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Corporate Accounting and Financial Management · Working Capital Management

Cash Management: Cash Budget, Baumol and Miller-Orr Models

Updated 11 October 2026 · Fact-checked

Cash management means keeping enough cash to meet payments without holding idle money. You plan it with a cash budget, which forecasts receipts and payments. You fix the optimum balance with the Baumol model, C = √(2 × U × P ÷ S), or the Miller-Orr model, which sets upper and lower control limits.

Understand Cash Management

Cash management is about having the right amount of cash at the right time. Too little cash means you cannot pay suppliers, wages or dues. Too much cash sits idle and earns nothing. The finance manager must balance these two risks.

A firm holds cash for three classic motives. The transactions motive is to meet routine payments such as wages, purchases and taxes. The precautionary motive is to keep a buffer for unexpected needs. The speculative motive is to take advantage of opportunities, such as a sudden bulk-purchase discount. Some books add a compensating motive: balances kept with a bank in return for its services or loans.

The main planning tool is the cash budget. It lists expected cash receipts and cash payments for each period and shows the closing balance. It does not include non-cash items like depreciation, provisions or bad debts written off. It shows when you will have a surplus to invest and when you will have a shortfall to finance.

To find the best cash level, two models are taught. The Baumol model treats cash like inventory. You use up cash at a steady rate and refill it by selling securities. It balances the transaction cost of each sale against the interest lost on holding cash. The Miller-Orr model is for uneven cash flows. It sets a lower limit, a return point and an upper limit. You act only when cash touches a limit.

Key rules to remember

Baumol optimum cash size
C = √(2 × U × P ÷ S)
U = total cash needed for the period, P = cost per transaction (conversion cost), S = interest rate per period on securities. Keep U and S on the same time basis.
Baumol number of transactions
Number of transactions = U ÷ C
Number of times securities are sold in the period.
Baumol total cost
Total cost = (U ÷ C) × P + (C ÷ 2) × S
At the optimum C, the ordering cost and the holding cost are equal.
Miller-Orr spread
Spread = 3 × [(3 × F × σ²) ÷ (4 × i)]^(1/3)
F = cost per transaction, σ² = variance of daily net cash flows, i = daily interest rate. Take the cube root of the whole bracket.
Miller-Orr limits
Upper limit = Lower limit + Spread; Return point = Lower limit + Spread ÷ 3
The lower limit is set by management. Average cash balance = Lower limit + 4 × Spread ÷ 9 (only if asked).
Cash budget closing balance
Closing cash = Opening cash + Receipts − Payments
Exclude non-cash items such as depreciation.

How to solve Cash Management questions

Most questions ask for a cash budget or for an optimum cash balance from a model. Identify which one first.

  1. 1Read the question and decide: cash budget, Baumol, or Miller-Orr.
  2. 2For a cash budget, draw columns for each month and rows for receipts, payments and balances.
  3. 3Convert sales and purchases into cash using the credit period given. A 1-month credit means a January sale is received in February.
  4. 4Remove non-cash items such as depreciation. Add items such as capital purchases, tax and dividend in the month they are paid.
  5. 5Compute net cash flow, add the opening balance and show the closing balance for each month.
  6. 6For Baumol, list U, P and S, check the time basis, then apply C = √(2UP ÷ S).
  7. 7For Miller-Orr, compute the spread, then the upper limit and return point from the lower limit.
  8. 8State the conclusion clearly: the closing balances, the optimum cash size, or the control limits.

Quickest way: Row-by-row cash budget and formula check

When to use it: Use this when time is short and the question gives monthly figures or model inputs.

  1. For a cash budget, first write a small timing line, such as 'sales received after 1 month'.
  2. Fill the receipts row for all months before touching payments.
  3. Fill the payments row, skipping depreciation, then compute net flow and closing balance.
  4. For Baumol, write U, P and S on one line, make S a rate (8% = 0.08), then calculate.
  5. For Miller-Orr, work out the bracket first, take the cube root, then multiply by 3.
  6. Check the answer: the closing balance of one month must equal the opening balance of the next.

Common mistakes in Cash Management

  • Including depreciation or provisions as cash payments in the cash budget.

    They appear in the cost data given in the question, so they look like expenses to pay.

    Fix: Include only items that involve actual cash movement. Leave out depreciation, provisions and write-offs.

  • Ignoring the credit period and showing sales as cash received in the same month.

    Students rush and copy the sales row into the receipts row.

    Fix: Shift each month's sales by the credit period. Note the timing before you start.

