WORKING CAPITAL LEVERAGE: A CONCEPTUAL CRITIQUE AND MODIFIED FORMULATION

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WORKING CAPITAL LEVERAGE: A CONCEPTUAL

CRITIQUE AND MODIFIED FORMULATION

Sandip Sinha1*

This working paper elucidates that the term ‘ working capital leverage ’ as per the traditional concept [i.e., the responsiveness of the initial value of the Return on Investment (ROI) to changes in the initial value of Current Assets (CA) ] is a misnomer because the leverage effect does not exist for an increase in the initial value of current assets. Also , the correct term for the traditional ‘working capital leverage’ should be ‘current asset elasticity of ROI’ [ or ‘(gross) working capital elasticity of ROI ’ ] . Moreover , the true connotation of the term ‘working capital leverage ’is manifested in a newly defined concept of ‘net operating working capital leverage’.

Keywords: Working Capital Leverage, Degree of Working Capital Leverage, Business Leverage, Operating Leverage, Operating Fixed Assets Leverage

*Corresponding Author: Sandip Sinha,  [email protected]

INTRODUCTION

The traditional concept of Working Capital Leverage (WCL) refers to the responsiveness of the initial value of the Return On Investment (ROI) to changes in the initial value of Current Assets (CA) [or ‘Gross Working Capital’], and the measure of such leverage is given by the Degree of Working Capital Leverage (DWCL) [the ‘elasticity coefficient’ measure of WCL] as:

CA of value initial the in change Percentage ROI of value initial the in change Percentage DWCL _...(1)

where ROI = (EBIT/TA) [ EBIT = Earnings Before Interest and Tax];

TA = Total Assets = (CA + FA)

1 _{Department of Commerce, Dwijendralal College (Affiliated to the University of Kalyani), Krishnagar, Nadia, West Bengal,}

India.

[FA = Fixed Assets].

For any change in CA, EBIT and FA are assumed to remain constant.

Hence, for a given change in the initial value of CA, the initial value of:

(a) TA varies directly; and (b) ROI varies indirectly. Now for:

(a) A finite decrease in the initial value of CA (CA_i) by CA, the finite increase in the initial value of ROI (ROI_i) is given by:

ROI = [{EBIT / (TA_i – CA ) }

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Int. J. Mgmt Res. & Bus. Strat. 2013 Sandip Sinha, 2013 [TA_i = initial value of TA ]

So from Equations (1) and (2) we get: DWCL = (ROI / ROI_i) / (CA / CA_i) , or

) i (CA/CA ) i A )]/(EBIT/T i (EBIT/TA -CA)} -i [{EBIT/(TA = DWCL or (on simplification), DWCL = [ CA_i / ( TA_i – CA ) ] ...(3) (b) A finite increase in the initial value of CA (CA_i) by CA , the finite decrease in the initial value of ROI (ROI_i) is given by:

ROI = [{EBIT / (TA_i +CA)} – (EBIT/TA_i)}] ...(4) So from Equations (1) and (4) we get : DWCL = {(ROI / ROI_i) / (CA / CA_i)} , or

) (CA/CA ) A )]/(EBIT/T (EBIT/TA -CA)} + [{EBIT/(TA = DWCL i i i i or (on simplification),

DWCL = [CA_i/ (TA_i+ CA)] ...(5) Since CA_i, TA_i, CA > 0, DWCL > 0.

The condition for the existence of WCL effect is given by: DWCL > 1 ; and we get:

(a) From Equation (2):

CA + FA ) < 0,

which is infeasible as CA > 0 and FA > 0.

So the WCL effect will :

(a) Exist when the initial value of current assets is more than the amount of fixed assets and the decrease in the initial value of current assets is more than the amount of fixed assets;

(b) Not exist for an increase in the initial value of current assets.

The traditional concept of WCL is thus misconceptualised. Let us probe further into the misconception of this concept by comparing it with the concept of ‘business leverage’ (arising from the concept of ‘physical leverage’), manifested in the traditional forms of operating leverage, financial leverage and total leverage .

manifested in the traditional forms of operating leverage, financial leverage and total leverage .

