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© 2003 The McGraw-Hill Companies, Inc. All rights

Project Analysis andEvaluation

Chapter

Eleven


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McGraw-Hill!Irwin © 2003 The McGraw-Hill Companies, Inc. All rights

11.2 Key Concepts and Skills

• Understand forecasting risk and sources ofvalue

• Understand and be able to do scenario and

sensitivity analysis• Understand the various forms of break-even

analysis

• Understand operating leverage• Understand capital rationing


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11.3 Chapter Outline

• Evaluating N! Estimates• "cenario and #ther $hat-%f &nalyses

• 'reak-Even &nalysis

• #perating (ash )lo*+ "ales !olume+ and'reak-Even

• #perating ,everage

• (apital ationing


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11. Evaluating NPV Estimates

• /he N! estimates are 0ust that estimates• & positive N! is a good start no* *e need

to take a closer look

)orecasting risk ho* sensitive is our N! tochanges in the cash flo* estimates+ the more

sensitive+ the greater the forecasting risk

"ources of value *hy does this pro0ect create

value


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11. Scenario Analysis

• $hat happens to the N! under different cashflo*s scenarios

• &t the very least look at4

'est case revenues are high and costs are lo* $orst case revenues are lo* and costs are high

5easure of the range of possible outcomes

• 'est case and *orst case are not necessarily probable+ they can still be possible


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11.6 New Project Eample

• (onsider the pro0ect discussed in the te7t• /he initial cost is 8299+999 and the pro0ect has

a -year life. /here is no salvage. :epreciation

is straight-line+ the re;uired return is 12< andthe ta7 rate is 3<

• /he base case N! is 1+6=


7/25McGraw-Hill!Irwin © 2003 The McGraw-Hill Companies, Inc. All rights

11.= Summary o! Scenario Analysis

Scenario Net "ncome Cash #low NPV "$$

%ase case &'()** +'()** &+(+,- &+.&/

0orst Case 1&+(+&* 23(3'* 1&&&(-&' 1&3.3/

%est Case +'(-4* ''(-4* &+'(+*3 3*.'/



11.> Sensitivity Analysis

• $hat happens to N! *hen *e vary onevariable at a time

• /his is a subset of scenario analysis *here *eare looking at the effect of specific variables

on N!• /he greater the volatility in N! in relation to

a specific variable+ the larger the forecasting

risk associated *ith that variable and the moreattention *e *ant to pay to its estimation



11.? Summary o! Sensitivity Analysis !or New Project

Scenario 5nit Sales Cash #low NPV "$$

%ase case ,*** +'()** &+(+,- &+.&/

0orst case ++** +4(2** 1)(22, &*.4/

%est case ,+** ,,(3** 4'(4+- &'.-/



11.19 Simulation Analysis

•"imulation is really 0ust an e7panded sensitivity andscenario analysis

• 5onte (arlo simulation can estimate thousands of possible outcomes based on conditional probabilitydistributions and constraints for each of the variables

• /he output is a probability distribution for N! *ithan estimate of the probability of obtaining a positivenet present value

• /he simulation only *orks as *ell as the information

that is entered and very bad decisions can be made ifcare is not taken to analy@e the interaction bet*eenvariables



11.11 6aking A 7ecision

• 'e*are Aaralysis of &nalysisB• &t some point you have to make a decision

• %f the ma0ority of your scenarios have positive N!s+ then you can feel reasonablycomfortable about accepting the pro0ect

• %f you have a crucial variable that leads to anegative N! *ith a small change in the

estimates+ then you may *ant to forego the pro0ect



11.12 %reak1Even Analysis

• (ommon tool for analy@ing the relationship bet*een sales volume and profitability

• /here are three common break-even measures

&ccounting break-even sales volume *here netincome C 9

(ash break-even sales volume *here operating

cash flo* C 9

)inancial break-even sales volume *here net

present value C 9



11.13 Eample8 Costs

• /here are t*o types of costs that are important in

breakeven analysis4 variable and fi7ed

/otal variable costs C ;uantity D cost per unit

)i7ed costs are constant+ regardless of output+ over some

time period /otal costs C fi7ed variable C )( vF

• E7ample4

Gour firm pays 83999 per month in fi7ed costs. Gou also

pay 81 per unit to produce your product.• $hat is your total cost if you produce 1999 units

