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Cash management: An inventory control limit approach
Journal
of Financial
Economics
3 (1976) 299-300.
Q North-Holland
Publishing
Company
BOOK REVIEW
Richard Homonoff and David Wiley Mullins, Jr.. Cash Management: Limit Approach (DC. Heath, Lexington, 1975) pp. xv+ 104.
An Inventory
Control
This book addresses the problem of corporate cash management. The authors develop and test a series of increasingly more sophisticated models of cash management under uncertainty and analyze the cost implications of their models through simulations performed on data collected from an actual firin. The underlying theory is the Miller-Orr model of cash management and its extensions. The tirst two chapters are introductory. Chapter three describes the statistical data, cost structure and cash management policies pertinent to the actual firm under consideration. These data are analyzed in chapter four to test the normality, stability, independence and seasonality of cash tlows of the firm. The statistical analysis is lucid but, since it relates to the cash Rows of one firm only, it should be properly considered as a prototype for testing the validity of MillerOrr’s assumption as applied to a specifi: firm rather than empirical evidence on the validity of these assumptions in gcncral. The following two chapters contain the theoretical substance of the book. Chapter five critically discusses the Miller-Orr‘and Wcitzman models and rccognires the need for refinement of the basic model. By analogy of the extension of the two-asset model to the three-asset model the authors formulate and solve a four- and five-asset model. The authors present an original variation of the basic model, the ‘matched loading’ model, which allows the firm to isxuc shortterm debt on days when the cash balance drops below the minimum cash balance constraint, rather than prematurely sell earning assets. thus avoiding the high transaction cost of selling earning assets before maturity. Furthermore the model divides time into fixed planning horizons, each of fixed duration. All assets and debt obligations mature on the last day of the planning horizon. The firm minimizes the total cost of each planning horizon separately. Although the optimal solution of this model can be obtained only numerically, the model is a constructive step towards the choice of maturation dates on debt instruments to reduce the level of transaction costs. In the remainder of this chapter the authors analyze simulation results which present the optimal policies and costs of the different models under various assumption on the level of fixed transaction costs. Chapter six discusses an interesting approach to the minimum overage cash balance constraint, which is a variation to Miller-Orr’s minimum ubsolure cash balance constraint. The ‘relaxed minimum average cash balance model with penalties’ is formulated, solved numerically and compared to the previous models. Chapter seven studies the effect of the length to maturity of short-term investment assets on the total cost of the cash management system. Simulations run over several of the models _.._.__ _I_.__.__.. :_1:__._ .L_. .L_ ___C._LII!... _‘-_ ___L _________. r(;rr..,r~., :.. ~18s .L- p~sr~vos ___.. C,...” cl~dpbcrs UIDLUJJGU 118 ~uu~cil~c tniit ,115 promaoli~ry 01 a casn management system increases with the purchase of longer-term assets in spite of the resulting inflexibility of the cash management policy. A very brief chapter eight discusses forecasting techniques in cash management and chapter nine concludes the topic. Some puzzling omissions are noted in the discussion of cash management models. First, proportional transaction costs are omitted from the discussion. The authors argue that the primary source of proportional transaction costs is the spread between the selling and buying
300
Book Review
price of certificates of deposit, and that these costs are never incurred if the firm holds the certificates of deposit to maturity. But as recognized elsewhere by Daelenbach (JFQA. September, 1974) there is normally an opportunity cost on funds tied up in transactions equal to at least one-day forgone interest. If the annual interest rate is 8 percent this gives rise to a proportional transaction cost k = 0.08,‘365 > O.CGO2. Using the data of HomonotT-hlullin~ table S-2. for a symmetric fixed transaction cost b = 510 per transaction. the average daily fixed transaction cost is $3.7 per day. The average number of transactions per day was 3Yil0J. The size of a transaction was S?SS.OOO for an increase in the cash balance and S615.OOU for a decrease. Even if all transactions w’ere of the smaller size of S.258.000, that would result in an averaee dailv nrnnortional trmf~ction rnct fwual tn 10 OOfl?~PW Iwx)~~W/loJ~ ., w Wl __L___L____.. _II. __- ner r_. day -.-o----, r--r-.-.-.----I--.- ._.____,~___,___,.__/__ which is an order of magnitude higher than the fixed transaction cost! The authors devote only a half-page discussion on proportional transaction costs fp. 44) to describe an algorithm which adjusts for proportional trans. ction costs. However. the authors do not seem to realize that proportional costs will change not only the parameters of the cash policy but also itsform. The incorporation of proportional transaction costs appears to be at least as important as many of the models discussed by the authors. The second omission refers to negative cash balances. Whereas many papers on cash management allow for negative cash balances, and whereas Homonoff-Mullins are bothered by the rigid minimum cash balance constraint and consider modifications of this constrant, nowhere in the book is there any mention of negative cash balances. Overall Homonoffand Mullins have written a clear and intcrcsting introduction to problems of cash management under uncertainty and many specialized students or practitioners of cash management will benefit from its study. For the general student of finance the hook is narrow in scope. for at the general level the topic of cash management should be studied within the more general framework of working capital management. Gcorgc M. Constnntinides Carnegie-Mellon University
of Financial
Economics
3 (1976) 299-300.
