Decision-making Under Risk and Uncertainty

8/12/2019 Decision-making Under Risk and Uncertainty

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CHAPTER 12: DECISION-MAKING UNDER RISK AND

UNCERTAINTY

Overview of Freemr! A""e# $i%er#

Freemark Abbey was a winery located in Californias Napa Valley. It produced only

premium wines. One of the partners that owned Freemark, illiam !ae"er, was

confronted with an important decision. #ecent weather reports su""ested that a storm

mi"ht hit the Napa Valley. If the storm hit the $alley, the rainwater could concei$ably

swell the berries and reduce their concentration. If so, the sellin" price of the wine would

decrease by %.&'(bottle. )he possibility also e*isted, howe$er, that the storm would

cause the botrytis mold to form on the "rape skins. If the mold formed, the wine would

be hi"hly $alued by connoisseurs and could be sold at more than double the normal price.

)he hi"her price, howe$er, would be partially offset by a decrease in the +uantity sold.

&EARNING O'(ECTI)ES

I% *+i, +.*er/ ,*0e%*, wi "e "e *o:

13 Se* 0. ei,io% *ree3

23 C0*e % i%*er.re* e4.e*e v0e3

53 C0*e ,*%r evi*io% % *+e oeffiie%* of

vri*io% % 0,e *+em *o i%fer *+e eve of ri,!3

63 A%#7e *er%*ive, w+e% ,0",e80e%* ei,io%, m0,*"e me3

93 U,e ei,io% *+eor# *o e*ermi%e *+e v0e of

i%form*io%3

3 E4.i% *+e imi**io%, i%+ere%* i% *+e m4imi% %

mi%im4 ri*eri3


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)he alternati$e would be to har$est the "rapes in ad$ance of the storm. If the

"rapes were har$ested immediately, the wine could be sold at a price of %-.&'(bottle. In

makin" his decision, !ae"er also had to determine the ramifications if he waited for the

storm and it did not hit the re"ion. ltimately, the price depended on the su"ar

concentration. In "eneral, the hi"her the percenta"e of su"ar concentration, the hi"her the

price. In determinin" whether to har$est the "rapes or wait for the storm, !ae"er had to

estimate the likelihood the storm would hit, the odds that the mold would form if the

storm hit, and the probabilities of $arious su"ar concentration le$els if the storm did not

hit the re"ion.Reev%* Reve%0e;Co,* A%#,i, % U%er*i%*#

/our firm is tryin" to decide where to locate its new retail outlet. /ou determine that if

you locate the outlet on the west side of town, it will "enerate operatin" profits of %'

million(year. If you position the outlet on the east side of town, it will produce an annual

profit of %& million. here should you build the outlet0

If only decisions were this easy. In the real world, a firms annual operatin"

profits are uncertain. hat if other firms locate an outlet near yours0 hat if they

launch an a""ressi$e marketin"(pricin" strate"y0 hat if property ta*es rise0 hat if

the minimum wa"e increases0

ntil now, we$e implemented rele$ant re$enue(rele$ant cost analysis under the

assumption that both the cost and re$enue fi"ures were known. In fact, that will rarely be

the case. In the real world, a firms re$enues and costs depend on a $ariety of factors.

)hese factors are often referred to as ,**e, of %*0rebecause they are beyond the

control of the firm. If the firm could control these factors, it would manipulate them to

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its benefit. Instead, the states of nature represent constraints the company must deal with.

As the states of nature $ary, the le$el of uncertainty associated with a strate"ic decision

increases, and uncertainty breeds risk. 1ence, in this chapter, we mo$e from discussin"

rele$ant re$enues and costs to rele$ant expectedre$enues and costs.

nfortunately, as the number of factors mount, the number of potential outcomes

increases, sometimes e*ponentially. )his can make it increasin"ly difficult for the firm

to di"est the information in such a way as to make an ob2ecti$e, accurate decision. In this

chapter, we will discuss the tools to allow a firm lay out its potential outcomes and to

utili3e simple summary statistics that make it relati$ely easy for firms to comparealternati$es and make decisions.

Dei,io% Tree,

)o help lay out the $arious outcomes associated with the firms initiati$e, we can piece

to"ether a ei,io% *ree. )he purpose of a decision tree is to create a roadmap of sorts

that lays out the $arious cost and re$enue fi"ures associated with a "i$en decision. )he

decision tree includes an assortment of branches, each one dictated by the states of

nature. 4ome will affect the firms re$enues, whereas others affect the firms costs. At

the end of each branch is an outcome and the probability the outcome is likely to occur.

)he first fork in the decision tree refers to the decision the mana"er wishes to

make. In the Freemark Abbey inery case, illiam !ae"er needed to decide whether to

har$est the "rapes immediately or lea$e them on the $ine and await a possible storm. If

he decides not to har$est the "rapes, his re$enues depend on whether the storm hits. If

the storm hits, his re$enues will depend on whether the mold forms. If the storm does not

hit, the sellin" price of a bottle of wine will depend on the le$el of su"ar concentration.

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Fi*ed costs> %5@@,@@@

Variable costs> %-(unit

)he )win Cities location has the followin" cost structure>

Fi*ed costs> %@@,@@@

Variable costs> %@(unit

)he firm belie$es there is a -@B chance the raw materials needed for production will be

in short supply. If so, the $ariable costs are e*pected to rise to %? in 8etroit and %5 in

the )win Cities. )his is incorporated into the decision tree throu"h a pair of branches

one branch shows the e*istin" cost structure and the other e*hibits the hi"her costs.Ne*t, the mana"er seeks to determine the rele$ant re$enues associated with each

location. 1e(she determines that unit sales are sensiti$e to the state of the economy. If

the economy is normal, the firm will likely sell 5'@,@@@ units per year in 8etroit and

5D',@@@ in the )win Cities. If the economy is in a recession, sales fall to -@@,@@@ units

per year in 8etroit and &@,@@@ in the )win cities. )he economy a$era"es one recession

e$ery four years.

Accordin"ly, then, the decision tree illustrates the uncertainty in unit sales by

creatin" a pair of branches at each location. If the firm locates in 8etroit and the

economy is normal, the firm will sell 5'@,@@@ units. If the economy falls into a recession,

unit sales will fall to -@@,@@@ units. On the other hand, if the firm locates in the )win

Cities, it will sell 5D',@@@ units if the economy is normal and &@,@@@ durin" a recession.

=ased on past history, the likelihood of a recession is -'B 9which, of course, implies the

probability of a normal economy is D'B


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#ele$ant re$enues are also affected by the price. )he price depends on whether

one of the firms competitors tri""ers a price war. ;rice wars tend to occur once e$ery

three years. ithout a price war, the firm can e*pect to char"e %-@(unit at either location.

8urin" a price war, the price is e*pected to fall to %'(unit in 8etroit and %5 in the )win

Cities. )he market demand for the "ood is fairly inelastic. If a price war breaks out, unit

sales will tend to rise by @B at either location.

e accommodate the uncertainty in prices in the decision tree throu"h a

subse+uent set of branches. In the absence of a price war, the firm e*pects to char"e

%-@(unit in 8etroit. 4hould a price war occur, the price will drop to %'. )he firm alsoe*pects to char"e %-@ in the )win Cities in the absence of a price war. 1owe$er, if a

price war were to take place, the firms price will fall to %5. )hese branches also

incorporate the chan"e in unit sales that may arise from a price war. )he firm anticipates

the likelihood of a price war to be 55B thus, the branches post the respecti$e

probabilities.

