Baumol Model of Cash Management: Meaning, Formula, Numerical & Limitations

What is Cash?

In the narrow sense, cash refers to currency and generally accepted cash equivalents such as cheques, drafts, and money orders.

In the broad sense, cash also includes near-cash assets such as marketable securities and time deposits with banks. These assets:

1. Can be readily sold and converted into cash
2. Serve as a reserve pool of liquidity
3. Provide short-term investment outlets for excess cash

Meaning of Cash Management

Cash management is concerned with managing:

• Cash inflows and outflows of the firm
• Cash movements within the firm
• Cash balances held at a particular point of time by financing deficits or investing surplus cash

The primary objective of cash management is to ensure the availability of adequate cash while avoiding unnecessary idle balances.

Cash Management Models

Efficient cash management requires effective cash forecasting and reporting systems to ensure optimal conservation and utilisation of funds.

The cash budget provides estimates of cash balances for a given period based on expected revenues and expenditures. However, it does not explain:

1. How cash shortages should be financed
2. How surplus cash should be utilised

These issues are addressed through cash management models.

Cash Planning

Cash planning is a technique used to plan and control the use of cash. It safeguards the firm’s financial condition by preparing projected cash statements based on expected cash inflows and outflows for a specific period.

The cash budget is the most important tool for planning and controlling cash receipts and payments.

Cash Budgeting and Forecasting

A cash budget is a summary statement of a firm’s expected cash inflows and outflows over a projected period.

Cash forecasting is required to prepare cash budgets and may be undertaken on:

1. Short-term basis
2. Long-term basis

The relationship can be expressed as: Cash Management → Cash Planning → Cash Budget → Cash Forecasting

Short-Term Cash Forecasting Methods

The commonly used short-term forecasting methods are:

1. Receipts and Disbursements Method
2. Adjusted Net Income Method

Determining the Optimum Cash Balance

One of the primary responsibilities of financial management is to maintain a sound liquidity position so that obligations are met on time. The optimum cash balance depends on the risk–return trade-off.

1. If the firm maintains a small cash balance:
• Liquidity position weakens
• Profitability improves as released funds can be invested in profitable opportunities
2. If the firm maintains a high cash balance:
• Liquidity position strengthens
• Profitability declines due to idle funds

Thus, determining the optimum cash balance depends on whether cash flows are predictable or unpredictable, requiring careful analysis and planning.

Baumol Model (1952) – EOQ Model of Cash Management

William J. Baumol proposed a model for cash management that is analogous to the Economic Order Quantity (EOQ) model used in inventory management. The Baumol model helps in determining the optimal cash conversion size, that is, the amount of cash a firm should obtain each time it sells marketable securities.

According to this model, firms meet their cash requirements by selling marketable securities whenever the need arises. The objective of the model is to minimise the total cost of holding cash, which consists of two components:

1. Opportunity Cost – the cost of holding idle cash instead of investing it in interest-earning securities
2. Transaction (Conversion) Cost – the cost incurred each time marketable securities are converted into cash

The total cost of cash holding is the sum of opportunity cost and transaction cost. The Baumol model aims to determine the cash balance that minimises this total cost.

Assumptions of the Baumol Model

The Baumol model is based on the following assumptions:

1. The firm can forecast its cash requirements with certainty.
2. Cash payments occur uniformly over the period.
3. The opportunity cost of holding cash is known and remains constant over time.
4. The firm incurs a fixed transaction cost each time it converts securities into cash.
5. The total cash requirement for a given period is known in advance.
6. Cash requirements are evenly distributed throughout the period.
7. Marketable securities can be sold immediately without any delay.
8. There are two clearly identifiable costs associated with cash holding:
• Opportunity cost
• Transaction cost
9. The transaction cost per conversion is constant, irrespective of the size of the transaction.
10. Opportunity cost is expressed as a fixed percentage of the average cash balance held.

Optimum Cash Balance under Certainty – Baumol Model

The Baumol Model treats cash management similarly to the inventory management problem, aiming to minimise the total cost of holding and managing cash.

Total Cost of Cash = Cost of Holding Cash + Transaction Cost

1. Holding Cost (Opportunity Cost)

The firm incurs a cost for maintaining cash balances, known as holding cost or opportunity cost, which is the return foregone on marketable securities.

If:

• k= Opportunity cost of holding cash
• C= Cash balance

Then the average holding cost is calculated as:

This is because the average cash balance held is C/2.

2. Transaction Cost

Whenever the firm converts marketable securities into cash, it incurs a transaction cost.

