Miller Orr Model Calculator

✖Cost of Conversion is the sum of direct labor and manufacturing overhead costs incurred to turn raw materials into a finished product.ⓘ Cost of Conversion [b]			+10% -10%
✖Variance is a measure of the spread or dispersion of a set of values.ⓘ Variance [σ]			+10% -10%
✖Interest Rate is the amount charged, expressed as a percentage of the principal, by a lender to a borrower for the use of assets.ⓘ Interest Rate [R]			+10% -10%

✖Miller Orr Model provides for cost efficient transactional balances and assumes uncertain cashflows and determines an upper limit and return point per cash balances.ⓘ Miller Orr Model [Z]

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Formula

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Miller Orr Model

Formula

`"Z" = 3*((3*"b"*"σ")/(4*"R"/360))^(1/3)`

Example

`"744.7635"=3*((3*"20"*"170")/(4*"0.06"/360))^(1/3)`

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Miller Orr Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3)
Z = 3*((3*b*σ)/(4*R/360))^(1/3)
This formula uses 4 Variables

Variables Used

Miller Orr Model - Miller Orr Model provides for cost efficient transactional balances and assumes uncertain cashflows and determines an upper limit and return point per cash balances.
Cost of Conversion - Cost of Conversion is the sum of direct labor and manufacturing overhead costs incurred to turn raw materials into a finished product.
Variance - Variance is a measure of the spread or dispersion of a set of values.
Interest Rate - Interest Rate is the amount charged, expressed as a percentage of the principal, by a lender to a borrower for the use of assets.

STEP 1: Convert Input(s) to Base Unit

Cost of Conversion: 20 --> No Conversion Required
Variance: 170 --> No Conversion Required
Interest Rate: 0.06 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z = 3*((3*b*σ)/(4*R/360))^(1/3) --> 3*((3*20*170)/(4*0.06/360))^(1/3)

Evaluating ... ...

Z = 744.763524183721

STEP 3: Convert Result to Output's Unit

744.763524183721 --> No Conversion Required

FINAL ANSWER

744.763524183721 ≈ 744.7635 <-- Miller Orr Model

(Calculation completed in 00.004 seconds)

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< 9 Cash Management Calculators

Merton Model

Go Distance to the Default = ln(Market Value of Company Assets/Market Value of Company Debt)+((Risk Free Interest Rate+(Volatility of Company Asset Value)^2/2)*Time to Maturity)/(Volatility of Company Asset Value*sqrt(Time to Maturity))

Baumol's Model

Go Cost of Providing a Service = sqrt((2*Cost of Conversion*Total Requirement of Cash)/Interest Rate)

Cash Conversion Cycle

Go Cash Conversion Cycle = Days Inventory Outstanding+Days Sales Outstanding-Days Payables Outstanding

Miller Orr Model

Go Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3)

Cash Surrender Value

Go Cash Surrender Value = mod(Enhanced Accumulated Value,Surrender Charges)

Cash Coverage

Go Cash Coverage = Earnings before Interest and Taxes/Interest Expense

Cash Burn Rate

Go Net Burn = Total Monthly Cash Sales-Total Monthly Cash Expenses

Implied Cash Runway

Go Implied Cash Runway = Cash Balance/Net Burn

Cash Budget

Go Cash Budget = Total Receipts-Total Payments

Miller Orr Model Formula

Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3)
Z = 3*((3*b*σ)/(4*R/360))^(1/3)

What is Miller orr model?

The Miller-Orr Model is a financial model used for cash management, particularly to determine when a firm should place an order to replenish its cash reserves. It was developed by economists Merton Miller and Daniel Orr in 1966.

The primary objective of the Miller-Orr Model is to strike a balance between the costs of holding too much cash (opportunity cost of funds) and the costs of replenishing cash when it falls below a certain level (transaction costs). The model operates on the assumption that cash balances follow a random pattern, and it sets upper and lower control limits to trigger actions.

How to Calculate Miller Orr Model?

Miller Orr Model calculator uses Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3) to calculate the Miller Orr Model, The Miller Orr Model formula is defined as a model which provides for cost efficient transactional balances and assumes uncertain cashflows. It determines an upper limit and return point per cash balances. Miller Orr Model is denoted by Z symbol.

How to calculate Miller Orr Model using this online calculator? To use this online calculator for Miller Orr Model, enter Cost of Conversion (b), Variance (σ) & Interest Rate (R) and hit the calculate button. Here is how the Miller Orr Model calculation can be explained with given input values -> 744.7635 = 3*((3*20*170)/(4*0.06/360))^(1/3).

FAQ

What is Miller Orr Model?

The Miller Orr Model formula is defined as a model which provides for cost efficient transactional balances and assumes uncertain cashflows. It determines an upper limit and return point per cash balances and is represented as Z = 3*((3*b*σ)/(4*R/360))^(1/3) or Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3). Cost of Conversion is the sum of direct labor and manufacturing overhead costs incurred to turn raw materials into a finished product, Variance is a measure of the spread or dispersion of a set of values & Interest Rate is the amount charged, expressed as a percentage of the principal, by a lender to a borrower for the use of assets.

How to calculate Miller Orr Model?

The Miller Orr Model formula is defined as a model which provides for cost efficient transactional balances and assumes uncertain cashflows. It determines an upper limit and return point per cash balances is calculated using Miller Orr Model = 3*((3*Cost of Conversion*Variance)/(4*Interest Rate/360))^(1/3). To calculate Miller Orr Model, you need Cost of Conversion (b), Variance (σ) & Interest Rate (R). With our tool, you need to enter the respective value for Cost of Conversion, Variance & Interest Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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