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NlT9*XX 1ѷ7Z<%kvxW~FF?p Tor$5 =1B ]^&=xNSAj`!1&@@"#PwF``&1qХ ,@})gw4vZj6g9_}_$|~2p/e_^ivE: _j#8*~CmK[ڍzuMawow#껣 ^4?xVվ+%!dUH*J C*MJ |Uϣ{ݴh#. ˍ^fߒ_WVV>m(Owaޘ%QT{ǜ  0ܩKpjJdHt:!NI"*JR!AS $MHS (MJ2 (KʂIǠ<)* s:h<5i&A3we%/933Vǎu14C>4퐃 *T xOЀ xOЀD?>(P!e@YRtL:IyPY h Tt/=X]@.Bxc;02a P`op a32pu0_qVp+,,Md``f Ơ}Sc&X cXcgLEq3!8x(*QMD ǃa&' F ⌮ȦڕE+49]lv0H2F"T9OKt&L6 `1CL@l.Nc0e4T*(.7Dᙡ Px2u -02t]:^,T"%& <̱|F.AsR@xJBA.*04A,BK\VFApH#VmQ!jӦM`FYf;w l$Oh6s`.hqD HlH ,,-W,#ʸ0.!z|)-7JزhY#pԾya$%,Ǽ-$ҏHd^8>8>TyϢvzˈ')٠)'mm;:U\νɺJn--l[ʦj3$J' ʐj3Ud,bL)WUoT*#9v}rG=cF3 ԷVگ{;!)ADf;'0(sEUv׊k1\gM1e2L01q1m9_и?nLz T"> A#D,XTd8xohUuǟbZKDC.[M+vt%L!InbnW&fE{U( +AWJ_$PH/aB>sg>~}>ޝs<^Q}U|y#5h Ga >h+{&w0A7hmsn߉nݢuXCӇڣuX-4uX;§#Z\5GC`:=Af6aMi4,>imÚ9`ims^ >EmÚ+\uX{zmÚ6;0mZ\5Ds0;Aimsߋ:=@z>mÚ_=uX;Nft\k&t f6?*\>O93 _g\`{9Z~uc2αF{س3z=kǜdbIֱi3Κ41Y_Ykf@n({p.]CC}\2#w>_]{"+t&hK٠kdb *=^W'NYM§{=GWVE?.f>Q?WcK5ŧ^I5k4YH|h[`MQ* TXq9uQVʢ 4R/x?hQ&&E/iRPJ#t:T(A\E,8RKlJ)(:8w^_s{/xIoYS w3} :NQeY%Dj3Kp((*1-"@̉X"" "bĪX."6@lm"bĎhh={"bľPD8X&"vAJubĂq31|5ɧpDŽ9g8aQE:Z&^ԓ%j#3n u9# $khmyCgYvUe:3fӌT9,1ql" dd@  @@`` 0t       "$B${`$~gzx2HѼB$wCd3.V'y$B$^PSy  ‡mBB$r$5 =1BwB$/=X|& $B$Hm{y B$"> AxB$Xq9uQVIB$QQb@#$$$$B$D1jԸ|ue  `1?0 J@  g4IdId]C\4Ȑ=(I8^ppp@ <4!d!d@^CaCʚ^C25ʚ;2Nʚ;<4dddd@^C5ʚ;2Nʚ;2ph___PPT2001D<4X\? %a$ Dealing with Uncertaintyn Assessing a Project s Worth under Uncertainty or Risk87 PreviouslyIn previous lectures, we assumed a high degree of confidence in all estimated values, that is we assumed certainty. In most situations, however, there is doubt as to the ultimate results that will be obtained from an investment - there is risk and uncertainty6i sRisk and UncertaintyDCaused by lack of precise knowledge regarding future business conditions, technological developments, synergies among projects, etc. Should be made explicit in any analysis Risk - Variability described by probability distributions Uncertainty - Probability distributions are not known Generally the terms are interchangeableED!Four major sources of uncertaintyInaccuracy of the estimates: cash inflow, savings in existing operating expenses, capital required Type of business involved Type of physical plant and equipment involved Length of the project and study period 5Non-probabilistic Methods for Describing Project RiskjBreakeven Analysis Sensitivity Analysis Scenario Analysis Risk-Adjusted MARRs Reduction of the useful lifeGBreakeven Analysis8Commonly used when selection among alternatives is dependent on a single factor (e.g., capacity, sales). Solve for the value of that factor at which the conclusion is a standoff. common measures include annual revenues and expenses, rate of return, market or salvage value, equipment life, capacity utilization).-Kinds of Breakeven AnalysisBreakeven Analysis - Example 1Suppose that the market value of Alternative 1 is known with certainty. What would the market value of Alternative 2 have to be so that the initial decision based on this information would be reversed? Use a MARR of 15% per year $Example 1 - cont dNAWA = $255 NAWB = $213 (MV = 1200) Choose A Find Breakeven Point for market value for B NAWA = NAWB 255 = -$6000 (A/P,15%,10) + $1350 +X(A/F,15%,10) Solve for X = 2050 Decision?