Journal of Business & Economics Research Volume 1, Number 10

Transcription

1 Annualized Invenory/Sales Journal of Business & Economics Research Volume 1, Number 1 A Macroeconomic Analysis Of Invenory/Sales Raios William M. Bassin, Shippensburg Universiy Michael T. Marsh ( mmars@ship.edu), Shippensburg Universiy Sefanie Walizer, Shippensburg Universiy Inroducion Mezler s (1941) research on he relaionship beween invenory and business cycles iniiaed serious ineres in invenory behavior and is effec on he behavior of firms. A flurry of relaed research ook place in he following wo decades. Research of he ime clearly demonsraed ha, a a macro level, he invenory behaviors are significan feaures in business cycles. One measure of invenory behavior inroduced and analyzed was he invenory-o-sales raio. We coninue o believe ha undersanding of invenory behavior a boh he macro and microeconomic levels is a prerequisie o undersanding facors ha deermine a firm s success, and ha analysis of he invenory-o-sales raio is imporan componen of invenory behavior. The U.S. Deparmen of Commerce and oher governmen and privae insiuions rack his raio and repor regularly. Financial analyss use boh a company's rend and is comparaive value wihin a secor o make invesmen decisions. The daa, sources, and explanaions can be easily found in boh hard copy and elecronic formas published by Federal Reserves Banks, U.S. Deparmen of Census, and U.S. Deparmen of Commerce. An in-deph service privae source is he Quarerly Raio Sudy provided by he Cener for Invenory Managemen. ( Early work in raio analysis by Feldsein and Auerbach (1976) posed he dilemma ha firms use long ime periods o adjus producion o variaions in sales levels even when he range of invenory levels is equivalen o only a few days of producion. Blanchard (1983) and Blinder (1981) used invenory-o-sales raios o reinforced his idea wih evidence ha producion is more variable han sales in mos indusries. Blinder and Maccini (1991) repored ha, even using he sophisicaed invenory managemen echniques developed and implemened in he 198 s, he aggregaed raio of he invenory-o-sales raio had no disinc rend for a four decade period. Since 1991, however, here has been a marked downward rend in he raio, which can be clearly seen in Figure 1. This paper examines some of he facors ha would accoun for his decline and proposes a model for invenory-o-sales raio. Figure 1: Hisorical Invenory/Sales Raio 13.5% 13.% 1.5% 1.% 11.5% 11.% 1.5% 1984:1 1988:1 199:1 1996:1 :1 Year:qr (Daa derived from he Economic and Financial Daabase a hp:// 37

2 The Theoreical Model As developed by Silver and Peerson (1985), he cycle sock invenory (CSI ) a ime for a firm using an opimal (EOQ) invenory managemen policy can be calculaed as follows: CSI n / * A / r * *exp p /8 (1) where n = he oal number of iems in a company s produc line (The same physical produc wih differen deailed characerisics such as size of package, flavoring, and he like, or in differen locaions couns as muliple iems.) A = adminisraive cos per order r = invenory carrying cos per dollar per year = mean cos of sales for he individual iems in he produc line p = he Pareo facor (For example, if p is 1.8, he op 5% of he SKU s 1 generae 9% of he cos of sales. If p is 1.64, he op 5% of he SKU s generae 95% of he cos of sales, and so on.) The cos of sales (CS ) for a company is CS = n * () I follows ha he heoreical raio of cycle sock invenory o he cos of sales ( ) can be expressed as 1/ * A / r * 1/ *exp p /8 CSI / CS (3) (The n erm drops ou, a leas emporarily.) The mean cos of sales for he individual iems in he produc line,, can be expressed as he produc of D and V, where D is he mean demand in unis for he iems in he produc line, and V is he mean uni cos for he iems in he produc line. Accordingly, can be rewrien as 1/ * A / * 1/ * 1/ r *exp p /8 (4) V and if is defined o be he value of he raio in year zero, hen 1/ * A / * 1/ * 1/ r *exp /8 v d p D (5) I follows ha he relaive value of hese wo raios can be defined by he following: (1/ )* A / V * 1/ D * 1/ r *exp( p / (1/ )* A / V * 1/ D * 1/ r *exp( p /8) /8) A / V r D exp( p / 8) * * * (6) A / V r D exp( p / 8) Insead of aemping o measure he mean demand, D, direcly, i is possible, even desirable, o measure hese values indirecly. I is inuiive ha 1 Sock keeping uni (SKU) is an idenificaion, usually alphanumeric, of a paricular produc ha allows i o be racked for invenory purposes. Typically, a SKU is esablished by he merchan and associaed wih any purchasable iem in a sore or caalog. 38