‘BUSINESS LEVERAGE’ AND

TRADITIONAL ‘WCL ’

The concept of ‘business leverage’ has been derived from the concept of physical leverage which refers to the mechanics of a lever . A lever is a simple machine that can magnify an applied effort (effort force) to overcome a resistance (load) by generating a magnified force (load force) by turning about a fixed point called the fulcrum.

The concept of ‘physical leverage’, based on Class I lever (where the fulcrum lies between the effort and the load), is illustrated in Figure 1 (Annexure).

‘Business leverage’ (based on the concept of ‘physical leverage’) may be defined as the ability of a business firm (Business lever) to magnify the effect of Business Effort (BE) [percentage change in the initial value (assumed to be not

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equal to zero) of an Independent Financial Variable (IFV)] on the Business Load (BL) [percentage change in the initial value (assumed to be not equal to zero) of a Dependent Financial Variable (DFV)], by employing Fixed Cost-Bearing Assets (FCBA) in its asset structure or/and Fixed Cost-Bearing Capital (FCBC) in its capital structure, which give rise to Fixed Cost (FC) in its cost structure, with FC acting as the Magnifying Business Fulcrum (MBF).

The concept of ‘business leverage’ is illustrated in Figure 2 (Annexure).

The cause [presence of FCBA in the asset structure or/and FCBC in the capital structure {and hence the presence of FC in the cost struc-ture}] results in the effect [magnified percentage change in the initial value of the DFV for a given percentage change in the initial value of the IFV, ceteris paribus in the functional relationship between the DFV and the IFV].

The basic features of the various types of traditional business leverages [viz., operating leverage, financial leverage and total leverage] are summarized in Table 1 (Annexure) .

The IFV and the DFV in the case of the tradi-tional concept of WCL are CA and ROI respec-tively, and the ‘business fulcrum’ represents FA the value of which remain constant in the inverse functional relationship between ROI and CA. But the ‘business fulcrum’ acts as a ‘magnifying business fulcrum’ (i.e., the leverage effect exists) only when the initial value of CA is more than the amount of FA and the decrease in the initial value

of CA is more than the amount of FA. For any increase in the initial value of CA, it fails to act as such.

Hence the traditional concept of ‘WCL’ cannot be construed to be a ‘business leverage’ at all. It may be termed as ‘current asset elasticity of ROI’ or ‘gross working capital elasticity of ROI’.

Let us now formulate the modified concept of WCL which can be construed to be a ‘business leverage’ in the truest sense.

MODIFIED CONCEPT OF ‘WCL’

The IFV and DFV in the case of traditional opera-ting leverage are Sales (quantity or revenue) and Earnings Before Interest and Tax (EBIT)1

respectively. The Net Operating Assets (NOA) structure [consisting of Operating Fixed Assets (OFA) and Net Operating Current Assets (NOCA) {or Net Operating Working Capital (NOWC)2_}]

which gives rise to the operating cost structure {consisting of Variable Operating Cost (VOC) and Fixed Operating Cost (FOC)} could be consi-dered. However , the segregation of NOA into ‘Variable Operating Cost-Bearing Net Operating Assets’ (VOCBNOA) and Fixed Operating Cost-Bearing Net Operating Assets (FOCBNOA) renders some complexity as NOCA give rise to both VOC (cash and non-cash) and FOC {in the form of Cash Fixed Operating Cost (CFOC)} whereas OFA give rise only to FOC {in the form of Non-Cash Fixed Operating Cost (NCFOC) {i.e., depreciation and amortization of OFA}. As a result, the explicit application of the NOA structure is subtly avoided from operating leverage analysis. Nevertheless, NOA may be brought into 1 _{Assuming the non-existence of non-operating (non-financing) revenues and costs, EBIT and Operating Earnings Before Tax (OEBT)}

[which should more appropriately be considered as the DFV] are equal .

2 _{NOWC refers to the net working capital acquired with investor—supplied funds and is the excess of the Operating Current Assets} (OCA) {such as cash or bank balance, account receivables, inventories, etc., required to maintain the firm’s normal operating capability} over Operating Current Liabilities (OCL) {such as account payables and accruals that arise spontaneously out of the firm’s normal business operations and bear no explicit interest charges}. It is assumed that NOWC > 0 .

