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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