Report on Business Decision Analysis, Pricing and CVP Analysis

This report provides a comprehensive analysis of decision-making processes, incorporating utility functions, standard gamble assessments, and various decision criteria such as optimistic, pessimistic, and regret approaches. It delves into expected monetary value (EMV) calculations, including the expected value of perfect information (EVPI), and explores the value of information through conditional probabilities and Bayesian analysis. The report also covers Monte Carlo simulation for profit forecasting and includes a section on regression analysis to determine overhead costs based on machine hours and batch sizes. Furthermore, it examines cost-volume-profit (CVP) analysis to assess break-even points and profit targets under different pricing scenarios. The analysis is supported by calculations, decision trees, and tables to illustrate key concepts and findings.

Contents
Decision Analysis............................................................................................................................2
Q1a...............................................................................................................................................2
Q1b...............................................................................................................................................3
Q1b1.........................................................................................................................................3
Q1b2.........................................................................................................................................3
Q1b3.........................................................................................................................................4
Q1b4.........................................................................................................................................4
Q1b5.........................................................................................................................................5
Q1b6.........................................................................................................................................5
Value of information........................................................................................................................6
Q2a...............................................................................................................................................6
Q2b...............................................................................................................................................7
Q1c...............................................................................................................................................7
Q1d...............................................................................................................................................8
Monte Carlo Simulation................................................................................................................12
Q3a.............................................................................................................................................12
Q3b.............................................................................................................................................12
Q3c.............................................................................................................................................13
New Pricing Strategy - Report...............................................................................................13
Regression Analysis.......................................................................................................................15
Q4a.............................................................................................................................................15
Q4b.............................................................................................................................................15
1 – Overhead cost vs Machine Hours.................................................................................16
3 – Overhead VS Machine hours + Batches.......................................................................17
Q4c.............................................................................................................................................17
Q4d.............................................................................................................................................18
CVP Analysis.................................................................................................................................18
Q5a.............................................................................................................................................18
Q5b.............................................................................................................................................19
Q5c.............................................................................................................................................19
Q5d.............................................................................................................................................19

Q5d1...........................................................................................................................................19
Q5d2...........................................................................................................................................19
References:....................................................................................................................................20

Decision Analysis
Q1a
Discuss how a utility function can be assessed. What is a standard gamble and how is it used
in determining utility values?
To assess a given Decision, the monetary value outcome of single decision choices made should
be normalized with the risk involved with the decision. In a decision choice after considering the
risk attached to it, the numeric representation is given by the Utility function.
Assessing utility function scenario consider the Decision as a gamble and alternative 1 with only
2 possible outcome, 0 as utility for worst outcome stat 1 and 1 to best outcome state 2. p & q are
probabilities involved. Then, q = 1-p
Finding utility for any other scenario, we consider Alternative 2 with worst and best outcome.
When we equate Alternative 1 and alternative 2 outcomes, then;
Utility of Alternative1
p(1)+(1−p)(0)=p
 Utility of Alternative 2=x
 Utility of Alternative 2(x)=Utility of Alternative 1= p
x= p
We can therefore assign utility value of any other outcome using the summary below
Below Decision stump summarizes the Standard gamble.
.

Q1b
Below are details of Barnes, Decision outcomes.
 Amount of Total Investment = 10000
 Investment option1 – share Market
Good return = 14%
Fair return = 8%
Bad return = 0%
 Investment option2 – Government bonds
Constant = 9%
Q1b1
The table below shows Decision Matrix of the the above values;
Decision matrix
Investment option
Share market Government bonds
Market
conditions
Good 1400 900
Fair 800 900
Bad 0 900
Q1b2
Which alternative would an optimist choose?
Optimist will go for maximum choice out of the maximum outcome on each of the market state.
Maximax-Optimist choice
Investment option Maximum
Share market Government bonds
Market
conditions
Good 1400 900 1400
Fair 800 900 900
Bad 0 900 900
Under optimistic criterion, the optimist choose, Share market as investment option.

Q1b3
Which alternative would a pessimist choose?
Pessimist will go for minimum choice among the minimum outcome in each market state.
Minimini-pessimist choice
Investment option Minimum
Share market Government bonds
Market
conditions
Good 1400 900 900
Fair 800 900 800
Bad 0 900 0
Under Pessimistic criterion, the pessimist will choose, Share market as investment option, with 0
return.
Q1b4
Which alternative is indicated by the criterion of regret?
Regret Criterion is given by the minimax opportunity loss state, where Opportunity loss for a
given state is the different between the state outcome and maximum outcome of a market state.
Example: Opportunity Loss for Government bonds in Good market state is;
1400(maximum of outcome for good market ) – 900( outcome of Govt bonds∈Good market )
¿ 500
Criterion for regret is state where opportunity loss is minimum, which is investment in
government bonds in good market state.