* ,C VQ $Example 1 - cont d Sensitivity AnalysisRelative magnitude of change in the measure of interest caused by one or more changes in estimated factors Common technique when one or more factors are subject to uncertainty. Assesses the impact of uncertainty in estimates on study results. !Sensitivity Analysis - Example 2A machine is considered for immediate installation. Because of the new technology built in, we want to investigate its NPW over a range of +/-40% in a) capital investment, b) annual net cash flow, c) market value, d) useful life. Use MARR = 10%8U U $Example 2 - cont dBase NPW = -$11,500 + $3000 (P/A,10%,6) + $1000 (P/F,10%,6) = $2,130 a) When capital invest. varies by +/- p%, NPW = - (1 + p/100) ($11,500) + & (linear function) b) When revenues vary by +/- a%, NPW = & + (1 + a/100) ($3000)(P/A,10%,6) + & (linear function) c) When market value varies by +/- s%, NPW = & + (1 + s/100) ($1000) (P/F,10%,6) (linear function) d) When the useful life varies by +/- n%, NPW = & + $3000(P/A,10%,(1 + n/100)(6)) + $1000 (P/F,10%, (1 + n/100) (6)) (nonlinear function) Z;Z+Z= Z"ZD Z(ZB Z*Zb Z ?+ #" &(         %      * IExample 2 - Spider Chart.Considering Several Factors: Scenario Analysis'also called optimistic-pessimistic estimation used to establish a range of values for the measure of interest typically, the optimistic estimate has 1 chance out of 20 to be exceeded by the actual outcome and the pessimistic estimate has 19 chances out of 20 to be exceeded by the actual outcome Scenario Analysis - Example 3|An ultrasound inspection device for which optimistic, most likely and pessimistic estimates are found below. The MARR is 8%..Making DecisionsCompare NAW(O) = 74,000 , NAW(M) = 4500, NAW(P) = -3300 Decision: If NAW(O) < 0 then Reject If NAW(P) > 0 then Accept Else Do more analysis or let the boss decide Z0 Z ZZZZZZ(Z Z0   ('Analyze all Combinations (NAW in $000s)WNAW > $50,000 for 4 out 27 combinations NAW < $0 for 9 out of 27 combinations Decision?XZX Risk-adjusted MARRs Involves the use of higher MARRs for alternatives that are classified as highly uncertain and lower MARRs for projects with fewer uncertainties Widely used in practice,C?!Risk-adjusted MARRs - Example 4  Two alternatives, both affected by uncertainty to different degrees. The firm s risk-free MARR is 10%."$Example 4 - cont dUsing prescribed risk-adjusted MARRs of 20% for P and 17% for Q, we get NPWP = $10,602 NPWQ = $8,575 => Choose Alternative P Contradictory resultLJ:N:u#$Example 4 - cont d/Risk - adjusted MARRs$Reduction of the useful lifeEstimated project life is reduced by a fixed percentage and each alternative is evaluated regarding its acceptability over this reduced life span%)Reduction of the useful life - Example 5NA proposed new product line has cash flows as below. Do an after tax analysis with an MARR of 15% The company  s maximum simple payback period is three years Decision?,Zy)'$Example 5 - cont d0Reduction of Useful Life(SummaryMethods are relatively simple to apply. They are also somewhat simplistic and imprecise in cases where we must deal with multifaceted project uncertainty. Probability concepts allow us to further analyze project risk and develop better recommendations.P ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@ ?lKd@  d @lA`  d n?" dd@   @@``PR    @ ` ` p>>   T (  8 z-  z-z@ a a   BC DEF18c8c? @   BC DEF18c8c?"" @b   BC DEF18c8c?#h# @Q   BgC DEF18c8c?"Df" @0   BFC DEF18c8c?!