Decision Support Tools for Investment, Production and Cost Analysis

This article covers various decision support tools such as utility function, decision matrix, EMV, Monte Carlo simulation, regression analysis and break-even analysis. It includes solved examples on investment, production and cost analysis. The article is relevant for students studying business, finance, economics or related courses in any college or university. Get expert guidance on Desklib.

DECISION SUPPORT TOOLS
Student Name
[Pick the date]

Question 1
a) Utility function tends to highlight the viewpoint of an individual investor towards value of
money and risk. The utility function is dynamic and tends to change with time. Also, it differs
from individual to individual. Besides, the magnitude of money also impacts the utility function.
Standard gamble is used often in the healthcare industry for assessment of utility values related
to a particular disease and death. With regards to gambling, considering the uncertain outcome,
hence it would be required for gamblers that atleast certainty equivalent should be ensured which
is the minimum risk free returns. Based on this, the utility values are computed (Flick, 2015).
b) 1) It is apparent that decision needs to be taken with regards to investment in share or bond
considering three states of nature i.e. good, fair and bad. The stock returns would change
according to the state while the bonds return would remain constant.
Returns in stock market in good state = 14% *10000 = $ 1,400
Returns in stock market in fair state = 8% *10000 = $ 800
Returns in stock market in poor state = 0% *10000 = $ 0
Returns for bonds in each of the three states = 9% of 10000 = $ 900
Hence, the relevant decision matrix is shown below.
2) An optimist would choose the investment which would provide maximum payoff
(MAXIMAX strategy) which is stocks considering the possibility of earning $ 1,400 as the
payoff or returns.
3) Minimum payoff for stocks = $ 0
Minimum payoff for bonds = $ 900
Hence, a pessimist as per MAXIMIN strategy would choose to invest in bonds.
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4) The regret matrix is shown below.
Maximum is in case of stocks and hence investment in stock would be recommended.
5) EMV (Stocks) = 0.4*1400 + 0.4*800 +0.2*0 = $ 880
EMV (bonds) = $900
Hence, as per the EMV criterion, bonds would be preferred.
6) The following formula may be used.
EVPI= ∑
i=1
S
{max U ( si , a)} p(si)−E ¿ ¿ ¿U/ a*)
EVPI = (0.4*1400 + 0.4*900 + 0.2*900) – 900 = $ 200
Question 2
a) The EMV or Expected Monetary Value of producing a new electric razor is highlighted
below.
EMV (Electric Razor) = 100000*0.5 + (-60000)*0.5 = $ 20,000
Since, EMV is positive, hence Jerry should produce the new type of electric razor.
b) The revision in the prior probability is shown below.
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Favourable study related probability revision is shown below.
Unfavourable study related probability revision is shown below.
c) The estimation of posterior probability is shown below.
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d) The utility of the researcher may be indicated using the following computations.
From the above computations, it is apparent the estimated value of perfect information would
exceed $ 5,000 and hence information from the friend must be taken.
Question 3
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Monte Carlo Simulation
(a) Simulation model to simulate the next 12 months average monthly profit for the year is
highlighted below.
Normal view
Formula view
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(b) Monthly average monthly profit for 12 months = $3778.68
(c) Tully Types has changed two main factors which are highlighted below.
 Average selling price by $40 ($160 will be $200 and $180 will be $220)
 Profit margin has increased from 22% to 32% in place of 20% to 30%
Normal view
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Formula view
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To: Manager, Tully Tyres
Date: September 19, 2018
Dear Sir
The projections have been prepared based on the changes made in the price. It is apparent that
the profit margins and also the profits of the operations have jumped in a significant manner. As
a result, this measure is a suitable one for the company’s shareholders. However, it is essential
that adequate precaution needs to be undertaken with regards to implementation so as to not