EFi"ure here

Fi"ure shows the decision tree. Note how the decision tree allows the mana"er

to determine the $arious profit outcomes arisin" from the rele$ant re$enues and costs at

each location. In this case, the branches of the tree lead to ei"ht different outcomes, each

one e*hibitin" the firms profits under $arious scenarios. Assumin" the states of nature

are independent of each other, the probability of any three states of nature occurrin"

simultaneously is the product of the indi$idual probabilities. For e*ample, if the

probability of a lower cost structure is @.&@, the probability of a normal economy is @.D'

and the probability of a price war is @.55, then the probability of all three occurrin"


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simultaneously is @.&@ * @.D' * @.55 G .?@-@. e can now combine the outcomes and

probabilities for each plant as shown in )able .

T"e 1

De*roi* Twi% Ci*ie,

Se%rio O0*ome Pro""ii*# O0*ome Pro""ii*#

7ow Cost(Normal Hconomy(No ;rice ar %-,'@@,@@@ .?@-@ %5,'@,@@@ .?@-@

7ow Cost(#ecession(

No ;rice ar %,5@@,@@@ .5?@ %,-@@,@@@ .5?@7ow Cost(Normal Hconomy(;rice ar %&'',@@@ .&@ %5D,'@@ .&@

7ow Cost(#ecession(;rice ar %5@,@@@ .@@ 9%,@@@< .@@

1i"h Cost(Normal Hconomy(No ;rice ar %,&@@,@@@ .@@' %-,@-',@@@ .@@'

1i"h Cost(#ecession(No ;rice ar %@@,@@@ .@55' %@,@@@ .@55'

1i"h Cost(Normal Hconomy(;rice ar %&',@@@ .@?' 9%@@,@@@< .@?'

1i"h Cost(#ecession(;rice ar 9%&@,@@@< .@' 9%@@,@@@< .@'

Althou"h the decision tree lists the $arious outcomes at each location and their

correspondin" probabilities, the mana"er is left to di"est the information. In the ne*t

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section of this chapter, we will discuss se$eral summary statistics that pro$ide concise,

yet accurate information from which an ob2ecti$e decision can be made.

E4.e*e )0e

7ets i"nore the probabilities for the time bein". )he outcomes associated with each

location are shown in )able -.

&

IMPORTANT IMP&ICATIONS FOR THE

MANAGER>

)he decision tree is a tool mana"ers can use toanticipate the $arious cash flows that mi"ht occur ifa "i$en decision is implemented. Hach branch of adecision tree details an e*ternal factor 9a.k.a. stateof nature< that could affect the firms price, output,and(or cost structure.


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T"e 2

De*roi* Twi% Ci*ie,

Se%rio O0*ome O0*ome

7ow Cost(Normal Hconomy(No ;rice ar %-,'@@,@@@ %5,'@,@@@

7ow Cost(#ecession(No ;rice ar %,5@@,@@@ %,-@@,@@@

7ow Cost(Normal Hconomy(

;rice ar %&'',@@@ %5D,'@@7ow Cost(#ecession(;rice ar %5@,@@@ 9%,@@@9%-,'@@,@@@ * .?@-@< L 9%,5@@,@@@ * .5?@< L 9%&'',@@@ * .&@< L 9%5@,@@@ * .@@

9%5,@@@,@@@ * .?@-@< L 9%,@@,@@@ * .5?@< L 9%',@@@ * .&@< M 9%',D'@ * .@@< L

9%,'@,@@@ * .@@'< L 9%?-,'@@ * .@55'< M 9%&@,-'@ * .@55'< M 9%D5?,5.'@ * .@' based on the numbers in )able 5, do you ha$e a preference0

4ome students may prefer 8etroit. If the firm locates at 8etroit, the worst case scenariois a ne"ati$e cash flow of %&@,@@@ as compared with a potential loss of %&@,-'@ at the

)win Cities location. Other students may prefer the )win Cities, based on the fact that

cash flows could potentially reach %5,@@@,@@@ as compared with a best case scenario of

only %-,'@@,@@@ 8etroit.

In "eneral, students who prefer 8etroit notice that the outcomes are fairly close

to"ether whereas the outcomes at the )win Cities are more dispersed. hen the

outcomes are fairly close to"ether, the decision6maker is willin" to fore"o the potential

for hi"hly desirable outcomes to a$oid the less desirable outcomes. )hese indi$iduals

ha$e ri,! ver,epreferences. )hose who prefer the )win Cities ha$e ri,!-,ee!i%

-

,

,

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decreases. )he bell6shaped %orm i,*ri"0*io%assumes the distribution of outcomes is

symmetric around the mean.

EFi"ure - here

In interpretin" the concept of standard de$iation $isually, note that in distribution

9a

9%-,'@@,@@@ 6 %,'&,&D.'@


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hat do these numbers mean0 If you e*amine the e+uation, youll see that the

standard de$iation is the s+uare root of the a$era"e s+uared de$iation between each

outcome and the mean outcome. If that e*planation lea$es your head spinnin", lets

simply note that your first operation in calculatin" standard de$iation is to take the

difference between each outcome and the mean outcome. )hese differences are then

s+uared to assure they do not cancel each other out when summed. )hus, the more

spread out the outcomes, the lar"er the difference between each outcome and the mean.

Conse+uently, the more dispersed the outcomes, the lar"er the standard de$iation.

=ecause the standard de$iation for the )win Cities is hi"her than for 8etroit, we knowthe ran"e of outcomes for the )win Cities is "reater.

4tatisticians apply C+e"#,+ev=, T+eoremto make inferences from standard

de$iation. Chebyshe$ pro$ed the proportion of any data set lyin" within k standard

de$iations of the mean is at least M (k-, where k is any positi$e number "reater than .

For e*ample, we can infer that at least 9 M P-


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Assumin" the distribution of cash flows are normally distributed, we can infer that @B

of the time, the annual cash flows in 8etroit will ran"e between %&, and

%-,,D. At the riskier )win Cities location, annual cash flows will ran"e between 6

%'5@,? and %5,D@-,D& @B of the time. Clearly, couplin" e*pected $alue with

standard de$iation allows the decision6maker to assess not only the a$era"e outcome but

also the le$el of risk associated with the alternati$es.

D


MANAGER>

. )he le$el of risk associated with a decision can beinferred from the standard de$iation 9

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Coeffiie%* of )ri*io%

Althou"h standard de$iation is a "ood tool to assess risk, it can be misleadin". )o

illustrate, lets take a look at the followin" alternati$es. A firm is considerin" launchin"

one of two initiati$es. )he outcomes associated with each initiati$e, alon" with the

correspondin" probabilities, appear in )able ?. )he e*pected $alue for Alternati$es A

and = are %D@ and %,@@@,@?@, respecti$ely.

T"e 6

A*er%*ive A A*er%*ive '

C,+ Fow Pro""ii*# C,+ Fow Pro""ii*#

%@ .@ %,@@@,@@ .@

6%@@ .@ %,&@@ .@

%5'@ .-@ %,@@@,'@@ .-@

%'@ .-@ %,'@ .-@

%@ .?@ %,@@ .?@hich alternati$e is riskier0 )he standard de$iation for Alternati$e A is>

9%@ 6 %D@


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At first "lance, = appears to be the riskier of the two because the standard de$iation is

nearly twice as lar"e for = as it is for A. =ut lets employ the empirical rule of thumb

used earlier. If A is initiated, @B of the cash flows will lie between 6%& and %5@. If

= is implemented, @B of the cash flows will lie between %,?' and %,@@@,?5'. 4o

which alternati$e is riskier0

In comparin" Alternati$es A and =, we need to distin"uish between ",o0*e ri,!

and re*ive ri,!. 4tandard de$iation allows one to infer absolute risk. On an absolute

dollar le$el, = does imply a "reater spread amon" likely outcomes after all, %,@@@,?5' 6

%,?' G %D@, which is "reater than %5@ M 9%&< G %?DD. 1owe$er, on a relati$ebasis, when one considers the e*pected $alue for each alternati$e 9%D@ for A and

%,@@@,@?@ for =


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A> %?'(%D@ G %-.@D and

=> %-?@(%,@@@,@?@ G %@.@@@-?

