Analytical Techniques For Financial And Business Decisions

Decision Analysis

Question 1: Decision analysis

1. So as to evaluate individual’s risk preference and their sense to the value of money, utility is used as the standard measure. This attitude towards risk is possible to be categorised numerically by assigning the value 0 for the worst-case scenario and 1 for the best-case scenario. The utility of an individual will therefore fall between 0 and 1 depending in the risk preference nature.

A utility function has three basic features, one, the function differs between individuals. Each person has a different value of money and risk nature hence the variation. Second the utility of a person is not constant, rather it changes with time. The third feature is that the utility function depends on a person’s magnitude of money (Grechuk & Zabarankin, 2016).

A utility can either be measured using the certainty equivalent method or the lottery equivalent technique.

A standard gamble is a technique applied in quantifying personal preferences in situations of uncertainty. The outcomes are noted as the values of utility to be applied when conducting clinical analysis and evaluating health programs.

By applying the normative expected utility arguments, standard gamble method is regarded as a golden technique for quantifying utility. The main difference between this style and other elicitation methods is that it incorporates risks.

Under the standard gamble the respondent is required to compare between the certainty of being in a health state to be valued over the remaining life expectancy with a gamble that gives a chance to live an optimal life though with a risk of immediate death. The technique applies a style where the respondent is asked to state the probability of the gamble that will make him/her indifferent to the choice between the two scenarios

1.  
2. The table below will summarise the alternatives and states of nature

The payoff table

Possible strategies	Market conditions
Good	Fair	Bad
Share market	$ 1400	$ 800	0
Government bond	$ 900	$ 900	$ 900

1. An optimistic; This decision maker selects the maximum value among the maximums under each alternative. Hence, he/she will assume that the market will be good attracting 14% return.

The optimal choice will be to invest in the share market.

1. A pessimist selects the maximum value among the minimums under each alternative. He/she will assume that the worst state of nature will occur. The optimal alternative under this case is therefore to invest in the government bonds. which will yield a profit of $ 900.
2. Under the regret criterion we choose the option with the minimum of all the maximum regrets. So first we compute the regret table as shown

The regret table

Actions	Market condition	Max
Good	Fair	Bad
share market	$ 0	$ 100	$ 900	$ 900
government bond	$ 500	$ 0	$ 0	$ 500

The optimum choice will be to invest in the government bonds

1. Expected monetary value (EMV)

The payoff table

Actions	Market condition	EMV
Good	Fair	Bad
Invest in share market	$ 1400	$ 800	0	$ 880
Invest in a government bond	$ 900	$ 900	$ 900	$ 900
Probability	0.4	0.4	0.2

The method selects the option with the highest EMV. In our case this is purchase of government bond.

1. EVPI (Expected Value of Perfect Information)

We use the payoff table given below.

Actions	Market conditions	EMV
Good	Fair	Bad
Invest in share market	$ 1400	$ 800	0	$ 880
Invest in a government bond	$ 900	$ 900	$ 900	$ 900
Prob	0.4	0.4	0.2

EVPI is the optimum amount the decision maker is willing to spend on additional information needed to make optimum choice.

These yields

Question 2: Value of information

1. The table below summarises the possible proceeds from the electric razor

Options	Market situation	EMV
Favourable	Unfavourable
electric razor	$100,000	-$ 60,000	$ 20,000
Status quo	0	0	0
Probability	0.5	0.5

By applying the EMV (expected monetary value criteria, its recommended that Jerry should proceed and produce the electric razor (Klebanov, Rachev, & Fabozzi, 2009). Out of the two available causes of action, undertaking the production will yield a higher expected profit of $ 20,000 which is a better value which he will expect should he abandon the investment opportunity.

1. Generation of the posterior probabilities

The table below gives a summary of the calculations

		Market conditions	Prior probability	Conditional probability	Joint probability	Posterior probability
Right	Favourable	0.5	0.7	0.35	0.47
Unfavourable	0.5	0.8	0.4	0.53
	P(positive)			0.75
Wrong	Favourable	0.5	0.3	0.15	0.6
Unfavourable	0.5	0.2	0.1	0.4
	P(negative)			0.25

1. From the tabular illustrations given above the posterior probability of a favourable market condition given that the firm has given an incorrect information is 0.6
2. The expected profit attained by consulting the friend is obtained from the calculations of the value of perfect information Expected gain of engaging the friend

This is given by

 charges $ 5000 for the information while the EVPI is $ 30000, its economical for Jerry to go ahead and consult the friend.

Question 3: Monte Carlo Simulation

1. The results

1. The model

1. The monthly profit for Tully Tyres will have a projected mean of $ 4223.21over the next 12 months period.

Report to the Manager of Tully Tyres

Tully Tyres

6547/22364 New Line st

New South Wales 7459434

Australia

17^th September 2018

Stephen Bush

Manager Tully Tyres

6547/22364 New Line st

New South Wales 7459434

Australia

REF: Analysis of Profit sensitivity

Dear Mr Bush,

As a response to your request for the analysis of the profit sensitivity to changes in profit margin and the selling price, the report gives an analysis regarding the same.

