**Arif Ahmed highlights on a concept that refines an investment’s return by measuring how much risk is involved in producing the yield…**

DO WE consider two climbers on top of Mount Everest equally competent when one has done that without oxygen cylinder?

Naturally not – the one without any oxygen support is considered to be a courageous climber provided he makes it to the top. Similarly we do not consider a developing economy and a developed economy with identical growth rate of Gross Domestic Product (GDP) as equally competent.

This is only fair as the economy which is fraught with economic problems needs a greater effort to achieve a rate of growth identical with a developed economy.

**Oblivious of risk**

I have often wondered that how come we drop our fine sense of evaluating the background while comparing financial performance measures of two corporate. We tend to consider them equal, if the financial measures are similar, irrespective of the different obstacles they might have faced. We seem to be totally oblivious of the risk issues that are hidden behind the performance measures.

It will not be fair to blame the finance professionals for the indiscretion as the faculty of accounting and finance still walks parallel with the faculty of risk management with occasional points of convergence driven by requirement of statutory of regulatory norms like IFRS 7.

Is convergence of this two faculties difficult or would it involve a major change over in the way they function?

The answer, fortunately, is in the negative.

The way current risk management faculty is dominated by mathematical models that apprehension of finance professionals to sue them is only expected. The reason perhaps lies in the genesis of the faculty of risk management which moved along the need to analyse economic uncertainties rather than corporate uncertainties. Thus the tools that were developed drew heavily from the subject of economics and statistics while finance remained honest to its requirement of reporting the past.

**Interest of stakeholders**

The expansion of corporate world promoted on one hand by greater global opportunity of growth and restricted on the other hand by ever increasing need to protect the interest of the stakeholders, resulted into a complex operational process involving the act of balancing between growth and stability.

The accounting and finance function became responsible not only for reporting the achievement but also to indicate whether the past is an accurate description of future. This boils down to analysis of uncertainties that can impede the path of maintaining or even improving the corporate performance. It also requires evaluation of the reward that a stakeholder would look to accept those uncertainties.

The complex world of risk management has finally sneaked into the world finance and accounting. Undeniably in the corporate world the finance industry were the pioneers of embracing the risk management techniques though more out of regulatory compulsion that as a matter of better housekeeping.

Be that as it may, this lead to development and design of various tools and techniques without which presently the financial industry cannot conceive of operating. It must also be noted that use of most of these techniques are restricted within the decision making process and does not influence the way finance and accounting function reports the performances.

However it is about time that we take notice of this weakness of the current reporting content and structure before another financial debacle prompted by lack of predictive quality of the accounting figures forces the regulators to bring in tough norms. Let us take a few strides into this interesting world where finance and risk management converges and allow me to assure you that it is a non-intimidating world though I cannot promise if you will remain the same person at the end of the walk.

**Claim of liability holders**

Let us commence our journey by asking why at all we are taking this walk.

All businesses face uncertainties of various kinds and we can classify them in two types – those which erode the value of an asset (or increases the value of a liability) and those which prevents improving upon or maintaining the current level of performance.

We can name these capital risk and performance risk respectively. Capital risk essentially signifies the risk of an organisation going insolvent as a result of their asset value declining or liability value increasing. This will happen as soon as the losses are greater than the capital base and the deficit will have to be met from the claim of other liability holders.

Performance risk will focus on whether the entity is likely to maintain the current level of performance, if not improve upon the same.

Let us give an example of one of the most common tools used in corporate finance – breakeven point analysis.

Conceptually this is the quantity required to be sold or the sales revenue required to be achieved to cover all costs. In other words the sales required to arrive at ‘no profit – no loss’ scenario.

The computation process, as we all know is pretty straight forward – divide the fixed cost by difference of unit sales price and unit variable cost – that is, contribution, and we get the break even quantity. This multiplied by the unit sales price gives us the break even sales volume. An extremely handy tool and I doubt whether there are any finance professionals who has never used this tool.

**The breakeven analysis**

I am also sure that there are many finance professionals who after computing the breakeven point wondered whether the volume is achievable. This is where the risk adjusted performance measure comes into play. It is quite simple to extend the breakeven analysis to find out the probability of achieving the breakeven volume.

