Miller-Orr Model
Unlike the Baumol's Model, Miller-Orr Model is a stochastic or like probabilistic model that creates the more realistic assumption of doubt in cash flows.
Merton Miller and Daniel Orr assumed such the distribution of daily total cash flows is around normal. Each day, the total cash flow could be the expected value of some lower and higher value drawn from a usual distribution. Consequently, the daily net cash tags a trendless alternatively walk. From the graph underneath, the Miller-Orr Model sets lower and higher control units, H and L respectively, and an objective cash balance, Z. Whenever the cash balance reaches H as like point A then H-Z shillings are transferred from cash to marketable securities. Correspondingly, when the cash balance hits L or like on point B then Z-L shillings are transferred from marketable securities cash.
The Lower Limit is generally set via management. The target balance is given via the given formula as:
Z = [3B δ^{2} / 4i] ^{1/3} + L
And the highest limit, H, is given via as:
H = 3Z - 2L
The average cash balance = (4Z - L) / 3
Whereas: Z = target cash balance
L = Lower Limit
H = Upper Limit
b = Fixed transaction costs
δ² = variance of net daily cash flows
i = Opportunity cost on daily basis