6课外补充Critical Sales.docx

1、6课外补充Critical SalesCritical Point of Sales and Probability of Distress: A Comprehensive Financial Risk Indicator Joseph M. ChengAssociate ProfessorSchool of BusinessIthaca CollegeIthaca, N.Y., 14850Email: ChengIthaca.edu(607) 274-3067 Critical Point of Sales: A Comprehensive Financial Risk Indicator

2、AbstractThis paper illustrates the drawbacks of conventional debt ratios and proposes the use of an alternative financial ratio for measuring bankruptcy risk: Critical Point of Sales, which measures the minimum sales a borrower must have in order to generate sufficient amount of cash flow to meet it

3、s interest obligations. In percentage terms, it means the percentage drop in revenue a borrower can withstand before being unable to meet its debt obligation. The ratio essentially combines all the financial and operating leverage ratios into one which lends itself to be more readily understood by s

4、tudents. This ratio is more user-friendly and is shown to provide a more comprehensive and meaningful picture on the degree of financial risk of firms than conventional debt ratios. This newly introduced concept has been taught with great success in finance classes and drawn much student interest.In

5、troduction Even the best finance students learning about financial statement analysis (and perhaps also some financial analysts) often misuse the financial leverage or debt ratios in assessing the degree of financial risk of firms. The conventional debts ratios lend themselves to be easily misinterp

6、reted because the focus of individual debt ratios on financial risk is narrow and there is no systematic procedure for interpreting all ratios simultaneously. This paper demonstrates how the times interest earned ratio, for example, can be misused, and sets forth an easy-to-understand financial indi

7、cator which provides a direct, intuitive, and comprehensive means of assessing default risk. The times interest earned ratio, which is operating income before interest and taxes divided by interest expense, is a debt coverage ratio commonly used by financial analysts. It is intended to be used as a

8、measure for the ability of firms in paying interest with its earning. A firm with higher times interest earned ratio is generally regarded as having lower bankruptcy risk than a firm with lower times interest earned ratio; however, this is an inferential trap into which many students and financial a

9、nalysts fall. The drawback of this ratio as a financial risk indicator is demonstrated in the following illustration. Consider two firms of equal size, Firm A and Firm B. Let us assume that the variable operating cost of A and B are 80% of revenue and 10% of revenue, respectively; and that the fixed

10、 operating cost of A and B are $40,000 and $530,000, respectively. If the revenues for both firms are $700,000, then their operating costs, the sum of variable and fixed costs, are calculated as follows:(1) operating cost (A) = .8 x $700,000 + $40,000 = $600,000(2) operating cost (B) = .1 x $700,000

11、 + $530,000 = $600,000Given that the interest expenses for Firm A and Firm B are $50,000 and $25,000, respectively, the partial current income statements for Firms A and B are presented in Table 1. Table 1. Current Income Statements Firm A Firm BRevenue $700,000 $700,000 Operating cost $600,000 $600

12、,000 _ _Operating income $100,000 $100,000Interest $50,000 $25,00 _ _Earnings before taxes $50,000 $75,000 The times interest earned ratio are:(3) Times Interest Earned (A) = $100,000/$50,000 = 2(4) Times Interest Earned (B) = $100,000/$25,000 = 4 According to the above results, Firm A has a lower t

13、imes interest earned ratio and thus is generally regarded as being more highly leveraged with debt than Firm B. A student or an unsophisticated financial analyst is often led into thinking that Firm A has higher default risk by virtue of a lower times interest earned ratio. However, such common infe

14、rence may be flawed, especially in the case where Firm A utilizes less fixed operating costs than Firm B. Suppose that revenues of both firms decline to $500,000, one might expect that A would be more likely to have problem meeting its interest payment than B. To analyze this proposition, let us exa

15、mine their relative abilities to meet interest obligations if revenues for both firms decline from $700,000 to $500,000. Based on the operating cost formulae (1) and (2), the operating cost for Firm A and Firm B are $440,000 and $580,000, respectively, at revenue level of $500,000.Table 2$500,000 Re

16、venue Scenario（行动的）方案; 剧情概要; 分镜头剧本; Firm A Firm BRevenue $500,000 $500,000Operating Cost $440,000 $580,000 _ _ Operating Income(Loss) $60,000 ($80,000)Interest Expense $50,000 $25,000 _ _Earnings Before Taxes $10,000 ($105,000)Note in Table 2 that Firm A still has sufficient operating income to cove

