Business Maths and Statistics Report: Scenario Analysis and Findings

This report analyzes three business scenarios, focusing on profit maximization, break-even analysis, and depreciation methods. The first section determines the optimal scenario based on net profit, emphasizing the importance of shareholder wealth maximization and the impact of profit margins. The second section explores the variances between the scenarios, highlighting the roles of cost of goods sold, markups, and unit contribution margins. The report then contrasts diminishing and straight-line depreciation methods and their tax implications. A break-even analysis is conducted, including graphical illustrations and discussions on its utility in determining minimum sales targets and assessing investment feasibility. Finally, an operating expense breakdown, visualized through a pie chart, reveals the distribution of costs within the most profitable scenario, highlighting the largest operating expense (wages), rent, depreciation, and other operating costs. References to relevant finance literature support the analysis.

BUSINESS MATHS AND STATISTICS
PART B - REPORT
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PART B
1) The key objective is to indicate the best scenario amongst the scenarios provided from the
perspective of client. For doing so, the net profit realised in each of the scenarios would be
the key selection criterion. It is imperative to focus on net profit as the investment in fixed
assets along with the loan amount assumed does not differ across the three scenarios that
have been presented. The profit margins realised in the three scenarios are different owing
to difference in market conditions.
Taking the projected income statement for the three scenarios into consideration, it
becomes evident that the maximum profits are earned by the company under Scenario 3.
With regards to Scenario 1, it is apparent that the business would realise a loss. However,
in Scenario 2, the business would realise profit but the amount realised is much lower than
in Scenario 3. The higher net profit is a suitable criterion as these would result in increased
internal accruals on the balance sheet. Further, higher amount of profits would also allow
for enhanced earnings per share which would lead to higher valuation for the underlying
business (Damodaran, 2015).
Considering that the real owners of the business are the shareholders, hence decision making
should be driven by maximisation of their wealth. Under scenario 3, the business would
create highest amount of wealth for the shareholders. This is because under this scenario, the
valuation of the business would be maximised which imply increased wealth from
shareholders’ perspective (Petty et. al., 2016). Therefore, driven by the interest of the
shareholders of the business, it makes sense that the Scenario 3 should be selected over the
other two scenarios that have been offered.
2) From the part A projections, it is evident that the variance witnessed with regards to the
three scenarios is not the result of amount of debt assumed and the fixed assets investment
as these parameters do not vary across the different scenarios. A key element which
accounts for the variance is the cost associated with the product which is not the same
across the three scenarios. Also, the mark-up given on these products tends to differ which
leads to significant difference in the sale price per unit. The effect of cost and mark up
differences is represented in the unit contribution margin which is the highest in case of
Scenario 3 (Parrino and Kidwell, 2014). The key contributor to the superior contribution
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margins of scenario 3 is the highest mark up which is available for products under this
scenario which is far greater than the other two scenarios.
Yet another contributing factor to variance in results is the units sold. Typically higher profits
would be expected under the scenario where unit sales are higher. However, this is not the
case here owing to difference in unit contribution margins. Even though the unit sales are the
highest in scenario 1 but it leads to losses primarily because the unit contribution margin is
the lowest on account of lowest mark up. On the contrary, the unit sales are the lowest in
scenario 3, but it leads to highest profits primarily because the unit contribution margin is the
highest on account of highest mark up (Brealey, Myers and Allen, 2014).
3) The primary difference between diminishing depreciation and straight line depreciation is
the varying assumption about pattern of asset usage. The diminishing depreciation
assumes that a greater usage of effect along with wear and tear would be incurred at the
beginning of the useful life. As a result, the maximum amount of depreciation is charged
in the first year and the depreciation expense charged tends to get lower with every
passing year (Damodaran, 2015). This is unlike the case with straight line depreciation
where it is assumed that there would be uniform usage of the underlying asset and hence
the corresponding wear and tear would be uniform. As a result, the total depreciable value
is evenly spread across the useful life of the asset. It is noteworthy that there are tax
implications attached with the method of depreciation chosen. The diminishing
depreciation method would tend to lower the profits at the beginning while provide a boost
in the later years (Petty et. al., 2016)
4) a) The computations related to breakeven analysis are summarised below.
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b) The above break-even can be graphically illustrated in the following manner.
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The break even is reflected by the intersection of the sales and cost graph. It is evident that
break even is achieved at higher unit sales for Scenario 1 and achieved at the lowest unit sales
level for Scenario 3.
c) Break even analysts tends to highlight the minimum unit and dollar sales that is required in
order for the business to break even. To break even would imply that the company is not
making any profits but is able to cover all the costs (i.e. fixed and variable). This is a very
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useful tool as it allows the company to understand a minimum sales target which it got to
achieve so that there are no losses. Higher sales than the break even sales would imply that
profits are made by the business (Damodaran, 2015).
d) A useful tool for determining the feasibility of new investments is break even analysis.
The crucial role played by this analysis is because it helps in highlighting the extent of
margin of safety that is available. For the proposed investment, there would be expected sales
which can be compared with the breakeven sales level to determine so as to determine the
extent of fall in sales that the company can bear without ending in losses. An investment or
project having a high margin of safety would be preferred considering that making a loss in
this case would be quite difficult. Additionally, an estimate is provided to the business in the
context of minimum sale target that it has to achieve for ensuring that no loss of money is
there on the operating level (Brealey,Myers and Allen,2014).
5) The operating expense breakup has been expressed considering Scenario 3.
The above pie chart clearly highlights that the most sizable operating expense in case of
the business is wages. Sales staff and other staff wages along with commissions constitute
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about 60% of the operating expenses as seen in Scenario 3. After wages, the next most
sizable expense would be rent expenses which accounts for 19% of the business operating
expenses. Besides, 11% of the operating expenses are related to the fixed assets
depreciation and finally 9% of operating expenses constitute other operating costs.
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References
Brealey, R. A., Myers, S. C. and Allen, F. (2014) Principles of corporate finance, 6thed. New
York: McGraw-Hill Publications , pp. 110-112
Damodaran, A. (2015), Applied corporate finance: A user’s manual, 3rd ed., New York:
Wiley, John & Sons, pp. 143-144
Parrino, R. and Kidwell, D. (2014) ,Fundamentals of Corporate Finance,4th ed., London:
Wiley Publications, pp. 98-100
Petty, JW, Titman, S, Keown, A, Martin, JD, Martin, P, Burrow, M. and Nguyen, H (2016),
Financial Management, Principles and Applications, 3rd ed., Sydney: Pearson Education &
French Forest Australia, pp. 123-125
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