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IMA Journal of Management Mathematics Advance Access published online on August 14, 2009
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpp015
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© The authors 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Organization size and the optimal investment in cash

Andrew Higson, Shinozawad Yoshikatsu and Mark Tippett{dagger}

Business School, Loughborough University, Leicestershire LE11 3TU, UK

{dagger} Email: m.tippett{at}lboro.ac.uk

Received on 10 September 2008. Accepted on 17 July 2009.

Miller & Orr (1966, Q. J. Econ., 80, 413–435) formulate a cash management model under which an organization's cash flow evolves in terms of a stationary random walk. This, in turn, implies that the organization's demand for cash will not grow over time. However, as organizations grow one would expect the demand for cash to grow as well. Given this, we formulate a cash management model under which movements in an organization's cash balance hinge on its current rate of output or an equivalent size measure. Cash is withdrawn and invested in interest-bearing securities when the cash to output ratio becomes too high, while securities are sold and the proceeds deposited in a non-interest-bearing bank account when the cash to output ratio becomes too low. The control limits are determined so as to minimize the expected annual cost of a unit of output. Our analysis shows that when organization's cash flows follow a non-stationary process, the optimal cash management policies are profoundly different to those obtained under the Miller & Orr(1966) model.

Keywords: cash; control limits; Wiener process


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