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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=
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11.= Summary o! Scenario Analysis
Scenario Net "ncome Cash #low NPV "$$
%ase case &'()** +'()** &+(+,- &+.&/
0orst Case 1&+(+&* 23(3'* 1&&&(-&' 1&3.3/
%est Case +'(-4* ''(-4* &+'(+*3 3*.'/
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11.> Sensitivity Analysis
• $hat happens to N! *hen *e vary onevariable at a time
• /his is a subset of scenario analysis *here *eare looking at the effect of specific variables
on N!• /he greater the volatility in N! in relation to
a specific variable+ the larger the forecasting
risk associated *ith that variable and the moreattention *e *ant to pay to its estimation
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11.? Summary o! Sensitivity Analysis !or New Project
Scenario 5nit Sales Cash #low NPV "$$
%ase case ,*** +'()** &+(+,- &+.&/
0orst case ++** +4(2** 1)(22, &*.4/
%est case ,+** ,,(3** 4'(4+- &'.-/
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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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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