How much cash should a business hold at any given time? Too little cash and operations stall; too much cash and the business loses the interest it could have earned. The Baumol cash management model, developed by economist William Baumol, answers this question by treating cash exactly like inventory.
What is the Baumol model?
The Baumol model is based on the idea that deciding on optimum cash balances is like deciding on optimum inventory levels. It assumes that cash is steadily consumed over time, and that a business holds a stock of marketable securities that can be sold whenever cash is needed.
Two types of costs are associated with a cash balance:
1. Transaction costs — the administration cost incurred each time marketable securities are converted into cash.
2. Holding costs — the opportunity cost of holding cash, i.e. the interest foregone from not investing the cash.
Both costs are variable in nature. When one falls, the other rises, and vice versa. The optimum (minimum) cash balance is reached when the total of these two costs is minimized. Because of this, the Baumol model uses an equation of the same form as the EOQ (Economic Order Quantity) formula used in inventory management.
The Baumol formula
Where:
1. D = the total amount of cash disbursed over the period (usually one year)
2. T = the transaction (administration) cost each time securities are converted into cash
3. C = the opportunity cost of holding one unit of cash for the period (the interest rate foregone)
4. Q = the optimum amount of cash to be raised in each transaction
As with the EOQ, costs are minimized when the optimum amount of cash to be converted in each transaction is transferred at regular intervals.
Worked example
Zeal Uganda Limited (ZUL) deals in the production and supply of soft drinks in the West Nile. ZUL has been realizing profits since incorporation and would like to expand its operations to North Eastern Uganda, as market research indicated viable opportunities in that region. ZUL's normal planning period is one year, and it generates surplus cash of Shs 3.0 million per month, which it invests in short-term securities. The interest earned from short-term securities is 8%, with an associated carrying cost per transaction of Shs 120.
Required: Calculate for ZUL:
(a) The optimum amount of cash to be invested in each transaction
(b) The number of transactions that will arise each year
(c) The carrying cost of the transactions
Solution
(a) Optimum amount per transaction
Applying the Baumol formula with D = Shs 36,000,000 (Shs 3.0 million × 12 months), T = Shs 120 and C = 8%:
The optimal amount of cash to be invested in each transaction is therefore Shs 328,654.
(b) Number of transactions per year
Annual cash disbursed ÷ optimum amount per transaction = 36,000,000 ÷ 328,654 ≈ 110 transactions per year.
(c) Carrying cost of the transactions
Number of transactions × cost per transaction = 110 × Shs 120 = Shs 13,200.
Drawbacks of the Baumol model
The model is elegant, but in practice it has limitations:
1. In reality, it is unlikely to be possible to predict the amounts of cash required over future periods with much certainty.
2. No buffer inventory of cash is allowed for, yet there may be costs associated with running out of cash.
3. There may be other normal costs of holding cash which increase with the average amount held.
Despite these limitations, the Baumol model remains a useful starting point for setting a target cash balance, especially for businesses whose cash usage is steady and predictable.
Source: "Baumol Cash Management Model - Definition, Formula, and Examples" by CPA Innocent Mugisha, Harvest Training and Consultancy (harvestuganda.net). The original article and image are © Harvest Training and Consultancy (U) Ltd.