If:

1. T= Total cash requirement for the period
2. C= Cash withdrawn per transaction
3. c= Cost per transaction

Then the number of transactions in the period is:

So, the total transaction cost is:

3. Total Cost of Cash

Combining both costs, the total annual cost of cash is:

4. Optimum Cash Balance

The optimum cash balance C*is the level of cash at which the total cost is minimized. Using calculus (or EOQ logic), we get:

Where:

1. C*= Optimum cash balance
2. c= Cost per transaction
3. T= Total cash required for the period
4. k= Opportunity cost of holding cash

This formula helps firms minimise total cash-related costs while ensuring adequate liquidity.

Optimum Level of Cash Balance

As the demand for cash C increases, the holding cost also increases because more funds remain idle. At the same time, the transaction cost decreases due to a reduction in the number of conversions of marketable securities into cash. Thus, there exists an inverse relationship between holding cost and transaction cost.

The optimum cash balance C* is the level of cash at which the total cost of cash management is minimum.

Formula for Optimum Cash Balance

Where:

1. C*= Optimum cash balance
2. T= Total cash required during the year
3. c= Cost per transaction
4. k= Opportunity cost of holding cash

Impact of Variables on Optimum Cash Balance

1. An increase in transaction cost (c) increases the optimum cash balance.
2. An increase in total cash requirement (T) increases the optimum cash balance.
3. An increase in opportunity cost (k) reduces the optimum cash balance, as holding cash becomes more expensive.

Numerical on Optimum Cash Balance (Baumol Model)

Question

Advani Chemical Limited estimates its total cash requirement at ₹2 crore per year. The opportunity cost of funds is 15% per annum. The cost per transaction for converting short-term securities into cash is ₹150.

Determine:

1. Optimum cash balance
2. Minimum total annual cost
3. Number of transactions (deposits) during the year

Given Data

• Total cash requirement (T) = ₹2,00,00,000
• Cost per transaction (c) = ₹150
• Opportunity cost (k) = 15% = 0.15

Formula  

(1) Calculation of Optimum Cash Balance

Optimum cash balance = ₹2,00,000

(2) Calculation of Minimum Total Cost

(a) Transaction Cost

(b) Holding (Opportunity) Cost

(c) Total Cost

Minimum total annual cost = ₹30,000

(3) Number of Deposits / Transactions

Number of deposits during the year = 100

Final Answers (for Exams)

1. Optimum cash balance = ₹2,00,000
2. Minimum total annual cost = ₹30,000
3. Number of deposits = 100

Limitations of the Baumol Model

1. The model does not allow for fluctuations in cash flows and assumes certainty in cash requirements.
2. It does not consider the use of bank overdrafts or other short-term borrowing facilities.
3. In reality, there are uncertainties in future cash flow patterns, which the model ignores.
4. The model assumes a constant rate of cash usage, whereas actual cash outflows are irregular and uneven.
5. Transaction costs are difficult to measure accurately, as they depend on the type and maturity of investments.
6. It assumes a constant disbursement rate, but in practice, cash payments occur at different times and due dates.
7. The model assumes no cash inflows during the planning period, while in reality, cash is continuously received and paid out.
8. No safety stock of cash is maintained, based on the assumption that marketable securities can be sold immediately, which may not always be practical.

Conclusion 

Due to these limitations, the Baumol Model is best suited for firms with stable and predictable cash flows. For firms facing uncertainty, models like the Miller–Orr Model provide more realistic solutions.

FAQs on Baumol Model of Cash Management

What is the Baumol Model of cash management? What is meant by optimum cash balance?

The Baumol Model is a cash management technique proposed by William J. Baumol in 1952. It applies the Economic Order Quantity (EOQ) concept to determine the optimum cash balance by minimizing holding and transaction costs. Optimum cash balance is the level of cash at which the total cost of cash management (holding cost + transaction cost) is minimum while maintaining adequate liquidity.

What are the main assumptions of the Baumol Model?

The model assumes certainty in cash flows, constant transaction cost, uniform cash usage, immediate sale of marketable securities, and no cash receipts during the planning period.

What costs are considered in the Baumol Model?

The Baumol Model considers two costs: • Holding (opportunity) cost of cash • Transaction (conversion) cost of selling securities

How does an increase in transaction cost affect optimum cash balance? How does opportunity cost affect optimum cash balance?

An increase in transaction cost leads to an increase in the optimum cash balance to reduce the frequency of conversions. An increase in opportunity cost reduces the optimum cash balance, as holding cash becomes more expensive.

Why is the Baumol Model considered unrealistic?

The model assumes certainty, constant cash usage, and no cash inflows, which do not reflect real-world business conditions.

Which model is more suitable under uncertainty?

The Miller–Orr Model is more suitable under uncertain and fluctuating cash flows.

Where is the Baumol Model commonly used?

It is mainly used for academic purposes and by firms with stable and predictable cash flows.

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