Risk Analysis II

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Project ManagementA Managerial Approach

Risk Analysis


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RISK ADJUSTED DISCOUNTRATE


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The risk adjusted discount rate method calls foradjusting the discount rate to reflect the project risk. Ifthe risk of the project is equal to the risk of the existinginvestments of the firm, the discount rate used is the

average cost of capital of the firm. If the risk of theproject is greater than the risk of the existinginvestments of the firm, the discount rate used ishigher than the average cost of capital of the firm.Finally if the risk of the project is less than the risk of

the existing investments of the firm, the discount rateused is less than the average cost of capital of thefirm.


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Risk adjusted discount rate is-

kkdnir

where

kr =risk adjusted discount rate

i= risk free rate of interest

n= adjustment for the firms normal risk

=adjustment for the differential risk of the projectkd


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Ir

ANPV

n

t k

t

1 )1(

Once the projects risk adjusted discount rateis specified, the project is accepted if NPV,

calculated as follows is positive.

t


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The Certainty Equivalent method isconceptually superior to the risk adjusteddiscount rate method because it does

not assume that risk increases with timeat a constant rate. Each years certaintyequivalent coefficient is based on thelevel of risk characterizing its cash flow.Despite its conceptual soundness it isnot as popular as the risk adjusteddiscount rate method.


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This is perhaps because it is inconvenientand difficult to specify a series ofcertainty equivalent coefficients but

seemingly simple to adjust the discountrate. Notwithstanding this practicaldifficulty, the merits of the certainty

equivalent method must not be ignored.


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SENSITIVITY ANALYSIS


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THIS WORKS SIMILAR TO PERT ANALYSIS---anexpected value for the main inputs to the projectis put into the calculations of the outcome including

an optimistic( +n%) &pessimistic (-n%) value( the value of n is often 10). This will show theeffect of a change in the variables considered on theoutcome and can show where management controlattention should be focused.


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Example

The price of materials & labour for a project is likely tofluctuate

Contract price needs to be fixed in advance.

Material is one of the major contributors to the cost ofthe project.

Overheads are calculated as 175% of direct labour.

Costs: material -$ 0.60 Direct labour- $0.20

Hence contribution to overheads- $0.35 Revenues: fixed at1.2$


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The calculations carried out in the table are as follows:

Revenue material costs- combined labour & overhead costs =profit

MATERIALS

-10% EXPECTED +10%

-10% 1.2-0.54-

0.495= +0.165

1.2-0.6-0.495

= +0.105

1.2-0.66-0.495

= +0.045

expected 1.2-0.54-0.55

= +0.11

1.2-0.6-0.55

= +0.05

1.2-0.66-0.55

= -0.01

+10% 1.2-0.54-0.605

= +0.055

1.2-0.6-0.605

= -0.005

1.2-0.66-0.605

= -0.065


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As can be seen , the effect of the changes in costs meansthat although on initial inspection this looks viable, the figuresindicate that should materials increase by 10%, unless thereis a drop in the labour costs of the project, it will make a loss.


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Advantages of Sensitivity Analysis

It shows how robust or vulnerable theproject is to changes in the values fo theunderlying variables

It indicates how sensitive is NPV tovarious factors and how the variability ofthese factors is to be contained

It is intuitively very appealing.


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Game Theory


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Game theory

Concerned with the study of decisionmaking in situations where 2 or morerational opponents are involved under

conditions of competition and conflictinginterests.


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Game theory attempts to mathematicallycapture behavior in strategic situations, wherean individual's success in making choices

depends on the choices of others. Whileinitially developed to analyze competitionswhere one individual does better at another'sexpense ZERO SUM GAMES, it has been

expanded to treat a wide class of interactions,which are classified according to severalcriteria


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A game consists of a set of players, a setof moves (or strategies) available tothose players, and a specification of

payoffs for each combination ofstrategies.


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For e.g., candidates for election,advertising& marketingcampaigns by competing business firms,countries involvedin military battle etc.all have conflicting interests.

In a competitive situation the courses ofaction(alternatives) for each competitor may be finite orinfinite.

IT CAN BE A 2-PERSON GAME OR AN n- PERSON GAMEDEPENDING ON THE NO. OF PLAYERS.


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In game theory zero-sum describes a situation in whicha participant's gain or loss is exactly balanced by thelosses or gains of the other participant(s). It is so namedbecause when the total gains of the participants are

added up, and the total losses are subtracted, they willsum to zero. Zero-sum can be thought of more generallyas constant sum where the benefits and losses to allplayers sum to the same value. Cutting a cake is zero-or constant-sum because taking a larger piece reduces

the amount of cake available for others. In contrast,non-zero-sum describes a situation in which theinteracting parties' aggregate gains and losses is eitherless than or more than zero. The sum of a negative anda negative always equal a negative.


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Some facts-

A competitive situation is called a GAME ifthere are finite no. of competitors/players.

Each player has a finite no. of

strategies/alternatives available to him A play of the game takes place when each

player employs his strategy

Every game results in an outcome e.g., loss orgain or a draw, usually called PAYOFF.


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Some facts-

PURE STRATEGY-players select the same strategyeach time. Player knows exactly what the other playeris going to do. Objective of the players is to maximizeprofit or to minimize losses.

MIXED STRATEGY-when the players use acombination of strategies and each player alwayskeeps guessing as to which course of action will beselected by the other player.

