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Corporate FinanceLecture 04-1: Risk Analysis and Capital Budgeting

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1 Decision Trees

• A fundamental problem in N! analysis is dealing "it#uncertain future outcomes$

• %#ere is usually a se&uence of decisions in N! pro'ectanalysis$

• (ecision trees are used to identify t#e se&uential decisionsin N! analysis$

• (ecision trees allo" us to grap#ically represent t#ealternati)es a)ailable to us in eac# period and t#e likely

conse&uences of our actions$

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Example of Decision Tree

(o not

study

*tudy

finance

+pen circles represent decisions to be made$

,illed circles represent receipt

of information e.g $ a test

score in t#is class$

%#e lines leading a"ay from t#ecircles represent t#e alternati)es$

.C/

.A/

.B/

.,/

.(/

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Example: Stewart Pharmaceuticals

• *te"art #armaceuticals Corporation is considering in)esting in t#ede)elopment of a drug t#at cures t#e common cold$

• A corporate planning group including representati)es from

 production marketing and engineering #as recommended t#at t#efirm go a#ead "it# t#e test and de)elopment p#ase$

• %#is preliminary p#ase "ill last one year and cost 1 billion$,urt#ermore t#e group belie)es t#at t#ere is a 02 c#ance t#at tests

"ill pro)e successful$

• 3f t#e initial tests are  successful  *te"art #armaceuticals can go a#ead"it# full-scale production$ %#is in)estment p#ase "ill cost 1$

 billion$ roduction "ill occur o)er t#e follo"ing 4 years$

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NPV following Successful Test

 Note t#at t#e NPV  is calculated as of date 1 t#e date at "#ic# t#e in)estment of 100 million is

made$ Later "e bring t#is number back to date 0$

3n)estment ear 1 ears 5-6

Re)enues 7000

!ariable Costs 89000

,i;ed Costs 81

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NPV following nsuccessful Test

 Note t#at t#e  NPV  is calculated as of date 1 t#e date at "#ic# t#e in)estment of 100 million is

made$ Later "e bring t#is number back to date 0$

3n)estment ear 1 ears 5-6

Re)enues 4060

!ariable Costs 81796

,i;ed Costs 81

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Decision Tree for Stewart Pharmaceuticals

(o not

test

%est

,ailure

*uccess

(o not

in)est

3n)est

3n)est

%#e firm #as t"o decisions to make:

%o test or not to test$

%o in)est or not to in)est$

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Decision to Test

• Let>s mo)e back to t#e first stage "#ere t#e decision boils

do"n to t#e simple &uestion: s#ould "e in)est?

• %#e e;pected payoff e)aluated at date 1 is: 

%#e N! e)aluated at date 0 is:

*o "e s#ould test$

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• +ne of t#e fundamental insig#ts of modern financet#eory is t#at options #a)e )alue$

• %#e p#rase .e are out of options/ is surely a signof trouble$

• Because corporations make decisions in a dynamicen)ironment t#ey #a)e options t#at s#ould be

considered in pro'ect )aluation$

Discounte! Cash Flows an! "ptions

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Discounte! Cash Flows an! "ptions• e can calculate t#e market )alue of a pro'ect as t#e sum of

t#e N! of t#e pro'ect "it#out options and t#e )alue of t#e

managerial options implicit in t#e pro'ect$

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%#e N! e)aluated at date 0 is:

The "ption to #$an!on

•*uppose *te"art #armaceuticals #a)e to make t#e

in)estment decision before t#e realiation of t#e test result$  %#us t#e )alue of t#e option is

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% Sensiti&it' #nal'sis( Scenario #nal'sis(

an! )rea*+E&en #nal'sis

• #en a #ig# N! is calculated one>s temptation isto accept t#e pro'ect immediately$

• 3t is possible t#at t#e pro'ected cas# flo" "ill gounmet in practice$

• %#ese tec#ni&ues allo" t#e firm to c#eck "#et#er t#e N! remains positi)e under different assumptions$

• %#ey also allo" us to look be#ind t#e N! number tosee from "#ere our estimates are$

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Sensiti&it' #nal'sis

3n t#e *te"art

#armaceuticals

e;ample re)enues

"ere pro'ected to be

7000000 per year$

3f t#ey are only

000000 per year

t#e N! falls to1941$4

Also kno"n as ."#at if/ analysisE "e e;amine #o" sensiti)e a particular N! calculation is to c#anges in t#e underlying assumptions$

$3n)estment ear 1 ears 5-6

Re)enues 000

!ariable Costs,i;ed Costs

(epreciation

reta; profit

%a; 8942 Net rofit

Cas# ,lo" -100

3n)estment ear 1 ears 5-6

Re)enues 000

!ariable Costs 89000,i;ed Costs

(epreciation

reta; profit

%a; 8942 Net rofit

Cas# ,lo" -100

3n)estment ear 1 ears 5-6

Re)enues 000

!ariable Costs 89000,i;ed Costs 81

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Sensiti&it' #nal'sis

• e can see t#at N! is )ery sensiti)e to c#anges inre)enues$ ,or e;ample a 142 drop in re)enue leads to a12 drop in N!

,or e)ery 12 drop in re)enue "e can e;pect roug#ly a

4$562 drop in N!

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Scenario #nal'sis

• A )ariation on sensiti)ity analysis is scenario analysis$• ,or e;ample t#e follo"ing t#ree scenarios could apply to*te"art #armaceuticals:

1$ %#e ne;t years eac# #a)e #ea)y cold seasons and sales e;ceed

e;pectations but labor costs skyrocket$5$ %#e ne;t years are normal and sales meet e;pectations$

9$ %#e ne;t years eac# #a)e lig#ter t#an normal cold seasons so salesfail to meet e;pectations$

• +t#er scenarios could apply to go)ernment appro)al fort#eir drug$

• ,or eac# scenario calculate t#e N!$

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)rea*+E&en #nal'sis

• Anot#er "ay to e;amine )ariability in our forecasts is break-e)en analysis$• 3n t#e *te"art #armaceuticals e;ample "e could be

concerned "it# break-e)en re)enue break-e)en sales )olumeor break-e)en price$

• e first compute t#e break-e)en OCF  BE :.

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)rea*+E&en #nal'sis• e can start "it# t#e break-e)en incremental after-ta; cas#

flo" and "ork back"ards t#roug# t#e income statement to back out break-e)en re)enue:

3n)estment calculation Cas# ,lo"

Re)enues

!ariable Costs

,i;ed Costs

(epreciation

reta; profit

%a; 8942

 Net rofit

Cas# ,lo" 604$76

3n)estment calculation Cas# ,lo"

Re)enues

!ariable Costs

,i;ed Costs

(epreciation

reta; profit

%a; 8942

 Net rofit D 604 - depreciation 104$76

Cas# ,lo" 604$76

3n)estment calculation Cas# ,lo"

Re)enues

!ariable Costs

,i;ed Costs

(epreciation

reta; profit D 104$76 F 81-$94 16

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)rea*+E&en #nal'sis

•  No" t#at "e #a)e break-e)en re)enue as 696

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Practical ,uestions

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Practical ,uestions

,or &uestion 19$c replace .accounting/ "it# .financial/$