# Corporate Finance

<<< Previous ADVANCE EVALUATION METHODS: Sensitivity analysis, Profitability analysis, Break even accounting, Break even - economic Next >>>

Corporate Finance ­FIN 622
VU
Lesson 12
The following topics will be discussed in this lecture.
Sensitivity analysis
Profitability analysis
Break even accounting
Break even - economic
SENSITIVITY ANALYSIS:
Sensitivity analysis is the study of how the variation in the output of a model (numerical or otherwise) can
be apportioned, qualitatively or quantitatively, to different sources of variation.
A mathematical model is defined by a series of equations, input factors, parameters, and variables aimed to
characterize the process being investigated. Input is subject to many sources of uncertainty including errors
of measurement, absence of information and poor or partial understanding of the driving forces and
mechanisms.
This imposes a limit on our confidence in the response or output of the model. Further, models may have
to cope with the natural intrinsic variability of the system, such as the occurrence of stochastic events. Good
modeling practice requires that the modeler provides an evaluation of the confidence in the model, possibly
assessing the uncertainties associated with the modeling process and with the outcome of the model itself.
Uncertainty and Sensitivity Analysis offer valid tools for characterizing the uncertainty associated with a
model.
Applications
Sensitivity Analysis can be used to determine:
1.  The model resemblance with the process under study
2.  The quality of model definition
3.  Factors that mostly contribute to the output variability
4.  The region in the space of input factors for which the model variation is maximum
5.  Optimal - or instability - regions within the space of factors for use in a subsequent calibration
study
6.  Interactions between factors
7.  Sensitivity Analysis is popular in financial applications, risk analysis, signal processing, neutrals
networks and any area where models are developed.
Methodology
There are several possible procedures to perform uncertainty (UA) and sensitivity analysis (SA). The most
common sensitivity analysis is sampling-based. A sampling-based sensitivity is one in which the model is
executed repeatedly for combinations of values sampled from the distribution (assumed known) of the
input factors. Other methods are based on the decomposition of the variance of the model output and are
model independent.
In general, UA and SA are performed jointly by executing the model repeatedly for combination of factor
values sampled with some probability distribution. The following steps can be listed:
1.
Specify the target function and select the input of interest
2.
Assign a distribution function to the selected factors
3.
Generate a matrix of inputs with that distribution(s) through an appropriate design
4.  Evaluate the model and compute the distribution of the target function
5.  Select a method for assessing the influence or relative importance of each input factor on the target
function.
PROFITABILITY ANALYSIS
Successful financial institutions today are able to effectively identify those products, customers, branches,
and other factors that impact overall profitability. But discovering what's actually profitable isn't always
straightforward. To really understand what's driving bank profitability, you need to be able to drill down
into the lowest level of detail, and analyze data with ease and precision.
Profitability is a dynamic, accountable solution for managing customer relationships and measuring
37
Corporate Finance ­FIN 622
VU
performance ­ providing a complete picture of your organization's profitability. It allows you to analyze
your business across unlimited dimensions. Beyond customer profitability, product profitability and
organizational profitability, it's sophisticated, multi-dimensional OLAP environment provides the unique
ability to calculate profitability at the account level, drill up and down through every level of the hierarchy,
and aggregate up for any reporting or analytical dimension, for improved accuracy and better decision-
making.
This flexibility allows you to analyze...
Customers who are 'at risk'
Performance of an officer that supports multiple business units
Business unit performance across a group of branches
Customer households reported in multiple market segments
Geographic views that aren't aligned with organizational units
Product success across a group of market segments
Origination trends by groups of officers, branches, or by market segment
BREAK-EVEN ACCOUNTING
This type of report is not one that is automatically generated by most accounting software, nor is it one that
is normally produced by your accountant, but it is an important analysis for you to have and understand.
For any new business, you should predict what gross sales volume level you will have to achieve before you
reach the break-even point and then, of course, build to make a profit. For early-stage businesses, you
should be able to assess your early prediction and determine how accurate they were, and monitor whether
you are actually on track to make the profits you need. Even the mature business would be wise to look at
their current break-even point and perhaps find ways to lower that benchmark to increase profits. The
recent massive layoffs at large corporations are directed at this goal, lowering the break-even point and
increasing profits.
Break-Even Is the Volume Where All Fixed Expenses Are Covered:
You will start a break-even analysis by establishing all the fixed (overhead) expenses of your business. Since
most of these are done on a monthly basis, don't forget to include the estimated monthly amount of line
items that are normally paid on a quarterly or annual basis such as payroll taxes or insurance. For example, if
your annual insurance charge is \$9,000, use 1/12 of that, or \$750 as part of your monthly budget. With the
semi variable expense (such as phone charges, travel, and marketing), use that portion that you expect to
spend each and every month.
