 2 n = 3 n = 4 n = 5Beginning
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
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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When Projects are Financed with Borrowed Funds
• Key issue: Interest payment is a tax-deductible expense.
• What Needs to Be Done: Once loan repayment schedule is known, separate interest payment from the annual installment.
• What about Principal Payment? As the amount of borrowing is NOT viewed as income to the borrower, the repayment of principal is NOT viewed as expenses either– NO tax effect.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Loan Repayment Schedule (Example 9.2)
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
Amount financed: $62,500, or 50% of total capital expenditureFinancing rate: 10% per yearAnnual installment: $16,487 or, A = $62,500(A/P, 10%, 5)
$16,487
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Additionalentries related
to debt financing
Table 9.4
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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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
Project Combined Operation
Taxable incomeIncome taxes (35%)
$100M
$35M
(10M)
?
$90M
$31.5M
Tax Savings = $35M - $31.5M = $3.5MOr (10M)(0.35) = -$3.5M
Tax savings
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Effects of Inflation on Project Cash Flows
Item Effects of Inflation
Depreciation expense
Depreciation expense is charged to taxable income in dollars of declining values; taxable income is overstated, resulting in higher taxes
Note: Depreciation expenses are based on historical costs andalways expressed in actual dollars
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Item Effects of Inflation
Salvage value Inflated salvage value combined with book values based on historical costs results in higher taxable gains.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Item Effects of Inflation
Loan repayments Borrowers repay historical loan amounts with dollars of decreased purchasing power, reducing the debt-financing cost.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Item Effects of Inflation
Working capital requirement
Known as working capital drain, the cost of working capital increases in an inflationary environment.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Item Effects of Inflation
Rate of Return and NPW
Unless revenues are sufficiently increased to keep pace with inflation, tax effects and/or a working capital drain result in lower rate of return or lower NPW.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Example 9.3 Cash Flow Statement for the Automated Machining Center Project
Income StatementInflation Rate 0 1 2 3 4 5
Revenues 5% 100,000$ 100,000$ 100,000$ 100,000$ 100,000$ Expenses: Labor 5% 20,000 20,000 20,000 20,000 20,000 Material 5% 12,000 12,000 12,000 12,000 12,000 Overhead 5% 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$
Cash Flow Statement
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) Salvage 5% 50,000 Gains Tax (6,613) Working Capital 5% (23,331) (1,167) (1,225) (1,287) (1,351) 28,361
Net Cash Flow (148,331)$ 41,978$ 47,020$ 43,458$ 40,894$ 109,980$
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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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)
Example 9.4 Applying Specific Inflation Rates
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Rate of Return Analysis under Inflation
• Principle:True (real) rate of return should be based on constant dollars.
• If the rate of return is computed based on actual dollars, the real rate of return can be calculated as:
n
Net cash flows in actual dollars
Net cash flows in constant dollars
01234
-$30,00013,57015,86013,35813,626
-$30,00012,33613,10810,036
9,307
IRR 31.34% 19.40% i i
f'
..
.40%
_
1
11
1 0 31341 0 10
1
19Not correct IRR
f_10%
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Cost of Capital
1. Calculating the after-tax cost of debt2. Calculating the cost of equity3. Calculating the weighted after-tax cost
of capital
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Methods of Financing• Equity Financing – Capital is
coming from either retained earnings or funds raised from an issuance of stock
• Debt Financing – Money raised through loans or by an issuance of bonds
• Capital Structure – Well managed firms establish a target capital structure and strive to maintain the debt ratio
Capital Structure
Debt
Equity
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Equity Financing
• Flotation (discount) Costs: the expenses associated with issuing stock
• Types of Equity Financing:– Retained earnings– Common stock
Retained earnings
Preferred stock
Common stock
+
+
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Debt Financing• Bond Financing:
– Incur floatation cost– No partial payment of principal– Only interest is paid each year (or
semi-annually) – The principal (face value) is paid in
a lump sum when the bond matures
• Term Loan:– Involve an equal repayment
arrangement. – May incur origination fee– Terms negotiated directly between
the borrowing company and a financial institution
Bond Financing
Term Loans
+
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Cost of Capital
• Cost of Equity (ie) – Opportunity cost associated with using shareholders’ capital
• Cost of Debt (id) – Cost associated with borrowing capital from creditors
• Cost of Capital (k) – Weighted average of ie and id
Cost of Equity
Cost of Debt
Cos
t of C
apit a
l
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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1. Calculating the after-tax Cost of Debt
i c c k t c c k td s d s m b d b m ( / ) ( ) ( / ) ( )1 1
where the amount of the term loan, the amount of bond financing, the before - tax interest rate on the term loan, the before - tax interest rate on the bond, the firm' s marginal tax rate, and
CCkktC C C
s
b
s
b
m
d s b
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Practice Problem• Alpha Corporation has
decided to finance the remaining $4 million by securing a term loan and issuing 20‑year $1,000 par bonds for the following condition.
