Breakeven Analysis and Profit Planning

This assignment explores breakeven analysis and profit planning for a company manufacturing two products (A and B). It involves calculating the breakeven point in units and dollars, determining the contribution margin per unit, and analyzing how production ratios affect profitability. The student is tasked with finding the number of units required to be sold for various profit targets before and after tax.

DECISION SUPPORT TOOLS
ASSIGNMENT - III
[Pick the date]
Student id

Question 1
(a)Decision under certainty refers to a situation when the concerned decision maker is in
possession of complete information about the various aspects of the decision such as the
alternative available and also the relative costs and benefits associated with each of these
alternatives. Decision making under certainty is quite easy and often based on established
conventions on how to deal with such issues (Eriksson, & Kovalainen, 2015).
On the contrary for decision under risk, some information is available about the future
outcomes but it could not be ascertained as to which outcome would be observed. This is a
more often faced decision making situation by the manager in comparison to decision under
certainty. The managers tend to work out the respective probabilities for the various outcomes
based on the available information and hence tend to map using decision tree as to what
decision would bring the largest possible profits for the company (Holsapple & &Whinston,
2013).
Decision making under complete uncertainty refers to a situation when no information si
available about the potential outcomes and hence the subjective probabilities of these cannot
be determined. These are most difficult to tackle considering the absence of information and
hence this situation usually requires creative solution from the managers which deviates from
the established techniques (Medhi, 2001).
b) 1) The optimist would choose investing in share market.
Maximum Maximum
Share Market $80,000 Best
Bonds $30,000
Real Estate $25,000
2) The pessimist would choose investing in bond market.
Minimum Maximum
Share Market -$20,000
Bonds $20,000 Best
Real Estate $15,000
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3) Based on criterion of regret investing in real estate would be chosen.
Good
Economy
Poor
Economy
Maximum Minimum
Stock Market 0 40,000 40,000
Bonds 50,000 0 50,000
Real Estate 55,000 5,000 55,000 Best
4) Expected monetary value (Stock Market) = 0.3*80000 + 0.7*(-20000) = $ 10,000
Expected monetary value (Bonds) = 0.3*30000 + 0.7*20000 = $ 23,000
Expected monetary value (Real estate) = 0.3*25000 + 0.7*15000 = $ 18,000
Hence, investment in bonds would be made.
5) We use the following formula
EVPI=∑
i=1
S
{max U ( si , a)} p(si)−E ¿ ¿ ¿U/ a*)
Hence, EVPI = 0.3*80000 + 0.7*20000 – 23000 = $ 15,000
Question 2
(a) The relevant computations are shown below.
Favourable market
(0.5 probability)
Unfavourable market
(0.5 probability)
EMV Maximum
Large Shop $80,000 -$40,000 20,000 Best
Small Shop $30,000 -$10,000 10,000
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In the given case, Jerry has two possibilities in the form of opening a large bicycle shop or to
open a small one. The respective profits from the shop under favourable and unfavourable
market conditions have been listed (Power, 2002).
EMV (Large Shop) = 80000*0.5 + (-40000)*0.5 = $ 20,000
EMV (Small Shop) = 30000*0.5 + (-10000)*0.5 = $ 10,000
Based on the above, Jerry should open a large bicycle shop.
(b) The prior probability revision is indicated below.
Good market Poor market
Favourable Study 0.8 0.4
Unfavourable study 0.2 0.6
1.0 1.0
The probability revision when a favourable study has been indicated is shown below.
Posterior Probability
State of nature
Conditional
Probability
P (Favourable
study/state of nature)
Prior
Probability
Joint
probability
P (State of
Nature/Favourable
study)
Good market 0.8 ×0.5 =0.4 0.40/0.60=0.67
Poor market 0.4 ×0.5 =0.2 0.10/0.60=0.33
Total 0.60
(0.4+0.2)
1.00
(0.67+0.33)
The probability revision when a unfavourable study has been indicated is shown below.
Posterior Probability
State of nature
Conditional
Probability
P (Unfavourable
study/state of nature)
Prior
Probability
Joint
probability
P (State of
Nature/Unfavourable
study)
Good market 0.2 ×0.5 =0.10 0.10/0.40=0.25
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Posterior Probability
State of nature
Conditional
Probability
P (Unfavourable
study/state of nature)
Prior
Probability
Joint
probability
P (State of
Nature/Unfavourable
study)
Poor market 0.6 ×0.5 =0.30 0.30/0.40=0.75
Total 0.40
(0.10+0.30)
1.00
(0.25+0.75)
c) The posterior probability can be predicted using the following table.