=y di$idin" the standard de$iations by the e*pected $alue, we are measurin" the

dispersion of outcomes per e*pected dollar in cash flow. For each e*pected dollar in As

cash flow, there is %-.@D in dispersion amon" outcomes. For each e*pected dollar in =s

cash flow, there is %@.@@@-? in dispersion amon" outcomes. Note how its easier to

compare the le$els of risk in A and = by measurin" the dispersionper expected dollar.

7ets return to our ori"inal 8etroit()win Cities e*ample 9)able

-@


MANAGER>

. 4tandard de$iation measures the absolute riskassociated with a decision.

-. hen comparin" alternati$es, mana"ers may wish toe*amine relati$e risk. )his can be done bycalculatin" the coefficient of $ariation 9R


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De*roi*:

H*pected Value> %,'&,&D.'@

4tandard 8e$iation> %&'?,@&

Coefficient of Variation> %.'?

Twi% Ci*ie,:

H*pected Value> %,D5&,'.'@

4tandard 8e$iation> %,-,'5?

Coefficient of Variation> %.D'

As the analysis indicates, the e*pected profit in the )win Cities 9%,D5&,'.'@

%,&-,'5@; L %@D,@9 M ;< G %-,@&&,?'@; L %@,?'9 M ;

-5


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%-,@D',@@@; L %'5,D'@9 M ;< G %-,?,D'@; L %-,5@@9 M ;


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One alternati$e is to conduct a test market in its retail outlets in Akron, Ohio. If

the product "enerates a positi$e profit contribution in Akron, it will be launched

throu"hout the re"ion. )he %- million profit contribution for the entire re"ion will be

inferred if the test market yields a profit contribution of %-@@,@@@. 4imilarly, the re"ion6

wide profit contributions of %@.' million and %@. million will be pro2ected if the test

market yields profit contributions of %@.@' million and %@.@ million, respecti$ely. )he

product will not be launched if the profit contribution in Akron is less than %@.@ million.

=y test marketin" the product, suppose the re$ised e*pected $alue for a re"ion6

wide launch is %- million * .'@ L %@.' million * .-' L %@. million * .@ L %@ * .', or%.5' million. O$er the anticipated fi$e6year life of the product, the discounted present

$alue is %?.'5 million. =ecause the discounted present $alue of the e*pected profit

contribution with the test market is %?.'5 million and the e*pected profit contribution

without the test market study is %?.5' million, mana"ement should be willin" to spend no

more than %?.'5 million 6 %?.5' million, or %&@,@@@ on the test market study.

e can also determine the $alue of information in the Freemark Abbey inery

case. !ae"er must determine whether to har$est the "rapes immediately or wait for the

upcomin" storm. 1ow much money would !ae"er be willin" to pay to find out if the

storm will hit the re"ion0 Ironically, the answer is nothin". If !ae"er knows with

certainty that the storm will hit, the e*pected re$enues total %5?,'&?, which is more than

what he would earn if he har$ested the "rapes before the storm. 9)his assumes he

determined in ad$ance that he would not bottle an inferior wine if the mold did not form


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hat does matter to !ae"er is whether a storm is conduci$e to the formation of

the botrytis mold. If he knew the storm would not likely result in the mold, he would

har$est the "rapes immediately and earn %5?,-@@. If he knew the storm was conduci$e to

the mold, but mi"ht not hit the re"ion, his e*pected earnin"s from waitin" for the storm

would be %?,?@@. For this reason, !ae"er would be willin" to spend up to %?,?@@ 6

%5',&- 9the e*pected re$enues from delayin" the har$est


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conditions may chan"e, competitors may enter or e*it the market, e*chan"e rates may

chan"e, "o$ernment re"ulations may increase costs or restrict production, etc. As these

states of nature chan"e, prices, output, and unit costs may rise or fall.

8ecision tree analysis can be an in$aluable tool for estimatin" a pro2ects future

cash flow. =y compilin" a list of scenarios, the mana"er can pro2ect a series of cash

flows based on a $ariety of circumstances. )he e*pected $alue of each years cash flow

can be discounted to its present $alue. :oreo$er, to pro$ide a sensiti$ity analysis, the

e*pected cash flows can be inflated or deflated by one to two standard de$iations.

One tool for de$elopin" a sensiti$ity analysis is throu"h a Mo%*e Cro

,im0*io%. )his is typically a$ailable throu"h simulation software packa"es or as an

add6on to :icrosoft H*cel. In simulation, the mana"er selects an e*pected $alue and

standard de$iation for each rele$ant $ariable> unit sales, price, a$era"e $ariable cost, etc.

)he distribution of $alues can either follow a normal, trian"ular, uniform, or lo"normal

distribution 9see Fi"ure 5


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Dei,io% Tree, % Se80e%*i Dei,io%,

)hus far, we ha$e introduced decision trees to determine a sin"le decision by

mana"ement. )he first fork in the decision tree defines the choices a$ailable to the

mana"er. Hach subse+uent fork refers to factors that influence the companys profits butare beyond the firms control. Suite often, howe$er, a decision tree may re+uire the

mana"er to make more than one decision. For e*ample, suppose a firm is tryin" to

decide whether to launch a new product. Clearly, the decision analysis must incorporate

the profits "enerated by the "ood. Of course, if the firm "oes ahead and launches the

product, it will ha$e to make a pricin" decision. Naturally, the decision to launch the

product hin"es on the assumption the mana"er will choose the optimal price as conditions

chan"e. 1ow can the mana"er determine the e*pected $alue of an initiati$e when some

of the outcomes re+uire additional decisions0

)he key to makin" se+uential decisions in decision tree analysis is to make the

decisions from ri"ht to left. In other words, the mana"er needs to e*amine the last

decision mandated by the tree. =y calculatin" the summary statistics, the mana"er can

determine what he(she would do if the situation were to arise. From this point, the

mana"er can backtrack to the ne*t decision and repeat the process. Once all subse+uent

-&


MANAGER>

?. 8ecision trees are especially useful for determinin"the cash flows associated with capital bud"etin"decisions.

'. :onte Carlo simulation, a$ailable in many

spreadsheet packa"es, allows the firm to simulate theimpact of $arious combinations of factors on cashflows.


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decisions ha$e been determined, the mana"er can utili3e decision analysis to e$aluate the

o$erall pro2ect.

e can see e*amples of the need for se+uential decision6makin" in the Freemark

Abbey inery case. If a storm hits the re"ion and the mold does not form, the winery

could either sell the wine in bulk, sell the "rapes directly, or bottle and sell the wine

anyway. Althou"h the latter option would "enerate twice as much re$enue in the short

run, sellin" an inferior wine could dama"e the winerys reputation and inhibit future

sales. 1ence, in piecin" to"ether the decision tree, !ae"er needs to determine at the front

end what he would do if a storm hit the re"ion but the mold did not form.7ets work throu"h our own e*ample to illustrate how se+uential decisions are

made. 4uppose a mo$ie studio is tryin" to decide whether to finance a %'@ million bi"6

bud"et film or two smaller films costin" %D@ million each. Suite often, the director

re+uests additional fundin" to make chan"es and(or additions to the film. 4ometimes the

additional funds impro$e the bo* office appeal of the mo$ie and increase the films "ross.