For the purpose of a model break-even, let's assume that the fixed expenses look as follows:
\$1,500
Rent
800
Utilities
300
Insurance
150
Taxes
210
Telephone
240
Auto expense
400
Supplies
100
Sales and marketing
300
Interest
100
Miscellaneous
400
Total
\$4,500
These are the expenses that must be covered by your gross profit. Assuming that the gross profit margin is
30 percent, what volume must you have to cover this expense? The answer in this case is 15,000--30
percent of that amount is \$4,500, which is your target number.
38
Corporate Finance ­FIN 622
VU
The two critical numbers in these calculations are the total of the fixed expense and the percentage of gross
profit margin. If your fixed expense is \$10,000 and your gross profit margin is 25 percent, your break-even
volume must be \$40,000.
This Is Not a Static Number:
You may do a break-even analysis before you even begin your business and determine that your gross
margin will come in at a certain percentage and your fixed expense budget will be set at a certain level. You
will then be able to establish that your business will break even (and then go on to a profit) at a certain level
of sales volume. But your pre-start projections and your operating realities may be very different. After
three to six months in business, you should compare projections to the real-world results and reassess, if
necessary, what volume is required to reach break-even levels.
Along the way, expenses tend to creep up in both the direct and indirect categories, and you may fall below
the break-even volume because you think it is lower than it has become. Take your profit and loss statement
every six months or so and refigure your break-even target number.
Ways to Lower Break-Even:
There are three ways to lower your break-even volume, only two of them involve cost controls (which
should always be your goal on an ongoing basis).
1. Lower direct costs, which will raise the gross margin. Be more diligent about purchasing material,
controlling inventory, or increasing the productivity of your labor by more cost effective scheduling or
adding more efficient technology.
2. Exercise cost controls on your fixed expense, and lower the necessary total dollars. Be careful when
cutting expenses that you do so with an overall plan in mind. You can cut too deeply as well as too little and
cause distress among workers, or you may pull back marketing efforts at the wrong time, which will give out
the wrong signal.
3. Raise prices! Most entrepreneurs are reluctant to raise prices because they think that overall business will
fall off. More often than not that doesn't happen unless you are in a very price-sensitive market, and if you
are, you really have already become volume driven.
But if you are in the typical niche-type small business, you can raise your prices 4 to 5 percent without much
notice of your customers. The effect is startling. For example, the first model we looked at was the
following:
Volume
\$15,000
direct cost
10,500
70%
gross profit
4,500
Raising the prices 5 percent would result in this change:
Volume
\$15,750
direct cost
10,500
67%
gross profit
5,250
You will have increased your margin by 3 percent, so you can lower the total volume you will require to
break even.
The Goal Is Profit:
You are in business to make a profit not just break even, but by knowing where that number is, you can
accomplish a good bit:
·  You can allocate the sales and marketing effort to get you to the point you need to be.
·  Most companies have slow months, so if you project volume below break-even, you can watch
expenses to minimize losses. A few really bad months can wipe out a good bit of previous profit.
·  Knowing the elements of break-even allows you to manage the costs to maximize the bottom line.
Once you have gotten this far in the knowledge of the elements of your business, you are well on your way
to success.
39
Corporate Finance ­FIN 622
VU
The breakeven point in economics is the point at which cost or expenses and income are equal - there is
no net loss or gain, one has "broken even".
The point at which a firm or other economic entity breaks even is equal to its fixed costs divided by its
contribution to profit per unit of output, which can be shown by the following formula:
The break even point is also the point on a chat indicating the time when something has broken even, and is
a general term for not having gained or lost something in a process.
The Contribution per Unit can be worked out using
Contribution = Price per Unit - Variable Costs per Unit
The break even point for a product is the point where total revenue received equals total costs associated
with the sale of the product (TR=TC). A break even point is typically calculated in order for businesses to
determine if it would be profitable to sell a proposed product, as opposed to attempting to modify an
existing product instead so it can be made lucrative. Break-Even Analysis can also be used to analyze the
potential profitability of an expenditure in a sales-based business.
In unit sales
If the product can be sold in a larger quantity than occurs at the break even point, then the firm will make a
profit; below this point, a loss. Break-even quantity is calculated by:
Total fixed costs / (price - average variable costs)
(Explanation - in the denominator, "price minus average variable cost" is the variable profit per unit, or
contribution margin of each unit that is sold.)