Posterior Probability
State of nature
Conditional
Probability
P (Unfavourable
study/state of nature)
Prior
Probability
Joint
probability
P (State of
Nature/Unfavourable
study)
Good market 0.2 ×0.5 =0.1 0.1/0.40=0.25
Based on the above, the desired posterior probability is 0.25.
d) The following table would reflect on the utility of the market researcher.
Case 1: Assuming the study is favourable
Good market Poor market Conditional Expected utility Maximum
Large Shop $80,000 -$40,000 $40,400
($80,000×0.67) +(-$40,000×0.33)
Best
Small Shop $30,000 -$10,000 $16,800
($30,000×0.67) +(-$10,000×0.33)
Probability 0.67 0.33
Case 2: Assuming the study is unfavourable
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Good market Poor market Conditional Expected utility Maximum
Large Shop $80,000 -$40,000 -$10,000
($80,000×0.25) +(-$40,000×0.75)
Small Shop $30,000 -$10,000 $0
($30,000×0.25) +(-$10,000×0.75)
Best
Probability 0.25 0.75
Expected utility = 40,400*0.6 + 0*0.4 = $ 24,240
EVSI (Expected Value of Sample Information) = 24,240 – 20,000 = $ 4,240
The cost of market research being done by a friend is $ 3,000
Hence, gain from market research = 4240 – 3000 = $1,240
From the above, it may be concluded that the market research provided by the friend should be
engaged because of the potential gains from the same as computed above.
Question 3
Monte Carlo Simulation
(a) The respective model to simulate the next 12 months average monthly profit for the given
year is shown below:
Normal view
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Formula view
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(b) Based on the above highlighted m Monte Carlo Simulation the value of average monthly
profit for the 12 months is $1049.21.
(c) The new model when the two parameters are changed by Tully Types are shown below:
 Average selling price increased by $20 (from $80 to $100 in place of $60 to $80)
 Profit margin would increase with a range starting from 22% to 32% in place of 20% to
30%.
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To: Manager, Tully Tyres
Date: September 19, 2017
Dear Sir
Revisions have been made in the projections based on the estimated average increase in pricing
by $ 20. In line with the assumptions provided, there is a rapid jump in both the profit margins
and also the absolute profits generated along with the average profits per month. Thus, this
seems to be a value accretive move for the shareholders of the company.
But caution needs to be observed during the implementation of the above as it could very well
adversely impact the sales volume and hence the realised profits may be significantly lower than
the above projections. Hence, it is advisable that the increased pricing should be introduced as a
pilot project and regularization of this must be carried out only when the sales level is
maintained. Based upon the reaction of customers, necessary action should be taken whether to
roll back or continue with the hiked prices.
Yours Sincerely
STUDENT NAME
Question 4
Given data set
(a) High- low method to determine the overhead costs based on the total machine hours
(MH).
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In this model, it is essential to compute the respective regression coefficients based on the
provided dataset (Mittra, 2006).
The respective equation
Here,
Per unit VC (variable cost) ¿ 48000−46000
3800−1800 =$ 1.00
FC (fixed cost) ¿ 48000− ( 3800∗1 )=$ 44,200
The regression equation based on high- low method
Total
head cost=FC+(Per unit VC∗Total machine hours )
Total
head cost=44200+(1∗Total machine hours )
Fortotal machine hours=3000 hrs
Hence,
Total
head cost=44200+ ( 1∗3000 ) =$ 47,200
(b) Regression model
 Regression analysis to represent the relation between overhead cost (Dependent variable) and
machine hours (Independent variable) is shown below:
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Regression equation
¿ head cost=59198.78−(2.30∗Machine hours)
Value of R square (R2) = 0.0109 (Significantly low)
Assuming 5% significance level, it can be said that p value for the slope coefficient machine
hours (MH) is 0.77. It is apparent that p value is higher than significance level and hence, the
slope is not statistically significant and thus, it can be assumed equal to zero. Further, from the
ANOVA table, it can be seen that the p value is also greater than significance level and hence,
the regression model is considered as not a good fit model (Hair, et. al., 2015).
 Regression analyse to represent the relation between overhead cost (Dependent variable) and
batches (Independent variable) is shown below:
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Regression equation
¿ head cost=6555.56−(234.57∗Batches)
Value of R square (R2) = 0.8313 (Significantly high)
Value of adjusted R square (R2) = 0.8102 (Significantly high)
Assuming 5% significance level, it can be said that p value for the slope coefficient batches is 0.
It is apparent that p value is lower than significance level and hence, the slope is statistically
significant and thus, it cannot assume to be equal to zero. Further, from the ANOVA table, it can
be seen that the p value is also lower than significance level and hence, the regression model is
considered good fit model (Halhn & Doganaksoy, 2011).
