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ESTIMATING RISK IN CREDIT CONDITION ANALYSIS: LATIN HYPERCUBE

SIMULATION

Pablo Rogers, Universidade Federal de Uberlndia msc_pablo@yahoo.com.br Krem C. S. Ribeiro, Universidade Federal de Uberlndia kribeiro@ufu.br

Almir Ferreira de Sousa, Universidade de So Paulo abrolhos@usp.br

Abstract That work has for objective to present a methodology that incorporates the analysis multi-periods in the changes of the credit conditions and that it considers the risk of the estimates in those changes. That last aspect will be gotten by the inclusion of the simulation process by Latin Hypercubes, it will allow to esteem the risk of the change in the credit conditions to produce value for companies. To conclude that the probability analysis as presented supplies useful information to the managers, when incorporating the value of the money in the time and to esteem the risk in credit conditions.

Key-Words: Credit Conditions, Latin Hipercube, Monte Carlo Simulation.

1. Introduction The word credit, conceptually speaking, refers to an individual or companys

willingness to give, for a certain period of time, part of its assets or provide a third party with outsourced services, expecting a future payment. According to Lemes Jnior, Rigo and Cherobim (2002, p.442) it implies in proceeding with receiving the value of the credit in a future date. Due to the fact that credit concession is a delivery of capital to third parties, it demands for a large amount of cash flow so that it can be financed, because credit concession is the same as investing in a client, when the investment is associated with a product or service (ROSS, WESTERFIELD and JAFFE, 1995, p. 574).

It becomes common to analyze credit policy in three main aspects: credit conditions or sales terms, credit analysis and selection and collection and monitoring policy (ASSAF NETO, 2003; BREALEY e MYERS, 1992; BRIGHAM e HOUSTON, 1999; GITMAN, 2002 e 2004; GITMAN e MADURA, 2003; LEMES JNIOR, RIGO e CCHEROBIM, 2002; ROSS, WESTERFIELD, e JAFFE, 1995; SANVICENTE, 1997; SCHERR, 1989).

In the relation to credit conditions, or sales terms, most finance manuals, as mentioned in the previous paragraph, base decisions on the examples of analysis of one only period of time (not considering future cash flows) and do not consider the risks of estimates not being fulfilled as expected (they are based on forecasted numbers). The current paper aims to present a methodology which overcomes these limitations by incorporating to multi-period analysis the HL simulation process. With the help of the Crystal Ball 2000.5 software, the analysis developed will allow us to measure the probability of changes to credit conditions in creating value for the company: the performance measure considered in the analysis was the additional net present value (NPV) calculated with the difference between the proposed credit condition and the currently used credit conditions.

Moreover, we aim to compare, specifically, the value of the (VPL) obtained through the LH process and the one obtained through the MCS (Monte Carlo Simulation). These two simulation methods are different in theory. The general and specific objective will be

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developed in a later section. The following section will describe the main concepts in regards of credit concession decisions, as well as, the LH simulation process in comparison to the MCS. In section four well list the main conclusions attained in the present article.

2. Bibliographical Review

2.1. Credit Conditions According to Scheer (1989, p. 159-162) the main key-variables affected by credit

decisions are: sales collection, investments in stock, sales costs, discount and uncollectible dept expenses, collection costs, capital expenses, effects on revenue taxes (IR) and sales rescue and recovery. Assaf Neto e Silva (2002, p. 109) classified these key-variables in main four:

Capital investment: sales volume increase, caused by a change in the credit policy may incentive a quicker recovery of investment, increasing its liquidity and reducing the risk.

Investment in stock: the smaller the sales volume of a company, the less the need for stock inversion before demand.

Collection expenses: Includes all incremental expenses resulting from collection department, letters sent to clients with outstanding debt, administrative staffs time, legal expenses, need for more employees, etc.

Expenses with debtor uncertainty: Probability of losses as a result of total sales in installments.