Investment option Max per state
Share market Government
bonds
State of market Good 1400 900 1400
Fair 800 900 900
Bad 0 900 900
Opportunity loss matrix
Share market Government
bond
Good 0 500
Fair 100 0
Bad 900 0
Maximum
opportunity loss
per option
900 500
Q1b5
Assuming probability of a good market = 0.4, a fair market = 0.4 and a bad market = 0.2, using
Expected monetary values what is the optimum action?
Probability per
market state
Investment option
Share market Government bond
Market
state
Good 0.4 1400 900
Fair 0.4 800 900
Bad 0.2 0 900
EMV =∑ total of Probability of market state∧outcomes attached .
EMV ( share market )=0.4 ×1400+0.4 × 800+0.2 ×0=880
EMV (Government bonds)=0.4 ×900+ 0.4 ×900+ 0.2× 900=900
Hence Optimum action would be investing in Government bonds.
Q1b6
What is the expected value of perfect information?
Expected Value with perfect Information is weighted average of maximum possible state of
available options and probability of occurrence of each state.
Thus;
EVwPI =0.4 × 1400+0.4 × 900+0.2 ×900=1100

Probability per
market state
Investment option Max in
state of
market
Share market Government
bond
Market state Good 0.4 1400 900 1400
Fair 0.4 800 900 900
Bad 0.2 0 900 900
Expected monetary value 1100
Expected value of Perfect Information is difference between the EVwPI and maximum of EVM
(900)
EVPI=1100 – 900=$ 200
Thus;
Expected value of Perfect Information is $200 for the given market state and investment options.
Value of information
 let P(FM) be the Probability for Market is Favorable.
 let P(UM) be the Probability for Market is Unfavorable.
 let P(FR|FM) be the probability for Research Favorable Given Market is Favorable.
 let P(UR|FM) be the probability for Research Unfavorable Given Market is Favorable.
 let P(UR|UM) be the probability for Research Unfavorable Given Market is Unfavorable.
 let P(FR|UM) be the probability for Research Favorable Given Market is Unfavorable.
 let P(FM|FR) be the Probability for Favorable Market given favorable Research
 let P(UM|FR) be the Probability for Unfavorable Market given favorable Research
 let P(FM|UR) be the Probability for favorable Market given Research Unfavorable.
 let P(UM|UR) be the Probability for Unfavorable Market given Research Unfavorable.
 let P(FR be the Probability for Favorable research
 let P(UR) be the Probability for unfavorable research
For a Razor Factory, If the market were favorable return is of $100,000, but if the market were
unfavorable loss is $60,000. Jim estimates the probability of a favorable market is 0.5
So, P( FM )=0.5∧P(UM )=0.5∧R (FM )=100000∧R (UM )=−$ 60000

Q2a
What should Jerry do? Show calculations
Jerry should calculate Estimated Monetary Value is either of the market conditions for either of
the 2 options, go for production or not go for production.
EMV is best of each condition weighted averaged against probability of occurrence for
condition.
EMV production={ R(FM )× P( FM )+ R( UM )× P (UM )}
EMV production=(0.5 ×100000+0.5 ×(−60000))
EMV production=20000
EMV no production={R(FM )× P( FM )+ R (UM )× P (UM )}
EMV no production=(0.5 × 0+0.5 ×0)
EMV no production=0
Option evaluation is best of EMV of either of 2 options. Which is corresponding to go for
production. Hence Jerry should go for Production.
Q2b
Revise the prior probabilities in light of his friend’s track record.
70% of friend’s past record is the time he would correctly provide a favorable market prediction
and 20% of the time he would incorrectly provide a favorable market prediction.
Prior Probabilities are prior probabilities for Favorable or unfavorable market conditions.
P( FM )=0.5
P(UM )=1 – P ( FM )=0.5
Q1c
What is the posterior probability of a good market given that his friend has provided an
unfavorable market prediction?
Posterior Probabilities, for Favorable Market given Favorable Research be P(FM|FR) and for
Unfavorable Market given Favorable Research be P(UM|FR).
To Calculate the Posterior Probabilities, Conditional Probabilities for P(FR|FM) and P(FR|UM)
is required.
As per friend’s track record.
P( FR∨FM )=0.7