cause any adverse impact on sales volume which can potentially drive profit lower. Therefore,
before full scale price increase, it makes sense that higher pricing should be attempted only on a
pilot basis to see the results especially with regards to the impact on the sales volume.
Yours Sincerely
STUDENT NAME
Question 4
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Deborah collected data shown below.
(a) High- low method
Variable cost per unit = 48000−46000
3800−1800 =$ 1.00
¿ cost=48000− (3800∗1 )=$ 44,200
Total machine hours=3000 hrs
Total
head cost=FC +(Variable cost per unit∗Total machine hours )
Total
head cost=44200+ ( 1∗3000 ) =$ 47,200
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(b) Regression model (Overhead cost and machine hours)
Regression equation
¿ head cost=59198.78−(2.30 × Machine hours )
R2=0.0109( Low)
Let the significance level = 5%
The p value for slope coefficient (MH) comes out to be 0.77 which is higher than the level of
significance. Hence, it can be said that slope is not significant. Also, the conclusion can be drawn
based on the ANOVA table that significance F is also higher than level of significance and thus,
the regression model is not good fit (Hair et. al., 2015).
Regression model (Overhead cost and batches)
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Regression equation
¿ head cost=6555.56−(234.57∗Batches)
R2=0.8313( High)
Adjusted R2=0.8102( High)
Let the significance level = 5%
The value for slope coefficient (batches) comes out to be 0.00 which is lower than the level of
significance. Hence, it can be said that slope is significant. Also, the conclusion can be drawn
based on the ANOVA table that significance F is also lower than level of significance and thus,
the regression model is good fit (Hillier, 2016).
Regression model (Overhead cost and batches, machine hours)
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¿−head cost=9205.66−( 0.93∗Machine hours )+(233.83∗Batches)
R2 = 0.8331 (high)
adjusted ( R2)=0.7854(high)
Let the significance level = 5%
The value for slope coefficient (batches) comes out to be 0.00 which is lower than the level of
significance. Hence, it can be said that slope coefficient for batches is significant. However, the
value for slope coefficient (MH) comes out to be 0.79 which is higher than the level of
significance. Hence, it can be said that slope coefficient for machine house is insignificant Also,
the conclusion can be drawn based on the ANOVA table that significance F is also lower than
level of significance and thus, the regression model is good fit (Eriksson & Kovalainen, 2015).
(c) The best model from the above choices is model 2 where the independent variable is
batches. This is because this model provides the highest value of R2 amongst the given
models. Also, machine hours is not a significant variable and hence must not be taken in
consideration as it lowers the predictive power (Hillier, 2016).
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(d) Based regression model equation
¿ head cost=6555.56−(234.57∗Batches)
Batches = 150
¿ head cost=6555.56−(234.57∗150)=$ 41,740.74
Question 5
(a) Per unit contribution margin
For A = $12-$8 =$4
For B = $15 -10$ =$5
(b) Number of units of break-even for product B
Number of units of break−even for product B=5000
5 =1000 units
(c) Number of units of break-even for product B
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Number of units of break−even for product B=5000
4 =1250 units
Breakeven sale volume = 1250*$10 = $12,500
(d) Manufacturing A and B with a ratio of 3:1
(i) Number of unit to get $3,500 before tax profit
Average contribution margin = (3/4)* 4 + (1/4)*5 = $4.25
Sale volume = (3500+5000)/4.25 = 2000 units
Number of A required = 2000 *(3/4) = 1500 units
Number of B required = 2000* (1/4) = 500 units
(ii) Number of unit to get $8,400 after tax profit
Assume, the monthly pre-tax profit is $x
x (1−0.30 )=8400
x=$ 12000
Sale volume = (12000+5000)/4.25 = 4000 units
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Number of A required = 4000 *(3/4) = 3000 units
Number of B required = 4000* (1/4) = 1000 units
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References
Eriksson, P. & Kovalainen, A. (2015) Quantitative methods in business research 3rd ed. London:
Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: 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.
Hillier, F. (2016) Introduction to Operations Research 6th ed. New York: McGraw Hill
Publications.
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