On other occasions, the mo$ie does +uite well if the director is held to the ori"inal

bud"et.

)he studio e*ecuti$es anticipate a re+uest for an additional %'@ million for the

bi"6bud"et film and a combined %-' million for the two smaller films. If the additional

funds for the bi"6bud"et film are appro$ed, the studio e*ecs e*pect an &@B chance it will

"ross %5@@ million, a @B chance it will "ross %-@@ million, and a @B chance it will

"ross %&@ million. If the bud"et increase is not appro$ed, the probabilities of a %5@@

million "ross fall to @B, with the likelihood of a %-@@ million risin" to -'B and the

probability of an %&@ million "ross increasin" to 'B.

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If the two smaller films are financed and bud"et increases of a combined %-'

million are appro$ed, the e*ecuti$es belie$e there is a @B chance the films will

collecti$ely "ross %5@@ million. )his probability falls to 5@B if the bud"et increases are

not appro$ed. 4imilarly, the likelihood the smaller films will "ross a combined %-@@

million is e*pected to be 5@B if the bud"et increase is appro$ed and ?@B if it is not

appro$ed. Finally, if the additional funds are appro$ed, the likelihood the films will

"ross %&@ million is @B and 5@B if not appro$ed.

hat makes this case different from the others discussed so far is that the studio

e*ecuti$es cannot decide whether to fund the bi"6bud"et film or the two smaller filmswithout first anticipatin" the effect of the ine$itable re+uest for a bud"et increase. Fi"ure

? sets this up as a decision tree to illustrate the studio e*ecuti$es dilemma.

EFi"ure ? here

)his is the essence of decision trees with se+uential decisions> to answer the broad

+uestion of whether to finance the bi"6bud"et film or the two smaller films, the studio

e*ecuti$es must decide whether they would appro$e the re+uest for additional fundin".

)he decision6maker must ultimately make decisions by sol$in" the decision tree from

ri"ht to left. In this case, the studio e*ecuti$es must first determine whether they would

appro$e a bud"et increase before they e*amine the lar"er issue of which mo$ie9s< to

finance.

7ets work with the bi"6bud"et mo$ie first. If the director re+uests an additional

%'@ million, the e*pected "ross is %5@@ million * .&@ L %-@@ million * .@ L %&@ million

* .@ 6 %'@ million, or %-& million if the bud"et increase is appro$ed, and %5@@ million *

.@ L %-@@ million * .-' L %&@ million * .', or %-?- million if it is not appro$ed.

5@


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1ence, if the studio e*ecuti$es based their decision e*clusi$ely on e*pected $alue, they

would not appro$e the additional %'@ million bud"et increase.

If the smaller films are financed and the directors re+uest an additional %-'

million in combined bud"ets, the e*pected combined "ross is %5@@ million * .@ L %-@@

million * .5@ L %&@ million * .@ 6 %-' million, or %--5 million if the increase is

appro$ed, and %5@@ million * .5@ L %-@@ million * .?@ L %&@ million * .5@, or %?

million if the additional financin" is not appro$ed. )herefore, should the studio finance

the smaller films, the studio e*ecuti$es would appro$e the bud"et increase.

Now that this decision has been made in ad$ance, the studio e*ecuti$es can workbackward to determine which film9s< to finance. =ecause the bud"et increase for the bi"6

bud"et mo$ie would not be appro$ed, its e*pected profits are %-?- million 6 %'@ million

G %- million. Assumin" the re+uest for additional funds for the smaller films are

appro$ed, their e*pected combined profits are e+ual to %--5 million 6 %?@ million G %&5

million. Absent risk considerations, therefore, the e*ecuti$es would appro$e the bi"6

bud"et mo$ie.

5


MANAGER>

hen the primary decision a mana"er must makein$ol$es one or more se+uential decisions, the mana"ershould use backward induction. 4pecifically, he(she

should determine what he(she would do if confrontedwith the last decision in the chain of e$ents and workbackward to the primary decision.


32/75

M4imi% % Mi%im4

)wo other simple tools for makin" decisions under risk and uncertainty are the m4imi%

and mi%im4methods. nfortunately, as youll soon see, whereas mana"ers are

attracted to these tools because of their simplicity, they suffer because of their simplicity

and are not recommended. nder ma*imin, the mana"er lays out the possible outcomes

associated with $arious alternati$es. 1e(she identifies the worst possible outcome

associated with each alternati$e and selects the alternati$e with the best worst6case

scenario 9hence, the mana"er m4imi3es the mi%imum outcome


33/75

In addition to its simplicity, ma*imin does not re+uire the decision6maker to know

the probability of each outcome, which adds to its appeal. 1owe$er, this is one of its

weaknesses. As we criti+ue ma*imin, we must note that o%# the worst case scenarios

matter. It i"nores not only other potential cash flows but also the likelihood that the

worst case scenario is "oin" to occur. 7ets use an e*a""erated e*ample to illustrate the

problems with ma*imin. 4uppose the mana"er is choosin" between two alternati$es.

)he cash flows associated with each alternati$e appear in )able . And, to make matters

worse, lets assume the probability state of nature T is "oin" to occur is in million.

T"e

S**e of N*0re 1 2

A*er%*ive A ?3@1 ?3@2

A*er%*ive ' -?3@1 ?1@@ miio%

nder the ma*imin criterion, Alternati$e A would be selected because its worst case

scenario is better than =s. )he fact that state of nature T- "enerates %@@ million 9as

compared to %.@- for A< is completely i"nored. :oreo$er, the fact that state of nature T

is hi"hly unlikely to occur is ne$er factored into the decision.

Another simple tool is minima*. 1ere, the mana"er seeks to minimi3e the

opportunity cost of makin" the wron" decision. 7ets return to the scenario in )able to

show how minima* works. e will show the ori"inal table and then use it to construct

the minima* table 9)able D


34/75

would ha$e lost %5 million more than if he(she had chosen A. 7ikewise, had he(she

chosen C, the mana"er would lose %- million more than if he(she had selected A.

T"e

S**e of N*0re 1 2 5 6

Pro>e* A 6%- million 6% million % million %5 million

Pro>e* ' 6%' million 6%@.' million %5 million % million

Pro>e* C 6%? million %@ million %- million %? million

S**e of N*0re 1 2 5 6

Pro>e* A %@ % million %- million ?5 miio%

Pro>e* ' ?5 miio% %@.' million %@ %@

Pro>e* C ?2 miio% %@ % million ?2 miio%

sin" minima*, the ob2ecti$e of the mana"er is to mi%imi3e the m4imum opportunity

cost associated with each pro2ect. For e*ample, by choosin" pro2ects A or =, themana"er could miss out on as much as %5 million. 1owe$er, by makin" the wron"

decision, the mana"er could ne$er miss out by more than %- million by choosin" C.

1ence, usin" minima*, the mana"er would choose pro2ect C. A"ain, as with ma*imin,

the weakness of minima* lies in the fact that it i"nores the probabilities associated with

each state of nature and focuses only on a sin"le outcome. In this case, C would be the

recommended alternati$e e$en if the odds that states of nature and ? were ten million to

one and the likelihood of state of nature T5 occurrin" was .BU )he lesson to be

learned is that, like the payback method described in the capital bud"etin" chapter,

5?