Firms may still decide not to sell low-profit products, for example those not fitting well into their sales mix.
Firms may also sell products that lose money - as a loss leader, to offer a complete line of products, etc. But
if a product does not break even, or a potential product looks like it clearly will not sell better than the break
even point, then the firm will not sell, or will stop selling, that product.
An example:
Assume we are selling a product for \$2 each.
Assume that the variable cost associated with producing and selling the product is 60 cents.
Assume that the fixed cost related to the product (the basic costs that are incurred in operating
the business even if no product is produced) is \$1000.
In this example, the firm would have to sell (1000/ (2 - 0.6) = 714) 714 units to break even.
In price changes
By inserting different prices into the formula, you will obtain a number of break even points, one for each
possible price charged. If the firm to change the selling price for its product, from \$2 to \$2.30, in the
example above, then it would have to sell only (1000/(2.3 - 0.6))= 589 units to break even, rather than 714.
40
Corporate Finance ­FIN 622
VU
To make the results clearer, they can be graphed. To do this, you draw the total cost curve (TC in the
diagram) which shows the total cost associated with each possible level of output, the fixed cost curve (FC)
which shows the costs that do not vary with output level, and finally the various total revenue lines (R1, R2,
and R3) which show the total amount of revenue received at each output level, given the price you will be
charging.
The break even points (A,B,C) are the points of intersection between the total cost curve (TC) and a total
revenue curve (R1, R2, or R3). The break even quantity at each selling price can be read off the horizontal,
axis and the break even price at each selling price can be read off the vertical axis. The total cost, total
revenue, and fixed cost curves can each be constructed with simple formula. For example, the total revenue
curve is simply the product of selling price times quantity for each output quantity. The data used in these
formulas come either from accounting records or from various estimation techniques such as regression
analysis.
In potential expenditures Break-Even Analysis can be used in the evaluation of the cost-effectiveness of a
new expenditure for a sales-revenue based business. Here, the cost can be evaluated in terms of revenues
needed to break even on the investment, or more specifically, to determine how much of an increase in
sales revenues would be necessary to break even.
An illustrative example of this is a retail lumberyard who is considering the purchase of a delivery truck. The
goal is to evaluate how large an increase in sales revenue is necessary to break even on the investment in a
delivery truck. For this example, the company's front-door margin (that is, sales revenue minus the cost of
goods sold and costs of doing business) is 5%, and the cost of the desired delivery truck is \$50,000. To
calculate the break-even level of expenditure, the following formula can be used:
Expenditure (\$) = (Front-door margin %) X (Revenue Increase needed to break even)
To break even using the above example, \$50,000 must equal 5% of the sales INCREASE ("SI") in order to
break even. The variable which must be isolated is the Sales Increase.
\$50,000 = 5% of SI
\$50,000 = .05 * SI
\$50,000/.05 = SI
\$1,000,000 = SI
Sales increase of \$1,000,000 is needed to break even on the investment on the delivery truck. The business
must then decide how it can use the delivery truck to help increase sales by \$1,000,000; if it can, then they
will break even, and if it can not, then it would be an ill-advised investment. If sales revenues pass the
break-even point, 5% of further increase would be bottom line profit.
Of course, in most cases, such an investment will not be paid out in lump sum or in one year, so
appropriate adjustments can be made for the payments, and the scenario can be focused on a monthly basis
during repayment, or can be extended out through and beyond the repayment period to evaluate a longer
term return. Also such calculations can be used with smaller-scale and shorter-term scenarios (such as a
temporary employee or a new computer) or on a much larger scale such as a new construction or
acquisition.
41
Corporate Finance ­FIN 622
VU
It is notable that, since most businesses have among their goals to be profitable, desired profits should be
added as a cost of doing business.
Limitations
·
This is only a supply side (i.e.: costs only) analysis.
·
It tells you nothing about what sales are actually likely to be for the product at these various prices.
·
It assumes that fixed costs (FC) are constant
·
It assumes average variable costs are constant per unit of output, at least in the range of sales (both
prices and likely quantities) of interest.
ECONOMIC BEAK-EVEN
The problem associated with accounting break even is that accounting earnings are calculated after the
deduction of all costs except the opportunity cost of the capital that is invested in the project.
Accounting for the cost of capital is simple, at least in principle, when working out income or profit, we
should also deduct the opportunity cost of capital employed just as we deduct all other costs. Income that is
worked out, as this (after deducting cost of capital) is known as economic profit or economic value added
(EVA). A project that has a positive EVA adds to firm value; one with a negative EVA reduces firm value.
42