Cash Management II: Cash Budgets, Baumol Model and Miller-Orr Model
Course: Business Finance / Corporate Finance
Lecture: 9 – Cash Management II
1. Learning Objectives
By the end of this lecture, students should be able to:
- Explain the purpose and structure of a cash budget.
- Apply the Baumol model to determine an optimal cash transfer size and cash balance.
- Understand the basic logic of the Miller-Orr model for managing cash when cash flows are uncertain.
2. Cash Budget
A cash budget is a forecast of expected cash inflows and cash outflows over a future period, such as a month or quarter. It is a planning tool that helps management anticipate periods of cash surplus or shortage. [web:81][web:84]
Typical elements of a monthly cash budget include:
- Opening cash balance at the start of the month.
- Cash inflows: customer receipts from credit sales, cash sales, loan proceeds, asset disposals, and other income.
- Cash outflows: payments to suppliers, wages and salaries, rent and utilities, interest, taxes, loan repayments, and capital expenditures.
- Closing cash balance for the month (Opening balance + inflows − outflows).
The cash budget highlights when the firm is likely to face cash deficits (and may need borrowing or cost cuts) and when it will have surpluses (which can be invested or used to repay debt). [web:81]
3. Baumol Cash Management Model
The Baumol model applies inventory management logic (similar to the Economic Order Quantity model) to cash balances. It helps determine the optimal cash transfer size that minimises the total cost of holding cash and converting marketable securities into cash. [web:76][web:77][web:78][web:82]
Assumptions include:
- Cash usage is steady and predictable over time.
- The firm can invest surplus cash in interest‑earning securities.
- Each time the firm converts securities to cash, it incurs a fixed transaction cost.
The Baumol model formula for the optimal cash transfer amount is:
C* = √( 2FT / i )
Where:
- C* = Optimal cash transfer size (the amount of cash to withdraw each time from investments).
- F = Fixed transaction cost per conversion (e.g., brokerage fee or bank fee).
- T = Total cash needed over the period (e.g., annual cash requirement).
- i = Interest rate (opportunity cost) per period on marketable securities. [web:76][web:82]
Interpretation:
- Higher transaction costs (F) or higher total cash requirement (T) → larger optimal transfer size C*.
- Higher interest rates (i) → smaller optimal cash balance, because holding cash becomes more expensive relative to investing.
Under the Baumol model, the firm starts with cash equal to C*, spends it steadily down to zero, then sells securities and “refills” cash back to C*. This cycle repeats throughout the period.
4. Miller-Orr Cash Management Model
The Miller-Orr model is used when cash inflows and outflows are uncertain and fluctuate randomly from day to day. Instead of assuming a constant usage rate, it sets upper and lower control limits for the cash balance. [web:80][web:83]
Key ideas:
- The firm chooses a lower control limit (L) for cash, below which the balance should not fall.
- Based on the variability of daily cash flows, transaction costs, and interest rates, the model determines:
- A target cash balance (Z), sometimes called the return point.
- An upper control limit (H).
The operating rules are:
- As long as cash remains between L and H, no action is taken.
- If cash falls to the lower limit L, the firm transfers enough funds in (e.g., by selling securities) to bring the balance up to the target level Z.
- If cash rises to the upper limit H, the firm invests the excess cash (H − Z) into securities, bringing the balance back down to Z.
Thus, the Miller-Orr model recognises the randomness of cash flows and provides a practical, rule‑based system for keeping cash within a desired range. [web:80][web:83]
5. Numerical Example – Baumol Model
Example: A firm estimates that it will need Rs. 1,200,000 in cash over the coming year. The cost of each transaction to convert marketable securities into cash is Rs. 600, and the annual interest rate on those securities is 6%.
Given:
- T = 1,200,000
- F = 600
- i = 0.06
Using the Baumol formula:
C* = √( 2FT / i )
Step 1 – Compute the numerator:
2FT = 2 × 600 × 1,200,000 = 1,440,000,000
Step 2 – Divide by i:
2FT / i = 1,440,000,000 ÷ 0.06 = 24,000,000,000
Step 3 – Take the square root:
C* = √(24,000,000,000) ≈ Rs. 154,919
Interpretation: The optimal cash transfer size is about Rs. 155,000. The firm should, on average, let its cash balance run down from Rs. 155,000 to zero and then replenish it back to Rs. 155,000 by selling securities. This policy minimises the total cost of holding and replenishing cash under the model’s assumptions.
Students can also be asked to estimate:
- Number of transactions per year ≈ T ÷ C*.
- Average cash balance ≈ C* ÷ 2.
6. Class Exercise – Simple Monthly Cash Budget
Exercise outline: Ask students, individually or in groups, to prepare a simple cash budget for one month for a small business.
Provide data such as:
- Opening cash balance at the start of the month.
- Expected cash inflows:
- Cash sales.
- Collections from credit sales (given as a percentage of prior months’ sales).
- Other cash receipts (e.g., a small loan or asset sale).
- Expected cash outflows:
- Payments to suppliers.
- Wages and salaries.
- Rent, utilities, and other operating expenses.
- Interest and loan repayments.
Students should:
- Prepare a table showing opening balance, total inflows, total outflows, and closing balance for the month.
- Identify whether there is a cash surplus or deficit.
- Suggest one action if there is a deficit (e.g., short‑term borrowing, cutting expenses) and one action if there is a surplus (e.g., investing in short‑term securities, early debt repayment).
This exercise reinforces the concept of cash budgeting as a planning and control tool. [web:81]
7. Homework – Cash Management II
Part A – Baumol model practice
- Assume a firm’s annual cash requirement is Rs. 800,000, the fixed transaction cost per conversion is Rs. 400, and the annual interest rate on marketable securities is 5%.
- Calculate the optimal cash transfer size using the Baumol model.
- Estimate the average cash balance and the approximate number of conversions per year.
Part B – Miller-Orr concept check
- In your own words (150–200 words), explain how the Miller-Orr model differs from the Baumol model in terms of assumptions about cash flows.
- Give one example of a business where the Miller-Orr model might be more appropriate than the Baumol model, and briefly explain why.
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