OPTIMUM STRATEGY-a course of action which puts

the player in the most preferred position, irrespectiveof the strategies of the competitors.


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VALUE OF THE GAME-expected payoff ofplay when all players of the game follow theiroptimum strategies. The game is fair if value is0, else unfair.

PAYOFF MATRIX: gains or losses can berepresented in the form of a matrix called thePAYOFF MATRIX.

In a ZERO SUM GAME-GAIN OF ONEPLAYER IS EQUAL TO THE LOSS OF THEOTHER, & viceversa.


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.

Hence it is sufficient to construct a payoff matrix only forone player. LET aij be the payoff which player A gains fromplayer B if A chooses strategy Ai and B chooses Bj. Thenthe payoff matrix to player A is (payoff matrix for B is

aij)pl.B

B1 B2 Bn

A1

pl A A2

Ammnmm

n

n

aaa

aaa

aaa

21

22221

11211

EXAMPLE :CONSIDER 2 PEOPLE TOSSING A COIN The game is B


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EXAMPLE :CONSIDER 2 PEOPLE TOSSING A COIN. The game is ---Bpays Rs. 7 to A if (H,H) occurs & Rs. 4 if (T,T) occurs; otherwise A paysRs.3 to B. As payoff matrix may be displayed as below:

Pl B

H T

H 7 -3

player A

T -3 4

With the MAXIMIN- MINIMAXprinciple for the selection of theoptimal strategies by the two players,saddle point where maximin value= minimax value, is found & the corresponding strategies are calledOPTIMUM STRATEGIES. The amount of payoff is called the value of thegame.

EXAMPLE


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EXAMPLE:

Pl. B

B1 B2

A1 9 2

Pl. A A2 8 6*+

A3 6 4

In symbols: maxi.(minj.(aij))= 6= minj.(maxi(aij))

Where i=1,2,3 & j = 1,2

RULES FOR DETERMINING SADDLE POINT:

Select the min. element of each row & mark *

Select the greatest element of each column & mark +.

If there appears an element having both the marks, that isthe saddle( equilibrium) point


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Exercise 1

Two leading firms-Nirmala Textiles Ltd. AndAditi Rayon ltd, for years have been sellingshirting, which is but a small part of both firms

total sales. The marketing Director of NirmalaTextiles raised the question-What should thefirms strategies be in terms of advertising for

the product in question? The systems group of

Nirmala Textiles developed the following datafor varying degrees of advertising.


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No advertising, medium advertising, heavy advertisingfor both firms will result in equal market share.

Nirmala Textiles with no advertising: 40% of the marketwith medium advertising by Aditi Rayons and 28% of the

market with heavy advertising by Aditi Rayons. Nirmala Textiles using medium advertsing:70% of the

market with no advertising by Aditi Rayons and 45% ofthe market with heavy advertising by Aditi Rayons.

Nirmala Textiles using heavy advertising: 75% of themarket with no advertising by Aditi Rayons and 52.5% ofthe market with medium advertising by Aditi Rayons.

Based on the above information, answer the marketing

directors question.


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Solution:

Noadvtg

Medadvtg

Heavyadvtg

Rowmin

b1 b2 b3

No advt a1

Medadvt

a2

Hvy advt a3

ColMaxima

Nirmalaextiles

Strategy

Aditi Rayons Strategy


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Solution:

Noadvtg

Medadvtg

Heavyadvtg

Rowmin

b1 b2 b3

No advt a1 50 40 28 28

Medadvt

a2 70 50 45 45

Hvy advt a3 75 52.5 50* 50

ColMaxima 75 52.5 50

Nirmalaextiles

Strategy

Aditi Rayons Strategy


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Solution contd.

Saddle point exists at the intersection ofa3 and b3. Thus optimal strategy foreach one is to engage in heavy

advertising and it will result in an evendistribution of the market between thefirms. Nirmala Textiles marketing

director should therefore resort to heavyadvertising.


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Two bakeries in a city, IB Ltd. & HA Ltd. Are theonly suppliers of bread & other bakery products tothe city. With an increase in demand for their

products, each has plans for future activities, suchas not to expand production, change the presentsize of the bakery or to open a branch depot in thesuburb. The payoff to the IB Ltd. In terms of %

gain/loss is given as follows.

Exercise 2


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HA Ltd. noexpansion

Increasepresentcapacity

Opendepot

IBLtd.

1. Noexpansion

0 -5 -15

2. Increasepresent

capacity

25 0 -10

3. Open adepot

15 10 0

Determine the optimal strategy for the two companies


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Exercise 3

Shruti Ltd has developed a sales forecasting functionfor its products and the products of its competitor,Purnima Ltd. There are four strategies S1, S2, S3 andS4 available to Shruti Ltd and 3 strategies P1, P2, P3

to Purnima Ltd. The payoffs corresponding to all thetwelve combinations of the strategies are given below.From the table we see that if S1 is employed by ShrutiLtd and P1 by Purnima Ltd., then there can be a gainof 30,000 in quarterly sales to the former. Other

entries can be similarly interpreted. Considering thisinformation what would the optimal strategy for ShrutiLtd. Be?


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PurnimaLtd

P1 P2 P3

ShrutiLtd

S130,000 -21,000 1,000

S218,000 14,000 12,000

S3 -6,000 28,000 4,000

S4 18,000 6,000 2,000

Risk Analysis II

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