• $hat if you produce 999 units



11.1 Average vs. 6arginal Cost

• &verage (ost

/( H I of units

$ill decrease as I of units increases

• 5arginal (ost

/he cost to produce one more unit

"ame as variable cost per unit

• E7ample4 $hat is the average cost and marginal cost

under each situation in the previous e7ample roduce 1999 units4 &verage C 1>+999 H 1999 C 81>

roduce 999 units4 &verage C =>+999 H 999 C 81.69



11.1 Accounting %reak1Even

• /he ;uantity that leads to a @ero net income• N% C J"ales !( )( :KJ1 /K C 9

• F vF )( : C 9

• FJ vK C )( :• F C J)( :K H J vK



11.16 5sing Accounting %reak1Even

• &ccounting break-even is often used as anearly stage screening number

• %f a pro0ect cannot break-even on an

accounting basis+ then it is not going to be a*orth*hile pro0ect

• &ccounting break-even gives managers an

indication of ho* a pro0ect *ill impact

accounting profit



11.1= Accounting %reak1Even and Cash #low

• $e are more interested in cash flo* than *eare in accounting numbers

• &s long as a firm has non-cash deductions+

there *ill be a positive cash flo*• %f a firm 0ust breaks-even on an accounting

basis+ cash flo* C depreciation

• %f a firm 0ust breaks-even on an accounting basis+ N! L 9



11.1> Eample

• (onsider the follo*ing pro0ect & ne* product re;uires an initial investment of 8million and *ill be depreciated to an e7pectedsalvage of @ero over years

/he price of the ne* product is e7pected to be82+999 and the variable cost per unit is 81+999

/he fi7ed cost is 81 million

$hat is the accounting break-even point each

year• :epreciation C +999+999 H C 1+999+999

• F C J1+999+999 1+999+999KHJ2+999 1+999K C 299units



11.1? Sales Volume and Operating Cash #low

• $hat is the operating cash flo* at theaccounting break-even point Jignoring ta7esK

#() C J" !( )( - :K :

#() C J299D2+999 299D1+999 1+999+999K

1+999+999 C 1+999+999

• $hat is the cash break-even ;uantity

#() C MJ-vKF )( : : C J-vKF )(

F C J#() )(K H J vK

F C J9 1+999+999K H J2+999 1+999K C 199

units



11.29 9hree 9ypes o! %reak1Even Analysis

• &ccounting 'reak-even $here N% C 9

F C J)( :KHJ vK

• (ash 'reak-even $here #() C 9

F C J)( #()KHJ vK Jignoring ta7esK

• )inancial 'reak-even $here N! C 9

• (ash 'E L &ccounting 'E L )inancial 'E



11.21 Eample8 %reak1Even Analysis

• (onsider the previous e7ample

&ssume a re;uired return of 1><

&ccounting break-even C 299

(ash break-even C 199

$hat is the financial break-even point• "imilar process to finding the bid price

• $hat #() Jor paymentK makes N! C 9

N C O ! C +999+999O %HG C 1>O (/ 5/ C 1+?>+>>? C #()

• F C J1+999+999 1+?>+>>?K H J2+999 1+999K C 269 units

• /he ;uestion no* becomes4 (an *e sell at least 269

units per year


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11.22 Operating :everage

• #perating leverage is the relationship bet*eensales and operating cash flo*

• :egree of operating leverage measures this

relationship /he higher the :#,+ the greater the variability inoperating cash flo*

/he higher the fi7ed costs+ the higher the :#,

:#, depends on the sales level you are starting

from

• :#, C 1 J)( H #()K


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11.23 Eample8 7O:

• (onsider the previous e7ample

• "uppose sales are 399 units

/his meets all three break-even measures

$hat is the :#, at this sales level

#() C J2+999 1+999KD399 1+999+999 C 2+999+999

:#, C 1 1+999+999 H 2+999+999 C 1.

• $hat *ill happen to #() if unit sales increases by

29


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11.2 Capital $ationing

• (apital rationing occurs *hen a firm ordivision has limited resources

"oft rationing the limited resources are

temporary+ often self-imposed

Pard rationing capital *ill never be available for

this pro0ect

• /he profitability inde7 is a useful tool *hen

faced *ith soft rationing


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M G Hill!I i © 2003 Th M G Hill C i I All i ht

11.2 ;uick ;ui<

• $hat is sensitivity analysis+ scenario analysisand simulation

• $hy are these analyses important and ho*

should they be used• $hat are the three types of break-even and

ho* should each be used

• $hat is degree of operating leverage• $hat is the difference bet*een hard rationing

and soft rationing

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