35/75

mana"ers should not be seduced by a methods simplicity6666if a decision6makin" tool

seems too easy, it probably isU

SUMMARY

. A mana"er can use a decision tree to lay out the outcomes associated with a

decision. )o build a decision tree, the mana"er must determine the factors that

influence the cash flows associated with a decision, infer the probability the e$ent

will occur, and estimate the cash flows that will e*ist if the e$ent occurs.

-. hen the probabilities of the outcomes associated with an initiati$e $ary, the

proper method to assess the mean outcome is to calculate the e*pected $alue. )he

5'

IMPORTANT IMP&ICATIONS FOR THEMANAGER>

. sin" a ma*imin criterion, the mana"er sorts out the$arious outcomes associated with alternati$es.1e(she then chooses the alternati$e with the mostfa$orable worst case scenario.

-. sin" a minima* criterion, the mana"er sorts out the$arious outcomes associated with alternati$es. For

each state of natureW, he(she determines theopportunity cost associated with makin" the wron"decision 9i.e. the difference in profits betweenchoosin" the ri"ht alternati$e $ersus the wron"alternati$e


36/75

e*pected $alue of a list of outcomes is a wei"hted a$era"e calculated by summin"

the outcomes multiplied by their e*pected probabilities.

5. )he le$el of absolute risk associated with a decision can be inferred from the

standard de$iation. )he lar"er the standard de$iation, the more risk associated

with the decision.

?. In choosin" between alternati$es, the le$el of relati$e risk can be inferred from

the coefficient of $ariation. )his is calculated as the standard de$iation di$ided

by the e*pected $alue. It reports the dispersion amon" outcomes for each unit of

e*pected $alue.'. )he $alue of information is the difference between the e*pected $alue of the

alternati$e with information less the e*pected $alue of the alternati$e without

information.

. hen mana"ers must make se+uential decisions, they should do so usin"

backward induction be"innin" with the last decision on the decision tree and

workin" backward until they reach the primary decision.

D. sin" the ma*imin criterion, the mana"er chooses the alternati$e that pro$ides the

most fa$orable of the worst case scenarios. sin" the minima* criterion, the

mana"er determines the opportunity cost associated with makin" the wron"

decision in each possible scenario, identifies the hi"hest opportunity cost for each

alternati$e, and selects the alternati$e that yields the lowest ma*imum opportunity

cost. )he weakness in either of these decision criteria is that they i"nore all but

one outcome and do not factor in the probability it will occur.

5


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Mi%i-C,e: &0


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conductin" a study to determine the le$el of interest in his business. )he market research

study would cost %5',@@@. 4hould Clayton start up the lu""a"e deli$ery business0

4hould he pay for the market research study0

PRO'&EMS

. A computer software company has to decide which of two ad$ertisin" strate"ies to

adopt> )V commercials or newspaper ads. 4ales depend on the total $iewership when the

commercials are run, and the total readership when the newspaper ads appear. H*perience

dictates the correspondin" le$el of sales when $iewership(readership is hi"h, medium, or

low>

)V Commercials Newspaper Ads

Viewership 4ales #eadership 4ales

1i"h %,@@@ 1i"h %-,@@@

:edium %-,@@@ :edium %@,@@@

7ow %&,@@@ 7ow %&,@@@

:edia reports show that $iewership is hi"h 5@B of the time, medium ?@B of the time,

and low 5@B of the time. Newspaper readership is hi"h ?@B of the time, medium ?@B of

the time, and low -@B of the time.

5&


39/75

)he cost of the tele$ision commercials is %',@@@, whereas the cost of the newspaper ads

is %'@@. Calculate the e*pected profit, standard de$iation, and coefficient of $ariation.

hich ad$ertisin" strate"y would you recommend0

-. A manufacturer of di"ital cameras is tryin" to decide whether to adopt a hi"h6price

strate"y or a low6price strate"y. )he firmXs profits depend on the competitorXs reaction to

the firms strate"y 9your competitor must also decide whether to use a hi"h6 or low6price

strate"y< and the state of the economy 9either a boomin" economy, a normal economy, ora recession


40/75

If its competitor uses the low6price strate"y at the same time the firm does, the firms

profits will be %5',@@@ in a boom, %5@,@@@ in a normal economy, and %-',@@@ in a

recession.

)he likelihood that its competitor will "o with a low6price strate"y if the firm does is

&@B.

1istorical data shows that the probability of an economic boom in any "i$en year is 5@B

and the probability of a recession is -@B.

Calculate the e*pected $alue, standard de$iation, and coefficient of $ariation associated

with each strate"y. hich strate"y would you recommend0 H*plain.

5. 8i"i:usic is a manufacturer of :;5 players. It has de$eloped a player that can hold

up to three times the $ideo and audio ima"es of competitors brands. )he company isconsiderin" applyin" for a patent. )he estimated cost of applyin" for a patent is %-@,@@@.

If the patent is appro$ed, 8i"i:usic belie$es it can earn a profit contribution of %'@(unit

and sell two million units(year o$er the -@6year life of the patent. Con$incin" the .4.

;atent and )rademark Office that their product is patentable is not a "i$en. Followin"

consultations with patent lawyers, 8i"i:usic belie$es there is a 5@B chance it will obtain

a patent.

:ana"ement e*pects the profit contribution will fall to %'@(unit after the patent e*pires

and unit sales will fall to '@@,@@@. 4imilarly, if 8i"i:usic "oes into production without

?@


41/75

seekin" a patent, it e*pects to earn %'@(unit and sell - million units for three years, after

which competition will reduce 8i"i:usics profit contribution and unit sales to %'@(unit

and '@@,@@@ units, respecti$ely. )he 4;)O publishes all patent filin" applications &

months after filin". 8i"i:usic is concerned this will "i$e competitors ad$ance notice of

its inno$ation. If 8i"i:usics patent application is not appro$ed, competitors will

manufacture their own brands one year earlier than would normally be e*pected.

8i"i:usic also worries about the possibility of patent infrin"ements. Competitors may

decide to manufacture their own brands and fi"ht a le"al battle o$er the infrin"ement

char"e. A prolon"ed le"al battle could cost 8i"i:usic %-'@ million. If 8i"i:usic wins

the le"al battle, it can obtain an in2unction a"ainst the firm $iolatin" the patent and obtain

le"al dama"es that essentially restore its profit contribution to its pre$ious le$el

throu"hout the infrin"ement period. In other words, it will not reco$er the le"al

e*penses, but can retain its monopoly position for the remainder of the patent. )he

company belie$es there is a -'B likelihood a competitor will $iolate the patent. If thisshould occur, le"al e*perts belie$e 8i"i:usics probability of ha$in" its patent upheld in

court to be &@B.

a. Create a spreadsheet to determine whether 8i"i:usic should fi"ht a le"al battle

o$er infrin"ements in each year of its patent 9i.e. is it worthwhile to fi"ht an

infrin"ement that occurs in the patents last year, ne*t6to6last year, etc.0


42/75

?. =aby #est, Inc., a manufacturer of car seats for babies, is a defendant in a product

liability case. )he plaintiff and defendant are preparin" for trial, but a 2ury has not yet

been selected. =ased on e*tensi$e communications with their attorney, the CHO belie$es

there is a @B chance a 2ury will award the plaintiff %' million, a 5@B chance it will

award % million, a 5@B chance it will award %'@@,@@@, and a 5@B chance it will award

%@. 4ustoko$ich !ury Consultin" Associates has offered its ser$ices. In preliminary

meetin"s, the consults claimed their ser$ices would reduce the likelihood of the %'

million award to 3ero percent and increase the likelihood of no award to ?@B. hat is

the ma*imum =aby #est should be willin" to pay for this ser$ice0

'. All )hin"s Christmas is preparin" for the upcomin" holiday season. :ana"ement is

tryin" to decide if it should offer "ift wrappin" as a free ser$ice durin" checkout.