Let me reassure that you will not need an expert knowledge of statistics to compute this. Let me give you an example.

Consider the following data for a new product – selling price $10, variable cost/unit $6, and fixed cost/year $2,000,000. The breakeven point is the point at which total cost equals total revenue, and can be computed as Total fixed costs / (Unit Price – Unit Variable cost). Thus the breakeven point in this case is 500,000 units.

Now we bring in the risk factors – say the expected average sale is 600,000 and it can be stated that there is 67% probability that the expected sale will remain within a range of 300,000 to 900,000 units. Rest is simple – from this data we can arrive at the standard deviation – which will be 309,278 units. Now we have enough data to assess the probability of achieving the breakeven volume, which is computed to be 62.6%.

**Monte Carlo simulation**

If you are interested in the computational process please read the computation annexure at the end of the article, otherwise do not bother as the entire iteration can be integrated with your financial information systems. We can similarly find out the probability of the profit being at least 400,000 and others. The probability of achieving breakeven point will allow the finance professional understand the risks associated with this projection.

One of the most common questions that I get after citing this example is how to assess the average value of sales if we do not have enough historical data. Well even if we have limited data we can use them and generate a large number of representative data through Monte Carlo simulation.

Before you start accusing me of being more complex, let me assure you that you can even do it in a spreadsheet like Excel.

Let me now extend this framework to pricing of a product.

Consider that there are two projects each reaching breakeven point at 15000 units. The only difference is that in case of one project the probability of achieving the same is 67% and in case of the other it is 53%. If we have to choose between one of them surely we will select the one with greater probability. If we can go ahead with both like in cases of two product lines, we should examine the possibility of charging higher price for the product line that is riskier. This will reduce the breakeven point which will improve its probability of achievement.

That is the point – in addition to having a project selection a benchmark of breakeven point as a percentage of capacity, we can also specify a minimum probability of achieving the breakeven point as another project hurdle rate.

**The economic capital**

The concept for pricing for risk will lead us to the need to define the economic capital requirement for each project. Economic capital may be loosely defined as the capital requirement adjusted for the risk of the project. This economic capital will include the fund requirement for investment plus a safety margin for probable losses.

Once we arrive at the economic capital requirement of a project, pricing for risk becomes rather easy to implement. All we need to do is to include an expected rate of return on the economic capital. This assumes further importance with introduction of IFRS 13 where the fair valuation of assets and liabilities will have direct impact on the equity base of a corporate.

There are various risk factors that would have an impact on balance sheet of a corporate. Most common are credit risk, liquidity risk, operational risk, and market risk though country risk, settlement risk, reputation risk, residual risk, and others often play a critical role. It is important for a corporate to assess potential adverse impact of these risk factors on equity base and ensure adequacy of capital to face these risks as well as to price the products and services to support the capital base.

Till such time we recognise the risk profile we may actually be paying out dividend from the minimum level of capital we need to maintain. I presume that all of you will agree that this is like drinking from a bottle without reading that the label that says ‘poison.’ It will have an adverse impact, sooner than later.

**Computational Annexure**

Broadly three standard deviations on both side of the mean cover the entire probability distribution. The range of 300,000 and 900,000 is two standard deviations on either side of the mean covering 67% of the probability distribution. Thus the area to the left of 900,000 represents 5/6th of the total area or 0.8333.

In the standard normal distribution table, the value z for which P (Z z) = 0.8333 is about 0.97. Thus the Z score, using the unknown standard deviation, of 900,000 units is 0.97.

Z= (900000-600000)/SD = 0.97

Solving for the same we arrive at the standard deviation (SD) at 309278. The Z score of the breakeven point of 500,000 is -0.323. The probability of breaking even, if Q is the sales volume, is P (Q > 500,000) = P (Q > -0.323) = P (Q 0.323) = 0.626

All these can be computed using a standard spreadsheet like Excel.

**Arif Ahmed** is professor and director with South Asian Management Technologies Foundation which is a NASBA accredited CPE sponsor. He hosts training sessions and provide strategic consulting in his areas of expertise. You can check www.south-asian.org to join his workshops on various topics including on the instant subject. Check the “anytime classroom” section of the website for a quiz on this article. You can contact him at a_ahmed@vsnl.com.