By Issa Bass
 

Because a Six Sigma project would be useless or even detrimental if it does not positively impact the bottom line of a business, it is necessary for a Six Sigma Black Belt to be able to accurately measure the financial results of her projects. For that reason, any Six Sigma practitioner should have a certain level of understanding of financial analysis.

The purpose of this article is to briefly introduce some basic financial metrics that a Black Belt should be acquainted with to properly execute her project.

Break-Even Analysis

In microeconomic theory, the cost of production of goods and services is generally subdivided into two sub-costs, the fixed cost and the variable cost. While the variable cost is proportional to the quantity of the output, the fixed cost would be incurred regardless on whether production is made . In other words, even if the business does not produce anything, it will be liable for the fixed costs.

The fixed cost in general would be the cost of the buildings, the machines, the electricity and so on, while the variable cost would be composed of the labor cost and the cost of the raw materials.

A Break-Even happens when the total revenue obtained from the sales of the goods or services equals the total cost of production.

TR = TC

With TC = F + VN

And TR = PN

 Where N is the quantity of output sold at P, F is the fixed costs, V is the variable cost per unit, P is the price of N and TR is the total revenue

So

F + VN = PN

Therefore

N = F/(P – V)

 For profit to be made, the revenue must be greater than the total cost, therefore N must be greater than the ratio of F/(P - V).

The following graph summarizes the discussion on Break even Analysis.

An increase in the fixed cost relative to the Total cost is risky because a small downward shift in sales will result in a fall in profits.

Let us now consider the following example. The financial statement bellow summarizes a computer repair company's accounting for the past quarter.

The purpose of conducting a Break Even analysis is to generate actionable data, i.e. data that can be used to improve management. In the previous example, if the fixed costs cannot be altered, the actions that might be envisaged should affect the parts and /or the labor. Labor cost can be cut through productivity improvement or overtime reduction. One metric our computer repair company might consider would be the "cost per unit repaired" since in this case it is what determines the profit level.

Interest Rate Evaluation

The interest paid on borrowed money can be defined as nothing but the price of acquiring money. A higher interest rate translates  into “more expensive money”. 

Even if the financial capital needed to fulfill some investment is available, it is sometimes more profitable to involve lenders in financial decisions. The analysis of the interest rate is complex because it involves not only the evaluation of the time necessary to repay the loans and the annuities but also the opportunity costs determination, that is, should the company use available funds for a given project or should it borrow the money and use the funds for other purposes?

The decision rules generally depend on the Interest Rates, the Annuities, the Present and Future Values of the money and the Frequent Compounding.

The interest rates are nothing but the cost of borrowing, if it is high, borrowing becomes less attractive and the opposite occurs when it is low.

Present and Future Values – A mathematical formulation

To better understand the rationale behind the evaluation of the annuities and the interest paid on loans, it is necessary to have a certain level of familiarity with Algebra.

For those who do not know their algebra, the formula obtained from the strenuous algebraic manipulations are plug-and- play and MS Excel offers an easy way out.                                 

Let's first define some of the terms that will be used

P = the principal. It is the sum of money available for use. It may have been borrowed.
i = the interest rate. It is a percentage of the principal paid usually per annum
n = number of periods payments are made
F = future value of the present principal
A = annuity. The amount of money paid per period

If i  is the interest rate, P  the principal and F  the future value, we can determine the value of next year.

If after a year, no money is paid,  becomes the principal for the next year therefore becomes:

 If no payment is made for n periods, then

Example

What is the Future value of $15,000.00 in 5 years if the interest rate is 5%?

Answer:

Using Excel, click here

We have four variables in the equation  which are F, P, i and n. If we know the values of any three variables, we can, with a few algebraic manipulations determine the fourth one.

 If n is unknown, it can be obtained using the following formula

If P is unknown, the following formula can be used

If i is unknown, it can be found using

About the author
Issa Bass is the managing editor of SixSigmaFirst. He can be reached at issa@sixsigmafirst.com

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