#E! @a @ fz-  fz-  S BjC1DEF1?0i0i 0 @z-   S BYC1DEF1?0X0X 0 @!z   S BHC3DEF1?2G0G 2 @2fz   ZHwawa1 ?pPp  T Click to edit Master title style! !@  Zwawa1 ? P&   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     SB  s *޽h ? P untitled 1լ [S(  A  Zwawa1 ? @  SClick to edit Master notes styles Second Level Third Level Fourth Level Fifth Level"     Tp  01 ?   B  s *޽h ? a( @ 0( 8<  B  s *޽h ? a(t  0( 35- gn l  C (@ p    C D `  $ PH___PPT2001$Q H  0޽h ? P  D(    # lwawa1 ? pPp   D  # lwawa1 ? 0& $ PH___PPT2001$Q H  0޽h ? P  D(    # lXwawa1 ? pPp   D  # lwawa1 ?00 $ PH___PPT2001$Q H  0޽h ? P  D(    # lxwawa1 ? pPp   D  # l8wawa1 ?` $ PH___PPT2001$Q H  0޽h ? P  `(D(  ( ( # lٷwawa1 ? pp   D ( # lٷwawa1 ?Pv$ PH___PPT2001$Q H ( 0޽h ? P  P,D(  , , # lַwawa1 ? pPp   D , # lطwawa1 ? & $ PH___PPT2001$Q H , 0޽h ? P   -(  l  C H0 pPp     C 0 P&   ! Comparing two alternatives: Find the value of some parameter that makes the NAW or NPW equal. Evaluating a single alternative: Find the value of some parameter that makes NAW or NPW equal to zero. To decide, judge whether the breakeven point can reasonably be expected.H  0޽h ? P  >6p0(  0 0 # lطwawa1 ? pPp   D 0 # lڷwawa1 ? P& $ PH___PPT2001$Q  0 TA ?1?6 X $DX2 0 B1? p` ,$D,H 0 0޽h ? P  \T4(  4 4 # lXwawa1 ? pPp    4 # lwawa1 ? P<$<  H 4 0޽h ? Pk  8(  8 8 # l8wawa1 ? pPp   Z 8 S A ?P@ jB 8 BD1?@  8 H1? >  GBreakeven Point = $2050H 8 0޽h ? P  <D(  < < # lHڷwawa1 ? pPp   D < # lh۷wawa1 ? & $ PH___PPT2001$Q H < 0޽h ? Pv  @(  @ @ # lַwawa1 ? pPp    @ # lH9wawa1 ?@ & <$<   @ BA ?1? 8 $D8H @ 0޽h ? P  \TD(  D D # liwawa1 ? pPp    D # ljwawa1 ?@ P <$<  H D 0޽h ? PH   Lp(  L L # lmwawa1 ? pPp    L 6A1?z1 ,$, L C B  <$<  JObservation: Solution is most sensitive to & Sensitivity analysis is useful for identifying factors that need to be estimated more carefullyZH L 0޽h ? P  \T0P(  P P # lxmwawa1 ? pPp    P # lmwawa1 ? <$<  H P 0޽h ? P  @8@T(  T T # l8nwawa1 ? pPp    T # lnwawa1 ? P& <$<   T TA ?1?_;X $DXH T 0޽h ? P\   (  l  C H> pPp     C < P& $ PH___PPT2001$Q H  0޽h ? P  @8PX( ^\^ X X # lXowawa1 ? pPp    X # lowawa1 ? P<$<   X TA  ?1?P` X  $DXH X 0޽h ? P  `\D(   \ \ # lpwawa1 ? pPp   D \ # l8qwawa1 ? `& $ PH___PPT2001$Q H \ 0޽h ? P  p`!(  ` ` # lswawa1 ? pPp    ` # lxswawa1 ?p<$<   ` TA  ?1? X  $DXI ` Zswawa1 ? h ,$, wAlternative P is thought to be more uncertain than Alternative Q. At 10%, both alternatives have the same NPW Decision?H ` 0޽h ? P  \Td( kc88A8 d d # l8twawa1 ? pPp    d # ltwawa1 ?V <$<  H d 0޽h ? PV  h~(  h h # lwawa1 ? pPp   ~ h BA ?1?d`E H h 0޽h ? Pv  & (  l  C h? pPp      C X P&   Subject to many pitfalls. One of them is that the uncertainty in the project is not made explicit. Not recommended when other techniques can be used. H  0޽h ? P  lD(  l l # lXwawa1 ? pPp   D l # lwawa1 ? 0& $ PH___PPT2001$Q H l 0޽h ? P   p(  p p # lxwawa1 ? pPp   D p # lؖwawa1 ? $ PH___PPT2001$Q ^  p 6A1?p H p 0޽h ? P  x(( W89/P x x # lwawa1 ? pPp    x  `A ?1? X $XL x Hx1?! T$ROR as a function of the useful life%% x <81?p_ = After-tax ROR x H1? & A  ; Useful Life H x 0޽h ? P  @(  l  C X pPp   p  C  P&   Heavy emphasis is placed on rapid recovery of investment capital in the early years of project Closely related to the discounted payback technique Neglects cash flows that occur later in life Not recommended $IH  0޽h ? P  \T|(  | | # lwawa1 ? pPp    | # lwawa1 ? P& <$<  H | 0޽h ? 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