ECON 204-05

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

Engineering Economic Decisions

• Evaluation of a Fixed Asset– Equipment– Buildings

• Valuation of Fixed Assets– Based on usable after-tax cash flows the asset

produces

General Cost Terms• Manufacturing Costs

Direct materialsDirect laborMfg. Overhead

• Non-manufacturing CostsOverheadMarketingAdministrative

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.

Cost Classification for Predicting Cost Behavior

• Volume index• Cost Behaviors

Fixed costsVariable costsMixed costs

• Average unit costs

Volume Index

• Def: The unit measure used to define “volume”

• Examples:– Automobile – “miles”

driven– Generating plant –

“kWh” produced– Stamping machine –

“parts” stamped

Fixed Costs

• Def: The costs of providing a company’s basic operating capacity

• Cost behavior: Remain constant over the relevant range

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

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.

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

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%

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%

$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%

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.

Types of Cash Flow Elements in Project Analysis

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

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

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%

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?

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.

• (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

(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

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

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

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

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

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

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%

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

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.

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

Additionalentries related

to debt financing

Table 9.4

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%)

$31.5M

Tax Savings = $35M - $31.5M = $3.5MOr (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 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

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 dollars 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.

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$

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

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:

Net cash flows in actual dollars

Net cash flows in constant dollars

-$30,00013,57015,86013,35813,626

-$30,00012,33613,10810,036

IRR 31.34% 19.40% i i

1 0 31341 0 10

19Not correct IRR

Cost of Capital

1. Calculating the after-tax cost of debt2. Calculating the cost of equity3. Calculating the weighted after-tax cost

of capital

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

Equity

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

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

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

t of C

apit a

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

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

$1.33M

$2.67M

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%.

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

i c c k c c kc c k

e r e r c e e

( / ) ( / )( / )

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

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

( . )( . ) ( . )( . ) ( . )( . ).

0167 0 205 0 666 0 2227 0167 0100819 96%

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

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.

3. Calculating the Weighted after-tax Cost of Capital

k 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.

Marginal Cost of Capital

• Given: Cd = $4 million, Ce = $6 million, V= $10 millions, id= 6.92%, ie=19.96%• Find: 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.

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

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)

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.

•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

• 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.

• 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.

• 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

V C Cd d e ed e , where

• 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.

ECON 204-05

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