Finance Manuals simplify variables, which affect credit decisions, where there are changes in the credit policy as: sales volumes, investments in receivables and expenses with debtor uncertainty. Credit conditions include the period for which the credit is granted, discount for cash purchase, and the credit tool type (ASSAF NETO, 2003; BREALEY e MYERS, 1992; BRIGHAM e HOUSTON, 1999; GITMAN, 2002 e 2004; GITMAN e MADURA, 2003; LEMES JNIOR, RIGO e CCHEROBIM, 2002; ROSS, WESTERFIELD, e JAFFE, 1995; SANVICENTE, 1997). In general, perhaps for didactic purposes, manuals analyze changes in credit conditions (especially discount and term) and its influence on sales volume investments on receivables and expenses with debtor uncertainty in one only period, as exemplified in chart 1.

As we can see in chart 1, this methodology measures the net profit considering the opportunity cost for the company in the period before changes in the credit conditions and the period of time after these changes: Changes in credit conditions are treated as any other investment decisions. However, for this decision making process the only cash flow considered relevant in measured in one period of time only. Actually, since changes in credit affect the value of receivables, we must treat these changes as investments or redeem of investments made by the company in its clients, therefore, studied with investment analysis techniques commonly accepted, specially through NPV and IRR (interest rate of return), once these express the economic reality of an investment.

Moreover, as all investment analysis processes include estimates, theres a possibility of prediction error, meaning, we must incorporate the risk in investment decisions through techniques such as: scenario analysis, sensitivity analysis, (certainty equivalents), discount rates adjusted to risk and simulation methods.

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Chart 1 Traditional Methodology for Credit Condition Decisions

Source: Rogers, Dami e Ribeiro (2004, p. 6).

Simulation methods application becomes more robust when basing investment decisions on results obtained within a confidence interval, thus allowing managers to visualize as infinity of possible scenarios.

2.2. Latin Hypercubes and the Monte Carlo Simulation In order for the simulation process to be present in the analysis, all we have to do is

verify if any variables of the problem assume the randomness condition. Specifically in the case of credit condition decisions, which can be analyzed as investments in clients cash flow, the simulation tool becomes a formal and efficient technique.

The simulation is an attempt to replicate a real system, through the construction of a mathematical model as similar to reality as possible. Opposed to the analytical deterministical methods which aim at finding great solutions for problems, simulation aims at modeling a system and observing how entry parameter variations affect its outputs variables / inputs variables. A practical visualization of the stages in the computer simulation process are described in Chart 2. With the advancements in computers the simulation process has become quite accessible for the analysis of various types of problems.

Consider that the Simulated Company is planning to introduce a 2% discount for payments to be made within 10 days after the purchase. The average collection time is thirty days, non-cash sales make up for a total of 6.000 units at a R$ 100,00 price per unit. Variable costs make up for R$ 60,00 per unit. The company estimates that by introducing the discount, sales will increase in 5%, and 50% will be of non-cash sales. We estimate that the average collection time will be reduced to fifteen days, and losses with uncollectable will decrease from 2% to 1% of sales. The return required by the company on investments with the same risk is 10%. Receivable flow

Original Plan =360

1230

= Proposeded Plan = 360 2415

=

Net Profit Increase Simplified Calculation

Increased Contribution Margin [ 300 units (100 60)] 12.000

(15.750) Increase Cost in Receivables

A) Investiment with Proposed Plan = (60 6.300)

24

B) Investiment with Original Plan = (60 6.000)

12

30.000

Cost of Increased Investiment [(B-A)0,10] 1.425 Increased Cost with debtor uncertainty C) Cost with Proposed Plan (0,016.300 100) (6.300) D) Cost with Original Plan (0,02 6.000 100) 12.000 Increased Cost with Uncollectables (C-D) 5.700 Cost of Financial Discount (0,02 0,50 100 6.300) (6.300) = Profit Variation result of the proposal 12.825

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We can highlight among many simulation methods, specifically applied to investment

analysis, the following: Latin Hypercubes and Monte Carlo Simulation. The Latin Hypercube simulation method aims at generating samples which describe, in a more accurate manner, a probability distribution. Such method consists on a complete stratification of the presented distribution, in equiprobable stracts, and also in the random selection of a value for each stract (FARIA, MELO and SALIBY, 1999. p. 4). Similar to the Monte Carlo Simulation, in the Latin Hyp