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Int. J. Mgmt Res. & Bus. Strat. 2013 Sandip Sinha, 2013 the analysis by considering Net Operating Assets

Turnover Ratio (NOATR) {=(Sales revenue (S)/ Average NOA)} and Return On Net Operating Assets (RONOA) {=(EBIT/Average NOA)} [Average NOA being assumed to remain constant in both the formulae] as another pair of IFV and DFV respectively

Now, operating leverage may be sub-divided into two types of business leverages arising from the presence of:

(a) NOCA in the net operating asset structure [and hence the presence of CFOC in the operating cost structure] of a business firm; and

(b) OFA in the net operating asset structure [ and hence the presence of ‘Depreciation and amortization of OFA’ (D) in the operating cost structure] of the firm.

Let us formulate these business leverages. Assuming the existence of perfect competition in the product and input markets with ‘selling price per unit’ (s) and ‘variable operating cost per unit’ (v) being independent of ‘quantity of sales’ (q), we get the linear ‘Sales revenue’ (S), ‘Total Operating Cost’ (TOC), EBIT and RONOA func-tions for a short-run period as:

S = sq ...(6)

TOC = VOC + FOC = v q + FOC ...(7) EBIT = S – TOC = (S – VOC) – FOC = C – FOC = cq – FOC

= r S – FOC ...(8) RONOA = ( EBIT / ANOA)

= r * NOATR – ( FOC / ANOA) ...(9) where c = contribution margin per unit of sales = (s – v);

C (contribution margin) = (S – VOC) = cq; r { ( profit/volume) ratio } = {(s – v)/s } = (c/s) = {1– (v/s) };

ANOA (Average NOA)

= { ( Opening NOA + Closing NOA ) /2 } ; NOATR (Net Operating Assets Turnover Ratio) = (S/ANOA);

q > 0 ; s > 0 ; 0  v < s [ i.e., 0 < c  s, so that the question of shutting down of operations does not arise] and 0 < r < 1 .

Now , EBIT and RONOA may segregated as :

EBIT = EBDIT – D ...(10)

EBDIT = (S – VOC) – CFOC = C – CFOC = cq – CFOC

= r S – CFOC ...(11) RONOA = (EBIT/ANOA)

= {(EBDIT – D)/ANOA}, or

RONOA = (EBDIT/ANOCA) * (ANOCA/ANOA) – (D/AOFA) * (AOFA/ANOA) or, RONOA = RONOCA * (ANOCA / ANOA) – {d * (AOFA/ANOA)} ...(12) RONOCA = (EBDIT/ANOCA), or

RONOCA = r * (S/ANOA) * (ANOA/ANOCA) – (CFOC/ANOCA), or

RONOCA = [r * {1 + (AOFA/ANOCA)}] * NOATR – (CFOC/ANOCA) ...(13) where EBDIT = Earnings Before Depreciation, Interest and Tax;

D (Depreciation and amortization of operating fixed assets) = d * AOFA;

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RONOCA (Return on Net Operating Current Assets) = (EBDIT/ANOCA);

ANOCA (Average NOCA)

= {(Opening NOCA + Closing NOCA) / 2 }; d = weighted average rate of depreciation and amortization of OFA ;

AOFA (Average OFA)

= { ( Opening OFA + Closing OFA ) / 2 }; ANOA = ANOCA + AOFA.

The presence of NOCA in the net operating asset structure of a business firm [and hence the presence of CFOC in the firm’s operating cost structure] may be said to give rise to a type of ‘business leverage’ which will enable the firm to magnify the effect of NOCA based Business Effort (NOCABE) [percentage change in the initial value (assumed to be not equal to zero) of Sales (quantity or revenue) {or ‘Net Operating Assets Turnover Ratio’ (NOATR)} [Independent Financial Variable (IFV)]] on ‘NOCA based Business Load’ (NOCABL) [percentage change in the initial value (assumed to be not equal to zero) of ‘Earnings Before Depreciation, Interest and Tax’ (EBDIT) {or ‘Return on Net Operating Current Assets’ (RONOCA)} [Dependent Financial Variable (DFV)]], ceteris paribus in the functional relationship between the DFV and the IFV, and which may be termed as ‘Net Operating Current Asset Leverage’ (NOCAL) or ‘Net Operating Working Capital Leverage’ (NOWCL), with CFOC acting as the Magnifying Business Fulcrum (MBF). The presence of OFA in the net operating asset structure of a business firm [and hence the presence of ‘Non-Cash Fixed Operating Cost’ (NCFOC) in the form of ‘Depreciation and amortization of OFA’ (D) in the firm’s operating cost structure] may be said to give rise to a type