1istorically, the store had not "ift6wrapped its items but offered "ift6wrappin" at an

additional char"e. #ou"hly 'B of purchasers paid e*tra for the "ift6wrappin", which

"enerated a profit contribution of %-(item 9the cost of "ift6wrappin" was %.'@(unit


43/75

4hould All )hin"s Christmas offer complimentary "ift6wrappin"0

. =ill is a seasonal farmer and "rows $e"etables durin" the sprin" and summer to sell at

the local farmers market. Accordin" to $arious sources 9;un*sutawney ;hil and the

Farmers Almanac


44/75


45/75

&. Office ;artners is considerin" e*tendin" its market into de$elopin" countries that show

the hi"hest percenta"e "rowth in personal computers. nfortunately, because it lacks

historical data, it can only make sales pro2ections based on $arious assumptions. At the

present time, Office ;artners has narrowed down its market to either Hli3ea or Hast Yatia.

)he net present $alues from market e*pansion in either country appear below.

Se, Pro>e*io%, )er# Poor Aver


46/75

HANDS-ON EXERCISES

Dei,io% Tree,

8ecision trees represent a con$enient way to lay out the outcomes associated with adecision. )he first branch defines the decision the mana"er wishes to make. 4ubse+uentbranches establish the factors that affect the outcomes of the decision.

#ead o$er the below scenario. ell build the decision tree based on the information.

A firm is tryin" to decide whether to build a manufacturin" plant in 8etroit, :ichi"an orthe )win Cities in :innesota. If it locates in 8etroit, its fi*ed costs will e+ual %5@@,@@@and it will incur $ariable costs of %-(unit. If the plant is located in :innesota, it willincur fi*ed costs of %@@,@@@ and $ariable costs of %@(unit. 1owe$er, there is a -@Bchance a decrease in supply will dri$e up $ariable costs. If so, the $ariable costs will riseto %? in 8etroit and %5 in the )win Cities.

nit sales will depend on the state of the economy. If economic conditions are normal,the firm e*pects to sell 5'@,@@@ units in 8etroit and 5D',@@@ in the )win Cities. If theeconomy is in a recession, it anticipates unit sales of -@@,@@@ units in 8etroit and &@,@@@in the )win Cities. 1istorically, recessions ha$e been known to occur once e$ery fouryears.

)he unit price will be %-@ in either location unless a price war occurs, in which case theprice will fall to %' in 8etroit and %5 in the )win Cities. hen price wars occur, unitsales tend to rise by @B. ;rice wars tend to occur once e$ery three years.

a. hat decision is the firm tryin" to make0 Indicate each alternati$e on one of thebranches.

?


47/75

b. )he first factor that could influence the firms profits is the cost structure. 7ist eachcost structure in the respecti$e branch and the probability it will occur.

8etroit

)win Cities

?D


48/75

c. )he ne*t factor that may influence profits is the state of the economy. 7ist eachpossibility and the probability it will occur on one of the branches.

7ow Cost Fi*ed> %5@@,@@@ Variable> %-(unit

; G .&@

1i"h Cost Fi*ed> %5@@,@@@

8etroit Variable> %?(unit; G .-@

)win Cities

7ow CostFi*ed> %@@,@@@ Variable> %@(unit ; G .&@

1i"h CostFi*ed> %@@,@@@Variable> %5(unit; G .-@

?&


49/75

c. )he last factor that affects profitability is the price war. 7ist each possibility andits correspondin" probability in each branch.

ZZZ

?

De*roi*

Twi%

Ci*ie,

7ow Cost Fi*ed> %5@@,@@@ Variable> %-(unit ; G .&@

Normal> S G 5D',@@@ ; G .D'

1i"h Cost>Fi*ed> %5@@,@@@Variable> %?(unit ; G .-@

7ow Cost>Fi*ed> %@@,@@@Variable> %@(unit ; G .&@

1i"h Cost>Fi*ed> %@@,@@@Variable>%5(unit ; G .-@

NormalS G 5'@,@@@ ; G .D'

NormalS G 5'@,@@@

; G .D'

NormalS G 5D',@@@; G .D'

Normal S G 5D',@@@ ; G .D'

#ecessionS G -@@,@@@; G .-'


#ecessionS G &@,@@@

; G .-'

#ecessionS G &@,@@@

; G .-'


50/75

a. Calculate the profit and probability associated with each branch. 9#ecall that theprobability of independent e$ents is the product of the indi$idual probabilities.

;rofit ;rob.

ZZZZZ ZZZZ

ZZZZZ ZZZZ

ZZZZZ ZZZZ

ZZZZZZ ZZZZ

ZZZZZ ZZZZ

ZZZZZ ZZZZ

ZZZZZZZZZ

ZZZZZZZZZ ZZZ ZZZZZ ZZZ

ZZZZZ ZZZ

ZZZZZZZZ

ZZZZZZZZ

ZZZZZ ZZZ

ZZZZZ ZZZ

'@

De*roi*

Twi%

Ci*ie,

7ow Cost Fi*ed> %5@@,@@@

Variable> %-(unit ; G .&@

Normal> S G 5D',@@@ ; G .D'

1i"h Cost>Fi*ed> %5@@,@@@Variable> %?(unit ; G .-@

7ow Cost>

Fi*ed> %@@,@@@Variable> %@(unit ; G .&@

1i"h Cost>Fi*ed> %@@,@@@Variable>%5(unit ; G .-@



Normal

S G 5D',@@@; G .D'

Normal S G 5D',@@@ ; G .D'



#ecessionS G &@,@@@; G .-'

#ecessionS G &@,@@@; G .-'


51/75

ZZZZZZZZZ

E4.e*e )0e

a. Fill in the profits for each of the below scenarios. Calculate the a$era"e profit at

each location.

De*roi* Twi% Ci*ie,

Se%rio O0*ome O0*ome

7ow Cost(Normal Hconomy(No ;rice ar ZZZZZZZ ZZZZZZZ

7ow Cost(#ecession(No ;rice ar ZZZZZZZ ZZZZZZZ

7ow Cost(

Normal Hconomy(;rice ar ZZZZZZZ ZZZZZZZ

7ow Cost(#ecession(;rice ar ZZZZZZZ ZZZZZZZ

1i"h Cost(Normal Hconomy(No ;rice ar ZZZZZZZ ZZZZZZZ

1i"h Cost(#ecession(No ;rice ar ZZZZZZZ ZZZZZZZ

1i"h Cost(Normal Hconomy(;rice ar ZZZZZZZ ZZZZZZZ

'


52/75

1i"h Cost(#ecession(;rice ar ZZZZZZZ ZZZZZZZZ

:ean ;rofit> ZZZZZZZ ZZZZZZZZ

b. )he below table shows both the outcomes and the probability that each outcomewill occur.