P( FR∨UM )=0.2 .
Posterior probability Calculations for Favorable Research
State of
events
Prior Conditiona
l
probability
Joint Posterior
Favorable
market
P(FM)=0.5 P(FR|
FM)=0.7
P(FR ∩FM)= P(FR|FM)×P(FM)=0.35 0.78
Unfavorabl
e market
P(UM)=0.
5
P(FR|
UM)=0.2
P(FR ∩UM)= P(FR|UM)×P(FM)=0.10 0.22
Probability of favorable research
P(FR)=0.45
Joint Probability for Favorable market and Favorable Research P(FR∩FM) is product of P(FR|
FM) and P(FM) as calculated above = 0.35
While, Joint Probability for unfavorable market and Favorable Research P(FR∩UM) is product
of P(FR|UM) and P(UM) as calculated above =0.10
Taking sum of P(FR∩FM) and P(FR∩UM) gives the absolute probability for a favorable
research, which is P(FR) = 0.45.
The Bayes Theorem−P( A∨B)× P (B)=P (B∨ A)× P( A)
Hence ,
P( FM ∨FR)=P( FR∨FM ) × P( FM )/P(FR)=P (FR ∩ FM )/P(FR)=0.35 ÷ 0.45=0.78
P(UM ∨FR)=P(FR∨UM ) × P(UM )/ P( FR)=P(FR ∩ FM )/ P(FR)=0.10 ÷ 0.45=0.22
Q1d
What is the expected net gain or loss from engaging his friend to conduct the market
research? Should his friend be engaged? Why?
Expected Gain or loss for engaging the Friend for research can be calculated using a decision
tree.
Let P1 through P11 represent decision stumps in the Decision tree, while N1 to N9 represent the
outcome leaf nodes.
Let

P1 Represents decision node for Research∨do not conduct Research .
P2 Represents decision node for go for Production∨not go for Production .
P3 represents decision node for Research Favorable∨Unfavorable.
P4 represents decision node for Favorable Market ∨Unfavorable Market .
P5 isa dummy decision node for no production .
P6 represents decision node for go for Production∨not go for Production .
P7 represents decision node for go for Production∨not go for Production .
P8 represents decision node for Favorable Market∨Unfavorable Market .
P9 is a dummy decision node for no production .
P10 represents decision node for Favorable Market ∨Unfavorable Market
P11 is a dummy decision node for no production.
Let, N1 N4 and N7 represent the lead node for Favorable market, while N2 N5 and N8 represent
for Unfavorable Market condition, N3 N6 and N9 represent for no production. Monetary value
attached with each of the nodes are as follows.
eaf odesL N Monetary Value
N1 MF $1,00,000.00
N2 MU -$60,000.00
N3 o roducti onN P $0.00
N4 M Research costF - $95,000.00
N5 M Research costU - -$65,000.00
N6 Research cost -$5,000.00
N7 M Research costF - $95,000.00
N8 M Research costU - -$65,000.00
N9 Research cost -$5,000.00
 ¿ P(FM ∨UR)
¿ P(UR∨FM ) × P(FM )÷ ¿
¿ 0.3 ×0.5 ÷ ¿
¿ 0.3 ÷(0.3+ 0.8)
¿ 0.27
 P(UM ∨UR)
¿ 1−P(FM ∨UR )
¿ 1 – 0.27
¿ 0.73
 P(FM ∨FR)

¿ P( FR∨FM )× P(FM )/((P ( FR∨UM )× P(UM ))+( P( FR∨FM )∗P(FM )))
¿( 0.7 ×0.5)÷ (0.7 ×0.5+ 0.2× 0.5)
¿ 0.7 ÷ 0.9
¿ 0.78
 P(UM ∨FR)
¿ 1−P(FM ∨FR)
¿ 1 – 0.78
¿ 0.22
 P(FR)
As per Bayes theorem for conditional probability explained above , we have−¿
P( FR∨FM )× P (FM )=P(FM ∨FR)× P ( FR)
¿ ¿
¿(0.7 ×0.5)÷ 0.78
¿ 0.45
 P(UR )
¿ 1 – P(FR)
Conditional Probability values for different events summarized below are as follows.
robability ValuesP
MP(F ) 0.5
MP(U ) 0.5
R MP(F |F ) 0.7
R MP(U |F ) 0.3
R MP(U |U ) 0.8
R MP(F |U ) 0.2
M RP(F |F ) 0.78
M RP(U |F ) 0.22
M RP(F |U ) 0.27
M RP(U |U ) 0.72
RP(F ) 0.45
RP(U ) 0.55
Plotting the above information on a decision tree, as per below diagram.

EMV at each Decision Points.
P 11=ResearchCost =−5000
P 10=P( FM ∨UR )× R ( FM −Researchcost )+ P(UM ∨UR)× R(UM – Research Cost )
¿ 0.27 × 95000+0.73(−65000)=−21800
P 9=Research Cost =−5000
P 8=P(UM∨FR)× R(UM – Research Cost )+ P(FM ∨FR)× R(FM – ResearchCost )
¿ 0.22(−65000)+0.78(95000)=59800
P 7=Maximum(P 10∧P 11)=−5000
P 6=Maximum(P 9∧P 8)=59800
P 5=0
P 4=P(FM )× R( FM )+P (UM )× R (UM )
¿ 0.5 ×100000+0.5 ×(−60000)=20000
P 3=P(FR)× P 6+ P(UR )× P 7
¿ 0.45(59800)+0.55(−5000)=24160
P 2=Maximum( P 4∧P 5)=20000
P 1 – As P 3 branch for Go for research EMV is greater than P 2 branch for no research.
Jerry should go for Research.