 Regression analyse to represents the relation between overhead cost (Dependent variable)
and batches and machine hours (Independent variable) is shown below:
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Regression equation
¿−head cost=9205.66−( 0.93∗Machine hours )+(233.83∗Batches)
Value of R square (R2) = 0.8331 (Significantly high)
Value of adjusted R square (R2) = 0.7854 (high)
Assuming 5% significance level, it can be said that p value for the slope coefficient machine
hours (MH) is 0.79. It is apparent that p value is higher than significance level and hence, the
slope is not statistically significant and thus, it can assume to be equal to zero. Also, it can be
said that p value for the slope coefficient batches is 0. It is apparent that p value is lower than
significance level and hence, the slope is statistically significant and thus, it cannot be assumed
to be equal to zero. From the ANOVA table, it can be seen that the p value is also lower than
significance level and hence, the regression model is considered as good fit model (Taylor &
Cihon, 2004).
(c) After considering all the above highlighted regression models, it can be concluded that
best suitable model is model 2 where, only batches has been considered as independent
variable. It is evident from the regression model, that the independent variable machine
hours is not statistically significant for the computation of total overhead cost. Further,
the value of adjusted R square is maximum for the regression model 2 which has batches
as the independent variable. However, the value of R square is maximum for the
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regression model 3 which has both batches and machine hours as the independent
variable. The final conclusion can be made after comparing the adjusted R square values
that regression model 2 would be adopted for the estimation of total over- head cost.
(Lind, Marchal & Wathen, 2012).
(d) The best regression model is shown below:
¿ head cost=6555.56−(234.57∗Batches)
Number of batches = 150
Hence,
¿ head cost=6555.56−(234.57∗Batches)
¿ head cost=6555.56−(234.57∗150)
¿ head cost=$ 41,740.74
Question 5
CVP Analysis
Given data set
Product A B Total
Sales price per unit $10 $20
Variable cost per unit $5 $12
Total fixed costs $4,000
(a) Unit contribution margin for the products is computed below:
Unit contribution margin for A = $10-$5 = $5
Unit contribution margin for B = $20-$12 = $8
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(b) Number of units of product B at breakeven point is shown below:
Breakeven point= Total FC
Unit contribution margin for B
¿ 4000
8 =500 units
(c) Number of units of product A at breakeven point is shown below:
Breakeven point= Total FC
Unit contribution margin for A
¿ 4000
5 =800 units
Breakeven sales volume for the months (in dollars) = 800*10 = $ 8,000
(d) Manufacturers have decided to produce product A and product B with a ratio to 2 of A to
1 of B.
(i) Number of units of each the product that needs to be sold to earn profit of $5,000 before
tax for the respective production month
Avg. contribution margin ¿ {( 2
3 )∗5 }+ {( 1
3 )∗8 }=$ 6
Desire profit of the company (profit before tax) = $5,000
Target sales volume= (Profit before tax+ FC)
Avg . contribution margin
¿ (5000+ 4000)
6 =1500 units
Units of product A required ¿( 1500)∗( 2
3 ) =1000 units
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Units of product B required ¿ ( 1500 )∗( 1
3 )=500 units
(ii) Desire profit of the company (post tax profit) = $21,000
Assume that pre-tax profit = $X
Hence,
x (1−30 % ) =21000
x=$ 30,000
Monthly profit (before tax) =$30,000
Target sales volume= (Profit before tax+ FC)
Avg . contribution margin
¿ 30000+4000
6 =5667 units
Units of product A required ¿(5667)∗( 2
3 )=3778 units
Units of product B required ¿ ( 5667 )∗( 1
3 )=1889 units
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Reference
Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research (3rd ed.).
London: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of
business research methods (2nd ed.). New York: Routledge.
Halhn, J. G. & Doganaksoy, N. (2011) The Role of Statistics in Business and Industry (7th ed.).
London: London: John Wiley.
Holsapple, C. & Whinston, B.A. (2013) Decision Support Systems: Theory and Application (6th
ed.). Sydney: Springer Science & Business Media.
Lind, A.D., Marchal, G.W. & Wathen, A.S. (2012). Statistical Techniques in Business and
Economics (15th ed.). New York : McGraw-Hill/Irwin.
Medhi, J. (2001). Statistical Methods: An Introductory Text (4th ed.). Sydney: New Age
International.
Mittra, S.S. (2006) Decision support System: Tools and techniques (5th ed.). London: John
Wiley.
Power, J.D. (2002) Decision Support Systems: Concepts and Resources for Managers (3rd ed.).
Sydney: Greenwood Publishing Group.
Taylor, K. J. & Cihon, C. (2004). Statistical Techniques for Data Analysis (2nd ed.). Melbourne:
CRC Press.
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