3 * n D * n CGS / IPD D CGS / IPD (7) where CGS = he cos-of-goods-sold (or sales, if cos of sales daa are no available) IPD = he implici GDP price deflaor, or anoher appropriae price index. This is because, when he D is muliplied by n, he resul is a rough index of he oal amoun of physical unis sold. The raio of hese values from one ime period o anoher is equivalen o a raio of deflaed dollar sales. Therefore, CGS / IPD CGS / IPD D * D n n (8) Subsiuing his expression ino equaion (6): A / V r CGS / IPD n exp( p / * * * * A / V r CGS / IPD n exp( p / 8) TR / 8) (9) where TR is he heoreical raio of he invenory o sales raios. An Economic Model of he Values of In consrucing a model for he values of, i is reasonable o hold consan, a leas for he ime being, hose variables whose values we canno now measure. Such variables would cerainly include he A / V raio, as he adminisraive coss of ordering, or se-ups, are nooriously difficul o measure. However, i is no unreasonable o assume ha deflaed adminisraive coss remain consan. The values of p are also unavailable a his ime. As a resul, equaion (9) reduces o r CGS / IPD n / * * TR (1) r CGS / IPD n Assume, as a firs approximaion, ha r is 15% plus he ineres rae on -bills. Then equaion (1) can hen be rewrien as (.15 b ) CGS / IPD n / * * TR (11) (.15 b ) CGS / IPD n where b is he ineres rae on reasury bills a ime. Daa are available o a leas approximae he values of he firs wo erms of his raio. Solid daa abou he raio of n / n is no available, bu he model can be examined wih differen raes of growh o see which yields he bes fi o available daa. Muliplying boh sides of equaion (11) by, yields he following: TR * (1) 39

4 Equaion (1) is he firs independen variable in an economic model ha allows a forecas of he values of he acual invenory o sales raio o be developed. The value of can be se equal o he acual raio for he firs ime period in which here are daa. Three addiional independen variables are proposed for his model. The firs relaes o he change in sales, above or below expecaions. The raionale is ha when here is such a change in he sales, invenories are run down below (or overshoo) planned levels. The second variable relaes o corporae profis. Sare (1999) finds ha, as profiabiliy grows, invenories expand ceeris paribus because he benefis of addiional safey socks are enhanced, hus adding o oal invenory levels. Recall ha equaion (1) applies only o cycle socks. Regardless, research indicaes ha businesses end o inves inernally as profis grow, wheher such invesmens are wise or no, and invenory growh is one such invesmen. This is consisen wih previous analysis by Bils and Kahn (). The hird variable is simply a ime rend. The model is herefore defined as follows: A S P, (13) where A = he acual raio of invenory o sales, = he heoreical raio of invenory o sales, from equaion (1) S = he sales change variable, P = he profiabiliy variable, = he ime rend variabl = an error erm, and he represens he parameers o be esimaed. Tesing he Model wih Macroeconomic Daa Figure shows resuls using quarerly macroeconomic daa beginning in 1Q/1984 and ending in 4Q/. (U.S. Deparmen of Commerce Seasonally Adjused Invenory o Sales Raios; U.S. Deparmen of Commerce Seasonally Adjused Toal Business Invenories; Federal Reserve Board of Governors (H.15 release) 3-Monh Treasury Consan Mauriy Rae) Business sales daa are used, as reliable cos-of-sales daa are no available. A range of growh raes in n were examined bu an assumed growh rae of zero percen gives he bes fi. Table 1 shows he regression resuls for he daa. I is noeworhy ha all variables are saisically significan, bu, as expeced, here is no inercep erm. The overall fi appears o be represenaive, wih some sysemaic under-fiing in he early 199 s and some sysemaic over-fiing immediaely hereafer. These paerns could be recession/recovery induced bu deermining he precise cause is beyond he scope of his paper. The sales change variable is calculaed as he raio of he change in sales o an eigh quarer moving average of changes. The sign of he esimaed coefficien for his variable is negaive, as migh be conjecured inuiively. Tha is, if sales are acceleraing, invenories should shrink relaive o sales. The profis variable is simply deflaed corporae profis. The sign of he esimaed coefficien is posiive, again, as migh be hypohesized. Figure 3 shows he decline in he raio, wih all oher facors bu ime adjused ou. The sysemaic paerns in he early 199 s, and immediaely hereafer again, sand ou. Oher researchers observed he same paerns of overand under-fiing and proposed reasonable raionale. King, e al. (1991) sugges he influence of moneary disurbances during ha period. Sare (1999) suggess hese variaions are a resul of JIT mehodology popular in he early 199 s. Bils and Kahn () and Ben Salem and Jacques (1996) find anomalies in he invenory/sales raio during periods of recession. Worhingon (1998) and Sare (1999) pose ineresing heories ha adopion of posiive innovaions in echnology influenced unexpeced variaions in he invenory-o-sales raio. These wo anomalies and poenial causes, while ineresing, does no affec he overall subsanial downward rend. 4