De*roi* Twi% Ci*ie,


7ow Cost(

Normal Hconomy(No ;rice ar %-,'@@,@@@ .?@-@ %5,'@,@@@ .?@-@

7ow Cost(#ecession(No ;rice ar %,5@@,@@@ .5?@ %,-@@,@@@ .5?@

7ow Cost(Normal Hconomy(;rice ar %&'',@@@ .&@ %5D,'@@ .&@





1i"h Cost(#ecession(;rice ar 9%&@,@@@< .@' 9%@@,@@@< .@'

'-


53/75

hich outcome is least likely to occur0 hich outcome is most likely to occur0

c. =ased on your answer to b, do you think the mean outcome is an accurateassessment of the a$era"e profit at each location0

hen the mean of a set of outcomes is calculated, it implicitly assumes the probabilityeach outcome will occur is the same. hen the probabilities differ, as they usually do forbusiness decisions, the appropriate method for determinin" the a$era"e outcome is tocalculate the e4.e*e v0e9J =

=n

i

iiXP

,

d. Calculate the e*pected $alue for each location.

De*roi* Twi% Ci*ie,


7ow Cost(Normal Hconomy(No ;rice ar %-,'@@,@@@ .?@-@ %5,'@,@@@ .?@-@

7ow Cost(

#ecession(No ;rice ar %,5@@,@@@ .5?@ %,-@@,@@@ .5?@

7ow Cost(Normal Hconomy(;rice ar %&'',@@@ .&@ %5D,'@@ .&@




'5


54/75


1i"h Cost(

#ecession(;rice ar 9%&@,@@@< .@' 9%@@,@@@< .@'

H*pected Value> ZZZZZZZZ ZZZZZZZZZZ

S*%r Devi*io%

a. 7ets alter the cash flows for the )win Cities. )he cash flows at the two locations

and their respecti$e probabilities are shown below. Calculate the respecti$e

e*pected $alues.De*roi* Twi% Ci*ie,


7ow Cost(Normal Hconomy(No ;rice ar %-,'@@,@@@ .?@-@ %5,@@@,@@@ .?@-@

7ow Cost(

#ecession(No ;rice ar %,5@@,@@@ .5?@ %,@@,@@@ .5?@

7ow Cost(Normal Hconomy(;rice ar %&'',@@@ .&@ %',@@@ .&@

7ow Cost(#ecession(;rice ar %5@,@@@ .@@ 9%',D'@< .@@

1i"h Cost(Normal Hconomy(No ;rice ar %,&@@,@@@ .@@' %,'@,@@@ .@@'

1i"h Cost(#ecession(No ;rice ar %@@,@@@ .@55' %?-,'@@ .@55'

'?


55/75

1i"h Cost(Normal Hconomy(;rice ar %&',@@@ .@?' 9%&@,-'@< .@?'

1i"h Cost(

#ecession(;rice ar 9%&@,@@@< .@' 9%D5?,5.'@< .@'

H*pected Value> ZZZZZZZ ZZZZZZZ

b. If your recommendation were based e*clusi$ely on the a$era"e annual profit ateach location, which location would you recommend0

c. Considerin" all of the information before you, which location would yourecommend0 H*plain.

d. hat do your answers to +uestions b and c su""est about usin" e*pected $aluee*clusi$ely to make your decision0

e. Qi$en all of the infomation, why mi"ht someone recommend 8etroit0 )he )winCities0

If you ha$e a preference in this scenario, you are considerin" risk alon" with e*pected$alue. )he more widely dispersed the outcomes, the "reater the risk. 4tandard de$iation9< calculates the dispersion of outcomes around the mean. It is calculated as>

-

,


56/75

f. Calculate the standard de$iations for 8etroit and the )win Cities.

8ecision6makers may not always seek to a$oid risk. In this scenario, whereas onedecision6maker may choose 8etroit because the outcomes are closer to"ether, anotherdecision6maker may prefer the )win Cities because it has the potential to pay off betterthan 8etroit. In other words, the person who prefers the )win Cities is willin" to risk oneof the lower payoffs in the )win Cities for a chance at one of the hi"her payoffs.

An indi$idual who prefers to a$oid risk 9and therefore prefers a smaller standardde$iation< has ri,! ver,epreferences. An indi$idual who prefers risk 9and thereforeprefers a lar"er standard de$iation< has ri,!-,ee!i%


57/75

Coeffiie%* of )ri*io%

7ocation A>

Outcomes ;robability of Occurrin"

. %@ .@

-. 6%@@ .@

5. %5'@ .-@

?. %'@ .-@

'. %@ .?@

7ocation =>Outcomes ;robability of Occurrin"

. %,@@@,@@ .@

-. %,&@@ .@

5. %,@@@,'@@ .-@

?. %,'@ .-@

'. %,@@ .?@

a. Calculate the e*pected $alue and standard de$iation for each of the locations.

H*pected Value 4tandard 8e$iation

A> ZZZZZZ ZZZZZZZZ

'D


58/75

=> ZZZZZZ ZZZZZZZZ

b. If you were to assess risk e*clusi$ely on the si3e of the standard de$iation, whichlocation would you ha$e indicated as the most risky0

c. As you "lance o$er the abo$e information, would you, in fact, identify this location asthe more risky of the two0

d. Is a simple comparison of standard de$iation fi"ures sufficient to assess risk0 hy orwhy not0

4tandard de$iation measures the actual dispersion of outcomes around the mean. In thismanner, it is a measure of ",o0*e ri,!. In this scenario, howe$er, a standard de$iationof %?' when the e*pected $alue is %D@ is, on a relati$ely basis, is fairly risky. On the

other hand, a standard de$iation of %-?@ when the e*pected $alue is %,@@@,@?@ is prettyclose to a sure bet.

hen the e*pected $alues of alternati$es differ, mana"ers may prefer to measure thele$el of re*ive ri,!. )his can be assessed by calculatin" the coefficient of $ariation 9R


59/75

Dei,io% Tree, wi*+ Se80e%*i Dei,io%,

A mo$ie studio is tryin" to decide whether to finance a %'@ million bi"6bud"et film or

two smaller films costin" %D@ million each. )he studio e*ecuti$es anticipate a

subse+uent re+uest for an additional %'@ million for the bi"6bud"et film and a combined

%-' million for the two smaller films well after the ori"inal financin" has been appro$ed

and production is under way. If the additional funds for the bi"6bud"et film are

appro$ed, the studio e*ecs e*pect an &@B chance it will "ross %5@@ million, a @B

chance it will "ross %-@@ million, and a @B chance it will "ross %&@ million. If the

bud"et increase is not appro$ed, the probabilities of a %5@@ million "ross fall to @B,

with the likelihood of %-@@ million risin" to -'B and the probability of an %&@ million"ross increasin" to 'B.

If the two smaller films are financed and bud"et increases of a combined %-'

million are appro$ed, the e*ecuti$es belie$e there is a @B chance the films will

collecti$ely "ross %5@@ million. )his probability falls to 5@B if the bud"et increases are

not appro$ed. 4imilarly, the likelihood the smaller films will "ross a combined %-@@

million is e*pected to be 5@B if the bud"et increase is appro$ed and ?@B if it is not

appro$ed. Finally, if the additional funds are appro$ed, the likelihood the films will

"ross %&@ million is @B and 5@B if not appro$ed.

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A"ain, lets build the decision tree from scratch. hat decision is the mo$ie studiotryin" to make0 7ist each alternati$e on one of the branches.

After the film is appro$ed, the studio anticipates re+uests for additional fundin"> %'@million if the bi"6bud"et film is appro$ed and %-' million 9combined< if the two smallerbud"et films are appro$ed. 7ist the se+uential decisions on the ne*t set of branches.