• 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 Amount Fraction Interest rate
Term Loan
Bond
$1.33M
$2.67M
0.333
0.667
12%
10.74%
id = 0.333 0.12 1 0.38 + 0.667 0.1074 1 0.38a fa fa f a fa fa f
= 6.92%.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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2. Calculating the Cost of Equity
• Cost of Retained Earnings (kr)
• Cost of issuing New Common Stock(ke)
• Cost of Preferred Stock (kp)
• Cost of equity: weighted average of kr ke, and kp
Cost of RetianedEarnings
Cost of IssuingNew Stock
Cost of IssuingPreferred Stock
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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i c c k c c kc c k
e r e r c e e
p e p
( / ) ( / )( / )
Calculating Cost of Equity based on Financing Sources
Where Cr = amount of equity financed from retained earnings, Cc = amount of equity financed from issuing new stock, Cp = amount of equity financed from issuing preferred stock, and Ce = Cr + Cc + Cp
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Determining the Cost of Equity
Source Amount Interest Rate
Fraction of Total Equity
Retained earnings
$1 M 20.50% 0.167
New common stock
$4 M 22.27% 0.666
Preferred stock
$1 M 10.08% 0.167
ie
( . )( . ) ( . )( . ) ( . )( . ).
0167 0 205 0 666 0 2227 0167 0100819 96%
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Calculating Cost of Equity based on CAPM
• The cost of equity is the risk-free cost of debt (20 year U.S. Treasury Bills around 7%) plus a premium for taking a risk as to whether a return will be received. The premium is the average return on the market (12.5%) less the risk-free cost of debt. This premium is multiplied by Beta, a measure of stock price volatility. Beta quantifies risk and is an approximate measure of stock price volatility. It measures one firm’s stock price compared (relative) to the market stock prices as a whole. A number greater than one means that the stock is more volatile than the market on average; a number less than one means that the stock is less volatile than the market on average. The following formula quantifies the cost of equity (ie).
• • where rf = risk free interest rate (commonly referenced to U.S. Treasury
bond yield)• rM = market rate of return (commonly referenced to average return
on S&P 500 stock index funds)
[ ]e f M fi r r r
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Practice Problem – Cost of Equity
• Alpha Corporation needs to raise $10 million for plant modernization. Alpha’s target capital structure calls for a debt ratio of 0.4, indicating that $6 million has to be financed from equity.
• Alpha is planning to raise $6 million from the financial market
• Alpha’s Beta is known to be 1.8, which is greater than 1, indicating the firm is perceived more risky than market average.
• The risk free interest rate is 6%, and the average market return is 13%.
• Determine the cost of equity to finance the plant modernization.
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3. Calculating the Weighted after-tax Cost of Capital
k i CV
i CV
d d e e
Cd= Total debt capital(such as bonds) in dollars,Ce=Total equity capital in dollars,V = Cd+ Ce,
ie= Average equity interest rate per period considering all equity sources,id = After-tax average borrowing interest rate per period considering all debt sources, andk = Tax-adjusted weighted-average cost of capital.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Marginal Cost of Capital
• Given: Cd = $4 million, Ce = $6 million, V= $10 millions, id= 6.92%, ie=19.96%• Find: k
k
0 0692 410
01996 610
14 74%
. ( ) . ( )
.
Comments: This 14.74% would be the marginal cost of capital that a company with this financial structure would expect to pay to raise $10 million.
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Cost of Capital
• Cost of Debt • Cost of Equity
Cost of Equity = Risk free return + Risk Premium= [ ]
where risk free return (U.S. Treasury Bills)
Average rate of return on market = stock price volatility
f M f
f
M
R R R
R
R
Cost of debt = debt interest rate (1 - tax rate)
Cost of Capital = (cost of debt) x (% of capital from debt) + (cost of equity) x (% of capital from equity)
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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Summary
• Identifying and estimating relevant project cash flows is perhaps the most challenging aspect of engineering economic analysis. All cash flows can be organized into one of the following three categories:
1. Operating activities.2. Investing activities3. Financing activities.
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•Cash Items
1. New investment and disposal of existing assets
2. Salvage value (or net selling price)
3. Working capital
4. Working capital release
5. Cash revenues/savings
6. Manufacturing, operating, and maintenance costs.
7. Interest and loan payments
8. Taxes and tax credits
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• Non-cash items1. Depreciation expenses2. Amortization expenses
• The income statement approach is typically used in organizing project cash flows. This approach groups cash flows according to whether they are operating, investing, or financing functions.
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• Methods of financing: 1. Equity financing uses retained earnings
or funds raised from an issuance of stock to finance a capital.
2. Debt financing uses money raised through loans or by an issuance of bonds to finance a capital investment.
• Companies do not simply borrow funds to finance projects. Well-managed firms usually establish a target capital structure and strive to maintain the debt ratio when individual projects are financed.
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• The selection of an appropriate MARR depends generally upon the cost of capital—the rate the firm must pay to various sources for the use of capital.
• The cost of the capital formula is a composite index reflecting the cost of funds raised from different sources. The formula is
k i CV
i CV
V C Cd d e ed e , where
Fundamentals of Engineering Economics © 2004 by Chan S. Park
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• The marginal cost of capital is defined as the cost of obtaining another dollar of new capital. The marginal cost rises as more and more capital is raised during a given period.