17、r its $50,000 interest expense whereas Firm B might have to default, although the latter originally has a higher times interest earned ratio. The reason for this paradox is that debt ratios do not reflect the degree of operating leverage (the extent to which fixed operating cost is utilized), which

18、measures the sensitivity of operating income to changes in revenue and is a key factor in determining default risk. This means that a firm with more favorable debt ratios might actually have greater default risk due to its high operating leverage, as is in the case of Firm B. In light of this drawba

19、ck in using such ratios, an alternative indicator which incorporates both financial and operating leverages to yield a more comprehensive measure of default risk would be desirable. To this end, a financial indicator called Critical Point of Sales (CPS) is devised, which represents the percentage de

20、cline in revenue that would reduce cash flows from operation to an amount just sufficient to cover interest payment. Since a firm might default on its interest obligations if its revenue in percentage terms declines by an amount greater than the CSP percentage, the probability of sales declining by

21、the CSP percentage amount is directly correlated with the probability of default. As can be seen, the appeal of the CSP lies in its simplicity of interpretation and its direct relationship to bankruptcy risk.Derivation of the CSP Formula The CSP can be derived by first solving for the critical level

22、 of revenue where cash flow from operation is just equal to interest expense (cash flows from operation can be written as revenue less variable cost and cash fixed operating costs (CFC):(5) revenue - variable operating cost - CFC = interest Variable operating cost can be rewritten as v revenue where

23、 v represents variable cost as % of revenue.(6) revenue - v revenue - CFC = interestSolving for that critical level of revenue (CR) alone, we get(7) revenue = CR = (interest + CFC) / (1-v)As stated, revenue in (7) represents the critical level of revenue (CR) where cash flows from operation equal in

24、terest expense. CSP is defined as the maximum sales drop in percentage term before reaching that critical level:(8) CSP = (current revenue - CR) / current revenue, which can be rewritten as(9) CSP = 1 - CR/current revenueSubstituting (7) into CR in (9), we get(10) CSP = 1 - (interest + CFC )/ curren

25、t revenue ( 1 - v),which represents the computation formula for CSP.Application of the CSP FormulaAssume cash fixed cost (CFC) is 75% of the total fixed operating cost for both firms. The amounts of cash fixed cost for A and B would be:(11) CFC (A) = .75 x $40,000 = $30,000(12) CFC (B) = .75 x $530,

26、000 = $397,500 Having computed CFC, we can proceed to calculate the CSPs for Firm A and Firm B by using (10):(13) CSP (A) = 1 - ($50,000+ $30,000)/$700,000(1-.8) = 43%(14) CSP (B) = 1 - ($25,000+$397,500)/$700,000(1-.1) = 33% Based on the above calculations, revenue would have to decline by 43% befo

27、re Firm A encounters cash flow problem in meeting its interest obligation, while Firm B would reach this critical threshold if its sales decline by only 33%. Thus, if both firms have similar revenue variability, then the CSP suggests that Firm B has greater default risk, which is consistent with the

28、 analysis in Table 2. However, the false signal generated by the times interest earned ratio may lead unsophisticated financial statement users into making an erroneous assessment of the relative default risk of the firms. The other conventional debt ratios are plagued with the same shortcomings sin

29、ce none of them takes into consideration the degree of operating leverage. The key advantages of the CSP over conventional debt ratios are that operating leverage is accounted for and that the risk is expressed in terms of the primary source of uncertainty- revenue. Because of its simplicity in comp

30、utation and interpretation, and its direct link to default risk, CSP should become an essential financial indicator among the set of debt ratios currently being used for financial statement analysis, in academia as well as in the real world.Probability of DistressAssume that sales next year has the

31、same distribution (mean and standard deviation) as the past. The probability that sales drop below the level of critical sales would be the probability of distress.Apply this theory to an actual firm with just one class of bond with known coupon interest for simplicity purpose. Use ValueLine for sal

32、es standard deviation., which should use the standard deviation of sales/asset instead of sales to adjust inflationary trend.ReferencesBrigham, Eugene F., Fundamentals of Financial Management (Dryden, 1995).Chambers, Donald R., and Nelson, J. Lacey., Modern Corporate Finance (Addison-Wesley, 1999)Collins, Robert A., An Empirical Comparison of Bankruptcy Prediction Models, Financial Management, Summer 1980, pp.52-57.Fras