=i"6bud"etFilm%'@ million

@


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)wo %D@millionfilms

7ist the anticipated "ross and the probabilities those "rosses will be reali3ed on thecorrespondin" branches.

Gro,, Pro""ii*#

ZZZZZZZZ ZZZZZZZ

Appro$e Additional ZZZZZZZZ ZZZZZZZ

%'@ million

'i< '0


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Notice that you cant determine the e*pected $alue, standard de$iation, and coefficient of$ariation for the bi"6bud"et and two smaller bud"et films until you first decide how todeal with the re+uest for additional financin".

7ist the outcomes and probabilities associated with the re+uest for additional fundin" for

the bi"6bud"et film. Gro,, Pro""ii*#

ZZZZZZZZZ ZZZZZZZ

%'@ million ZZZZZZZZ ZZZZZZZ Appro$ed

ZZZZZZZZ ZZZZZZZZ

%'@ million Not Appro$ed ZZZZZZZZ ZZZZZZZZ

ZZZZZZZZ ZZZZZZZZ

ZZZZZZZZ ZZZZZZZZ

8etermine the e*pected $alue, standard de$iation, and coefficient of $ariation associatedwith the bud"et increase re+uest 9dont for"et to subtract the additional bud"et cost ifappro$ed ZZZZZZZZZZZZZZZZZZZZZZZ

4tandard 8e$iation> ZZZZZZZZZZZZZZZZZZZZ

Coefficient of Variation> ZZZZZZZZZZZZZZZZZZ

ould you appro$e the bud"et increase0 H*plain.7ist the outcomes and probabilities associated with the re+uest for additional fundin" forthe smaller6bud"et film. Gro,, Pro""ii*#

ZZZZZZZZZ ZZZZZZZ

%-' million ZZZZZZZZ ZZZZZZZ Appro$ed

ZZZZZZZZ ZZZZZZZZ

%-' million Not Appro$ed ZZZZZZZZ ZZZZZZZZ

ZZZZZZZZ ZZZZZZZZ

ZZZZZZZZ ZZZZZZZZ

8etermine the e*pected $alue, standard de$iation, and coefficient of $ariation associatedwith the bud"et increase re+uest 9dont for"et to subtract the additional bud"et cost ifappro$ed ZZZZZZZZZZZZZZZZZZZZZZZ

4tandard 8e$iation> ZZZZZZZZZZZZZZZZZZZZ

Coefficient of Variation> ZZZZZZZZZZZZZZZZZZ

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ould you appro$e the bud"et increase0 H*plain.

#e6do the decision tree with the subse+uent decisions pre6determined.

Gro,, Pro""ii*#

%'@ million ZZZZZZZZZ ZZZZZZZ =i"6=ud"et

Additional %'@ million ZZZZZZZZ ZZZZZZZ Not appro$ed

ZZZZZZZZ ZZZZZZZZ

)wo %D@ million ZZZZZZZZ ZZZZZZZZ

films %-' million additional =ud"et appro$ed ZZZZZZZZ ZZZZZZZZ

ZZZZZZZZ ZZZZZZZZ

8etermine the e*pected $alue, standard de$iation, and coefficient of $ariation associatedwith the bi"6bud"et and two smaller6bud"et films.

H*pected Value 9bi"6bud"et ZZZZZZZZZZZZZZZZZZZZZZZ

4tandard 8e$iation 9bi"6bud"et ZZZZZZZZZZZZZZZZZZZZ

Coefficient of Variation 9bi"6bud"et ZZZZZZZZZZZZZZZZZZ

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H*pected Value 9two smaller films ZZZZZZZZZZZZZZZZZZZZZZZ

4tandard 8e$iation 9two smaller films ZZZZZZZZZZZZZZZZZZZZ

Coefficient of Variation 9two smaller films ZZZZZZZZZZZZZZZZZZ

T+e )0e of I%form*io%

A firm is considerin" launchin" a new product into the re"ion. If launched throu"hout its

retail outlets, it anticipates the followin" annual outcomes and probabilities>

Profi* o%*ri"0*io% Pro""ii*#

%- million .'@

%@.' million .-'

%@. million .@

9%@.- million< .@

9%@.' million< .@'

a. Calculate the e*pected $alue.

b. )he product mana"er anticipates the "ood will ha$e a life of fi$e years, after which it

will become obsolete. =ased on a cost of capital of &B, estimate the present $alue of the

income stream.

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c. An alternati$e to launchin" the product throu"hout the re"ion is to conduct a test

market in a sin"le market. )he profit contribution for the re"ion will be inferred from the

followin" test market results.

Te,* Mr!e* Re,0* I%ferre Re


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M4imi% Cri*erio%

;art I. A firm is tryin" to decide between three pro2ects 9A, =, and Ce* A 6%- million 6% million % million %5 million



a. Circle the least fa$orable outcome associated with each pro2ect.

b. hich of the circled outcomes is the most fa$orable0

nder the ma*imin criterion, the pro2ect that has the most fa$orable worst case outcomeis selected.

D


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;art II.

4uppose a firm is tryin" to choose between alternati$es A and =. )he outcomesassociated with each alternati$e are shown below.

S**e of N*0re 1 2

A*er%*ive A %.@ %.@-

A*er%*ive ' 6%.@ %@@ million

a. Circle the least fa$orable outcome associated with each pro2ect.

b. hich of the circled outcomes is the most fa$orable0

c. hich alternati$e would you choose based on ma*imin0

d. ould your decision remain the same if the probability of state T was @B0 [email protected]

e. =ased on the abo$e implications, what weakness is associated with the ma*imincriterion0

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Mi%im4 Cri*erio%

a. =ased on the below table, circle the most fa$orable outcomes correspondin" to eachstate of nature.

S**e of N*0re 1 2 5 6

Pro>e* A 6%- million 6% million % million %5 million



b. In the below table, calculate the opportunity cost associated with choosin" the wron"

alternati$e correspondin" to each state of nature. For e*ample, if state of nature T took

place, the best alternati$e is A, which loses %- million. 1ad the firm chosen A, it could

not ha$e done better, so its opportunity cost is %@. 1ad it chosen =, it would lose %'

million, which is %5 million worse than if it had chosen A. 1ad it chosen C, it would lose

%? million, which is %- million worse than if it had chosen A. Complete the table.

S**e of N*0re 1 2 5 6

Pro>e* A %@ ZZZZZ ZZZZZ ZZZZZ

Pro>e* ' %5 million ZZZZZ ZZZZZ ZZZZZ

Pro>e* C %- million ZZZZZ ZZZZZ ZZZZZ

c. Circle the ma*imum opportunity cost associated with each pro2ect.


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d. hich pro2ect has the lowest ma*imum opportunity cost0

sin" the minima* criterion, the pro2ect that has the lowest ma*imum opportunity cost

will be selected.

e. )he below table shows the opportunity cost table. Accordin" to the table, ;ro2ect C

has the smallest ma*imum opportunity cost.

S**e of N*0re 1 2 5 6

Pro>e* A %@ % million %- million ?5 miio%

Pro>e* ' ?5 miio% %@.' million %@ %@

Pro>e* C ?2 miio% %@ % million ?2 miio%

1ow mi"ht your decision chan"e if the probabilities of the states of nature were as

follows0

S**e of N*0re Pro""ii*#

.@

- .D

5 .@

? .@

f. hat is the primary limitation of the minima* criterion0

D@


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Decision-making Under Risk and Uncertainty

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