5 Invenory/Sales Raio Journal of Business & Economics Research Volume 1, Number 1 Figure : Aggregae Analysis wih Zero Annualized Growh Rae in n 13.5% 13.% 1.5% 1.% 11.5% 11.% 1.5% Acual Fied Table 1: Regression Resuls for Aggregae Analysis wih Zero Annualized Growh Rae in n Variable Coeff. Sd. Dev. Sa Theoreical Raio Sales Chg Profis.46%.73% 6.78 Time -.444%.66% Muliple R 74.9% R Square 55.18% Adj. R Square 51.5% Sandard Error.415% Observaions 68 The ime variable shows a reducion in he invenory o sales raio of more han.4% per quarer, or reducion of abou.178% per year. 41

6 Adjused Inv./GCS Raio Journal of Business & Economics Research Volume 1, Number 1 Figure 3: Aggregae Analysis (regressed on ime only) 14.% 13.5% 13.% 1.5% 1.% 11.5% 11.% 1.5% Figure 4 and associaed Table show ha wih an assumed annualized growh rae in n of 4%, he fi of he equaion, while nearly idenical o ha in Figure, is acually worse. Upon firs examinaion his does no seem reasonable, as he number of sku s has grown over he years. However, preliminary research indicaes ha companies are reducing he marginal coss of addiional produc configuraions and locaions, such ha he number of sku s gives he appearance of being consan. A he same ime he invenory o sales raio is declining wih ime over and above his effec. The regression resuls for he ime variable shows an unreasonably large reducion in he invenory o sales raio of abou.44% per year, which is significanly differen from ha when he assumed growh rae is zero. I is eviden ha he average invenory levels (developed under an economic order quaniy sraegy) are a funcion of he square rood of annual uni demand. Therefore, if uni demand doubles, average invenory does no double and, by exension, neiher do carrying coss. This is an applicaion of economies of scale. However, suppose ha demand doubles and he produc is produced in wo versions (mild and "zesy", for example), simulaneously. Then average invenory for boh versions combined will double bu no economies of scale will resul. A direc resul will be an increase in n, he number of SKU's. This may be considered as an applicaion of diseconomies of scope, i.e. produc diversiy. The high degree of firs-order correlaion among he regression residuals is evidenced by a Durbin-Wason saisic of.48. This does no indicae ha here is bias in he parameer esimaes bu raher ha he esimaes of he sandard errors of he esimaes are undersaed, resuling in oversaemen of he -saisic. However, he esimaes of sandard error can be correced by muliplying hem by As a resul, he correced sandard error As noed in Pindyck and Rubinfeld, Economeric Models & economic Forecass (1981), he value of he Durbn Wason saisic is approximaely equal o (1-r), where r is he firs order correlaion coefficien among he residuals. Seing his expression equal o.48 implies ha r is.74 resuling in a correcion facor or

7 Invenory/Sales Raio Journal of Business & Economics Research Volume 1, Number 1 for he ime coefficien esimae is.11% = *.656%. This leads o a revised saisic of -.444%/.11% = , a highly significan resul. This resuls suppors he regression resuls. Figure 4: Aggregae Analysis (4% growh rae in n) 13.5% 13.% 1.5% 1.% 11.5% 11.% 1.5% Acual Fied Table : Regression Resuls for Aggregae Analysis wih 4% Annualized Growh Rae in n Variable Coeff. Sd. Dev. Sa Theoreical Raio Sales Chg Profis.559%.81% Time -.11%.64% Muliple R 65.9% R Square 4.37% Adj. R Square 38.11% Sandard Error.47% Observaions 68 43