  • Using an annual interest rate with a monthly cash requirement in Baumol.

    The time basis of U and S is not checked.

    Fix: Keep both on the same basis. If U is annual, S is the annual rate.

  • Forgetting the cube root in the Miller-Orr spread.

    The formula looks like a plain fraction, so the power of 1/3 is dropped.

    Fix: Compute 3Fσ² ÷ 4i first, take the cube root, then multiply by 3.

  • Treating the lower limit as zero in Miller-Orr without being told.

    Students assume no minimum balance.

    Fix: Use the lower limit given in the question. Use zero only if it says so.

  • Not stating a conclusion after the calculation.

    The number feels like the end of the answer.

    Fix: Add a final line, for example 'The firm should sell securities worth ₹20,000 each time.'

Worked examples

Example 1

A company needs ₹6,00,000 cash in a year. Cash is spent evenly. The cost of each sale of securities is ₹300 and the interest rate on securities is 12% a year. Using the Baumol model, find the optimum cash size, the number of transactions and the total annual cost.

Show the solution
  1. U = ₹6,00,000; P = ₹300; S = 0.12.
  2. C = √(2 × 6,00,000 × 300 ÷ 0.12).
  3. 2 × 6,00,000 × 300 = 36,00,00,000. Dividing by 0.12 gives 3,00,00,00,000.
  4. C = √3,00,00,00,000 = ₹54,772 (approximately).
  5. Number of transactions = 6,00,000 ÷ 54,772 = 10.95, about 11.
  6. Ordering cost = 10.95 × 300 = ₹3,286 (approx). Holding cost = (54,772 ÷ 2) × 0.12 = ₹3,286 (approx).
  7. Total cost = ₹3,286 + ₹3,286 = ₹6,573 (approx).

Answer: Optimum cash size is about ₹54,772. The firm makes about 11 transactions a year. The total annual cost is about ₹6,573.

Example 2

Prepare a cash budget for January to March from this data. Opening cash on 1 January is ₹20,000. Sales: December ₹1,00,000; January ₹1,20,000; February ₹1,40,000; March ₹1,60,000. All sales are on credit and received in the month after sale. Purchases paid in the month of purchase: January ₹60,000; February ₹70,000; March ₹80,000. Wages paid each month: ₹25,000. Depreciation is ₹5,000 a month. Machinery of ₹50,000 is bought and paid for in February.

Show the solution
  1. Receipts: January = December sales ₹1,00,000; February = ₹1,20,000; March = ₹1,40,000.
  2. Payments exclude depreciation. January = 60,000 + 25,000 = ₹85,000.
  3. February = 70,000 + 25,000 + 50,000 = ₹1,45,000.
  4. March = 80,000 + 25,000 = ₹1,05,000.
  5. January: opening 20,000 + 1,00,000 − 85,000 = closing ₹35,000.
  6. February: opening 35,000 + 1,20,000 − 1,45,000 = closing ₹10,000.
  7. March: opening 10,000 + 1,40,000 − 1,05,000 = closing ₹45,000.

Answer: Closing cash: January ₹35,000; February ₹10,000; March ₹45,000. February is the tightest month because of the machinery purchase.

Exam tips

  • Practise at least three cash budget questions with credit-period shifts. They are the most common written format here.
  • Show the Baumol formula with values substituted. Marks are given for the method even if the arithmetic slips.
  • Write out the three motives with one-line examples. Theory parts are short and easy to score.
  • Draw the Miller-Orr limits as a simple sketch with upper limit, return point and lower limit if you are asked to explain the model.
  • Round only at the end, and state your assumption if the question is unclear.

Practice questions from Working Capital Management

Cash Management in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Cash Management: frequently asked questions

What are the motives for holding cash?

The main motives are transactions, precautionary and speculative. The transactions motive covers routine payments. The precautionary motive covers unexpected needs. The speculative motive covers chances to gain from market opportunities.

What is the difference between the Baumol and Miller-Orr models?

Baumol assumes cash is used at a steady, known rate. Miller-Orr allows cash flows to be random and sets upper and lower control limits. Baumol gives one optimum size. Miller-Orr gives a range and a return point.

How do I calculate the optimum cash balance in the Baumol model?

Use C = √(2 × U × P ÷ S). U is the cash needed, P is the cost per transaction and S is the interest rate. Keep the time basis the same for U and S.

Is depreciation shown in a cash budget?

No. Depreciation is a non-cash expense, so it does not change the cash balance. Leave it out of the payments.