Should the selling price go up to between $ 200 and $ 220 with no alterations on the sales quantity there will be a positive impact experienced by the net profit earned.

The changes in the two mentioned variables will increase the expected net profit to $ 6358 from the current predicted value of $ 4223. It is therefore recommended that the firm goes ahead to implement the suggested changes.

Despite the predicted positive income generation, the implementation of the suggestions should be done cautiously as an increased selling price may lead to unfavourable sales volume in the long term.

Sincerely,

Sam Smith

Management Accountant

Question 4: Regression Analysis

1. Compute overhead cost per machine hours

	OH Cost	MH
Highest	80000	2400
lowest	33000	1800
Slope	78.33333

From the slope, we obtain that the overhead cost is $ 78.33 for each machine hour

In a month where 3000 machine hours are consumed, the estimated overhead cost will be

1. Regressing overhead cost against machine hours

First let y represent the overhead cost,  represent batches.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.1042363
R Square	0.0108652
Adjusted R Square	-0.112777
Standard Error	15447.614
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	20969866	20969866	0.087877	0.774444
Residual	8	1.91E+09	2.39E+08
Total	9	1.93E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	59198.785	21473.78	2.756793	0.024797	9680.152	108717.4	9680.152	108717.4
MH	-2.304381	7.773522	-0.29644	0.774444	-20.2302	15.62139	-20.2302	15.62139

From the regression output the cost equation will be

The value of r is given as 0.1042 indicating that there is a weak positive correlation between the overhead cost and the machine hours. From the R square of 0.0108, it can be deduced that only 1% of the changes in the overhead cost are explained by the changes in machine hours.

Regressing overhead cost against Batches

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9117666
R Square	0.8313184
Adjusted R Square	0.8102332
Standard Error	6379.2197
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.6E+09	1.6E+09	39.42662	0.000238
Residual	8	3.26E+08	40694444
Total	9	1.93E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6555.5556	7666.868	0.85505	0.417394	-11124.3	24235.38	-11124.3	24235.38
Batches	234.5679	37.35716	6.279062	0.000238	148.4221	320.7137	148.4221	320.7137

The cost equation is given by

The value of r is obtained as 0.9118, hence we can conclude that there is a strong positive correlation between the overhead cost incurred and the number of batches. Using the R square value of 0.8313, it can be concluded that up to 83% of the changes in the variable cost are explained by the changes in the number of batches.

Regression OH cost against MH and Batches

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9127334
R Square	0.8330823
Adjusted R Square	0.7853915
Standard Error	6783.9217
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1.61E+09	8.04E+08	17.46842	0.0019
Residual	7	3.22E+08	46021593
Total	9	1.93E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9205.6579	12704.92	0.724574	0.492215	-20836.7	39248.02	-20836.7	39248.02
MH	-0.930667	3.4218	-0.27198	0.793484	-9.02194	7.160604	-9.02194	7.160604
Batches	233.82745	39.82029	5.872068	0.000617	139.6674	327.9875	139.6674	327.9875

The equation of the cost from the regression outputs will be

From the three regression outputs the multiple regression is the favourable to analyse the case as it accounts for all the variables of concern.

1. By comparing the output of the two simple regressions the regression of overhead costs against batches indicates a strong positive relationship and thus can best be applied in the estimations of the overhead cost.
2. Using the multiple linear regression case, the equation of the cost will be given by

The overhead cost

Question 5: CVP Analysis

1. Unit contribution margin

Contribution margin is the value of the selling price minus variable costs.

For product A

Contribution margin

For product B

contribution margin

1. Product B

Fixed cost is $ 5000

Contribution margin $ 5

The breakeven point

The producer will need to manufacture 1000 units of product B in order to operate at a breakeven pint.

1. Product A

Fixed price $ 5000

Contribution margin $ 4

Breakeven

1. Manufacture of both A and B
2. Ration of

Selling price of A is 12 and selling price of b is 15

Now the overall contribution margin is

To get a profit if 3500 we need to sell

This will be distributed as follows 1500 units of A and 500 units of B

1. Tax is given by 30c per dollar

Fixed cost is 5000

Net contribution margin is 4.25

To generate a profit of $ 8400, the firm need to generate a revenue of

This will need  The units will be distributed as follows; 3000 for A and 1000 for B

References

Grechuk, B., & Zabarankin, M. (2016). Inverse portfolio problem with coherent risk measures . European Journal of Operational Research, 740-750.

Klebanov, L. B., Rachev, S. T., & Fabozzi, F. J. (2009). Non-Robust Models in Statistics. New York: Nova Scientific Publishers, Inc.