8 Conclusions and Exensions In his paper, we have proposed and esed a model for forecasing he invenory-o-sales raio a a macro level. The model was esed wih quarerly daa using sandard regression mehodology. These general findings emerge from he empirical work: 1. Invenory-o-sales raios are declining wih ime even afer oher deermining facors are accouned for.. I is difficul, or even impossible, o deermine wha impac he number of iems in a company s produc line has simply by observing changes in he invenory o cos-of-goods-sold raio. This knowledge, or raher lack of, may play an imporan role in he decisions influenced by analysis of he raio. 3. I is possible o obain a reasonably represenaive regression fi wih a limied number of assumpions and wihou a large hisorical daabase. The parameer values in he model presened in his paper are all saisically significan and he impac of biases appears o be fel mainly in response o macro-economic facors raher han on company s invenory conrol policies. 4. These resuls suppor research ha indicaes U.S. businesses are doing an increasingly beer job of managing invenories, and as a resul, affording economies of scope. Mos noable are he observaions ha, even hough he number of sku s is increasing, he number appears o be consan due o efficien managemen and he consisency in reducion of he invenory o sales raio, he average reducion being.178%. 5. The regressions indicae ha zero growh in sku's fis he daa bes, even hough i is well know ha he number of sku's for many producs is higher han in he pas. For example, here are eigh varieies of Triscuis oday where only one exised in 197. I is unclear, however, wheher supply chains are reaing a diverse range of produc versions or varieies as homogeneous unis hus making i difficul for consumers o be confiden ha he desired version will be available a a paricular ime. Several avenues of fuure research are suggesed by his research: 1. I would be informaive o conduc sensiiviy analysis over ineres raes, adminisraive coss, invenorying carrying coss, growh rae, and he Pareo facor o assess he impac of he assumpions on he resuls.. Try differen funcional forms of he equaions in he model as well as differen ways of measuring he sales change and profiabiliy variables. 3. Addiional analysis of he models presened here o include ess for mulicollineariy, heeroskedasiciy, and serial correlaion. 4. Survey companies o deermine changes in he values of n and p. 5. The auhors are currenly applying he model o microeconomic daa. Preliminary resuls have been obained using he invenory, cos-of-sales, and profi daa from 37 food processing companies and 19 chemical/pharmaceuical companies. References 1. Ben Salem, Melika and J-F Jacques, (1996). Abou he Sabiliy of he Invenory-Sales Raio: An empirical Sudy wih US Secoral Daa. Applied Economic Leers 3,

9 . Bils, Mark, and J.A. Kahn, (). Wha Invenory Behavior Tells Us Abou Business Cycles. American Economic Review 9 (3), Bivin, David, (1988). The Behavior of Manufacurers Invenories: , 1 (1), Blanchard, O.J., (1983). The Producion and Invenory Behavior of he American Auomobile Indusry. Journal of Poliical Economy 9, Blinder, A.S., (1981). Reail Invenory Behavior and Business Flucuaions. Brookings Papers on Economic Aciviy, Blinder, A.S. and L.T. Maccini, (1991). Taking Sock: Assessmen of Recen Research on Invenories. Journal of Economic Perspecives 5 (1), Feldsein, Marin and A. Auerbach, (1976). Invenory Behavior in Durable Goods Manufacuring: The Targe-Adjusmen Model. Brookings Papers on Economic Aciviy, Hirsch, Alber A., (1996). Has Invenory Managemen in he U.S. Become More Efficien and Flexible? A Macroeconomic Perspecive. Inernaional Journal of Producion Economics 45, Kahn, James A., (1987) Invenories and he Volailiy of Producion. American Economic Review 77 (4), Mezler, Louis A., (1941). The Naure and Sabiliy of Invenory Cycles. Review of Economic Sudies 3, Sare, Pierre-Daniel G., (1999) An Empirical Invesigaion of Flucuaions in Manufacuring Sales and Invenory wihin a Sicky-Price Framework. Federal Reserve Bank of Richmond Economic Quarerly 85 (3), Silver, E.A. and Peerson, R., (1985). Decision Sysems for Invenory Managemen and Producion Planning. John Wiley, New York. 13. Worhingon, Paula R., (1998). The Increasing Imporance of Reailers Invenories. Economic Perspecives (3), -13. Noes 45

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