of ‘ business leverage’ which will enable the firm to magnify the effect of ‘OFA based Business Effort’ (OFABE) [percentage change in the initial value (assumed to be not equal to zero) of ‘Earnings Before Depreciation, Interest and Tax’ (EBDIT) {or ‘Return on Net Operating Current Assets’ (RONOCA)} [Independent Financial Variable (IFV)}]] on ‘OFA based Business Load’ (OFABL) [percentage change in the initial value (assumed to be not equal to zero) of ‘Earnings Before Interest and Tax’ (EBIT) {or ‘Return on Net Operating Assets’ (RONOA) [Dependent Financial Variable (DFV)}]], ceteris paribus in the functional relationship between the DFV and the IFV, and which may be termed as ‘Operating Fixed Asset Leverage’ (OFAL), with NCFOC (or D) acting as the ‘Magnifying Business Fulcrum’ (MBF).

Even though there is an apparent likelihood to construe NOCAL and OFAL as ‘Cash Operating Leverage’ (COL) and ‘Non-Cash Operating Leverage’ (NCOL) respectively, such a view is not logically tenable as ‘variable operating cost’ (arising from NOCA) can also be segregated into cash and non-cash components .

The basic feature of the components of operating leverage are summarized in Table 2 (Annexure).

CONCLUSION

The term ‘WCL’ [as per the traditional concept] has thus been proved to be a misnomer, the correct term for which should be ‘current asset elasticity of ROI’ [or ‘gross working capital elasticity of ROI’]. However, the importance of the traditional concept of ‘WCL’ in the context of working capital management cannot be undermined. Never-theless, the true connotation of the term ‘WCL’ as manifested in the newly

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Int. J. Mgmt Res. & Bus. Strat. 2013 Sandip Sinha, 2013

ANNEXURE

Figure 1: Physical Leverage

Figure 2: Business Leverage defined concept of ‘net operating WCL’ must be

emphasized in business finance literature.

REFERENCES

1. Banerjee B (1995), Financial Policy and

Management Accounting, The World Press

Private Ltd.

2. Gitman L J (2006), Principles of Managerial

Finance, Pearson Education Inc.

3. Chandra P (2001), Financial Management:

Theory and Practice, Tata McGraw-Hill

Publishing Company Ltd .

4. Ram Tripathi et al. (1986), Concise Physics – ICSE, Selina Publishers.

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Table 1: Traditional Business Leverages

Business Leverage Operating Leverage Financial Leverage Total Leverage

Independent Financial Variable (IFV)

Sales [quantity or revenue] Earnings Before Interest and Tax (EBIT)

Sales [quantity or revenue]

Dependent Financial Variable (DFV)

Earnings Before Interest and Tax (EBIT)

Earnings Per Share (EPS ) Earnings Per Share (EPS )

Magnifying Business Fulcrum (MBF)

Fixed Operating Cost (FOC) Fixed Financing Cost (FFC) Total Fixed Cost (TFC) [ = (FOC + FFC)]

Table 2: Components of Operating Leverage

Business Leverage

Net Operating Current Asset Leverage (NOCAL)

or

Net Operating Working Capital Leverage

(NOWCL) Operating Fixed Asset

Leverage (OFAL)

Operating Leverage

Independent Financial Variable (IFV)

(a) Sales [quantity or revenue] (b) NOATR

(a) EBDIT (b) RONOCA

(a) Sales [quantity or revenue] (b) NOATR

Dependent Financial Variable (DFV) (a) EBDIT (b) RONOCA (a) EBIT (b) RONOA (a) EBIT (b) RONOA

Magnifying Business Fulcrum (MBF)

Cash Fixed Operating Cost ( CFOC )

Non-Cash Fixed Operating Cost (NCFOC)

[Depreciation and amortization of OFA] Fixed Operating Cost (FOC)

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