Q North-Holland
Publishing
Company
BOOK REVIEW
Richard Homonoff and David Wiley Mullins, Jr.. Cash Management: Limit Approach (DC. Heath, Lexington, 1975) pp. xv+ 104.
An Inventory
Control
This book addresses the problem of corporate cash management. The authors develop and test a series of increasingly more sophisticated models of cash management under uncertainty and analyze the cost implications of their models through simulations performed on data collected from an actual firin. The underlying theory is the Miller-Orr model of cash management and its extensions. The tirst two chapters are introductory. Chapter three describes the statistical data, cost structure and cash management policies pertinent to the actual firm under consideration. These data are analyzed in chapter four to test the normality, stability, independence and seasonality of cash tlows of the firm. The statistical analysis is lucid but, since it relates to the cash Rows of one firm only, it should be properly considered as a prototype for testing the validity of MillerOrr’s assumption as applied to a specifi: firm rather than empirical evidence on the validity of these assumptions in gcncral. The following two chapters contain the theoretical substance of the book. Chapter five critically discusses the Miller-Orr‘and Wcitzman models and rccognires the need for refinement of the basic model. By analogy of the extension of the two-asset model to the three-asset model the authors formulate and solve a four- and five-asset model. The authors present an original variation of the basic model, the ‘matched loading’ model, which allows the firm to isxuc shortterm debt on days when the cash balance drops below the minimum cash balance constraint, rather than prematurely sell earning assets. thus avoiding the high transaction cost of selling earning assets before maturity. Furthermore the model divides time into fixed planning horizons, each of fixed duration. All assets and debt obligations mature on the last day of the planning horizon. The firm minimizes the total cost of each planning horizon separately. Although the optimal solution of this model can be obtained only numerically, the model is a constructive step towards the choice of maturation dates on debt instruments to reduce the level of transaction costs. In the remainder of this chapter the authors analyze simulation results which present the optimal policies and costs of the different models under various assumption on the level of fixed transaction costs. Chapter six discusses an interesting approach to the minimum overage cash balance constraint, which is a variation to Miller-Orr’s minimum ubsolure cash balance constraint. The ‘relaxed minimum average cash balance model with penalties’ is formulated, solved numerically and compared to the previous models. Chapter seven studies the effect of the length to maturity of short-term investment assets on the total cost of the cash management system. Simulations run over several of the models _.._.__ _I_.__.__.. :_1:__._ .L_. .L_ ___C._LII!... _‘-_ ___L _________. r(;rr..,r~., :.. ~18s .L- p~sr~vos ___.. C,...” cl~dpbcrs UIDLUJJGU 118 ~uu~cil~c tniit ,115 promaoli~ry 01 a casn management system increases with the purchase of longer-term assets in spite of the resulting inflexibility of the cash management policy. A very brief chapter eight discusses forecasting techniques in cash management and chapter nine concludes the topic. Some puzzling omissions are noted in the discussion of cash management models. First, proportional transaction costs are omitted from the discussion. The authors argue that the primary source of proportional transaction costs is the spread between the selling and buying
300
Book Review
price of certificates of deposit, and that these costs are never incurred if the firm holds the certificates of deposit to maturity. But as recognized elsewhere by Daelenbach (JFQA. September, 1974) there is normally an opportunity cost on funds tied up in transactions equal to at least one-day forgone interest. If the annual interest rate is 8 percent this gives rise to a proportional transaction cost k = 0.08,‘365 > O.CGO2. Using the data of HomonotT-hlullin~ table S-2. for a symmetric fixed transaction cost b = 510 per transaction. the average daily fixed transaction cost is $3.7 per day. The average number of transactions per day was 3Yil0J. The size of a transaction was S?SS.OOO for an increase in the cash balance and S615.OOU for a decrease. Even if all transactions w’ere of the smaller size of S.258.000, that would result in an averaee dailv nrnnortional trmf~ction rnct fwual tn 10 OOfl?~PW Iwx)~~W/loJ~ ., w Wl __L___L____.. _II. __- ner r_. day -.-o----, r--r-.-.-.----I--.- ._.____,~___,___,.__/__ which is an order of magnitude higher than the fixed transaction cost! The authors devote only a half-page discussion on proportional transaction costs fp. 44) to describe an algorithm which adjusts for proportional trans. ction costs. However. the authors do not seem to realize that proportional costs will change not only the parameters of the cash policy but also itsform. The incorporation of proportional transaction costs appears to be at least as important as many of the models discussed by the authors. The second omission refers to negative cash balances. Whereas many papers on cash management allow for negative cash balances, and whereas Homonoff-Mullins are bothered by the rigid minimum cash balance constraint and consider modifications of this constrant, nowhere in the book is there any mention of negative cash balances. Overall Homonoffand Mullins have written a clear and intcrcsting introduction to problems of cash management under uncertainty and many specialized students or practitioners of cash management will benefit from its study. For the general student of finance the hook is narrow in scope. for at the general level the topic of cash management should be studied within the more general framework of working capital management. Gcorgc M. Constnntinides Carnegie-Mellon University