Cash is the most liquid but least productive asset — earning low (or no) returns. Excessive cash is inefficient; insufficient cash risks insolvency. Optimal cash management minimises the total cost.

Motives for holding cash (Keynes):

Transactional: Day-to-day payments to employees, suppliers, tax authorities
Precautionary: Buffer against unexpected outflows (machine breakdown, customer default, market downturn)
Speculative: Available for investment opportunities (acquisitions, favourable market conditions)

Cash budgets:

Detailed monthly (or weekly) forecast of cash receipts and payments
Shows expected cash balance at each period end
Identifies financing needs (overdraft peaks) or surpluses (investment opportunities)
Key inputs: sales forecasts with timing of receipts (allowing for credit periods), purchase forecasts, payroll, tax payments, capital expenditure, dividends, interest, debt repayments
Used to: negotiate overdraft facilities, schedule investments, manage short-term surpluses

Baumol model (cash as an inventory problem — EOQ-style):

Assumes STEADY, PREDICTABLE cash outflows. Cash is replenished periodically by selling marketable securities or drawing from an account. Trade-off: cost of converting securities/transferring funds (order cost) vs opportunity cost of holding cash (= forgone interest on securities).

Optimal cash withdrawal (Q*)

=

√(2 × F × T / K)

Where:

F = fixed cost per transfer (transaction cost of converting securities to cash)
T = total cash needed in the period (e.g., annual)
K = opportunity cost of holding cash (interest rate foregone per period)

Average cash balance = Q*/2. Number of transfers = T/Q*.

Worked example: Annual cash requirement £1.2m (assumed steady). Transfer cost £25 per transaction. Interest rate on securities 5%.

Q* = √(2 × 25 × 1,200,000 / 0.05) = √(1,200,000,000) = £34,641
Average cash balance = £34,641 / 2 = £17,321
Number of transfers per year = £1,200,000 / £34,641 ≈ 35 transfers
Annual cost: transfer cost 35 × £25 = £866; opportunity cost £17,321 × 5% = £866 (equal at optimum)
Total annual cost ≈ £1,732

Baumol limitations:

Assumes STEADY, PREDICTABLE cash outflows — unrealistic in practice
Only models cash outflows — doesn't capture the reality of cash also coming IN unpredictably
Rigid assumptions — not useful for most real businesses

Miller-Orr model (stochastic cash flows — more realistic):

Assumes cash flows are random (unpredictable). Sets three levels:

Lower limit (L): Set by management (can be zero or a positive floor)
Return point (Z): Target cash balance
Upper limit (H): When cash balance hits this, invest excess in securities to return to Z

When cash reaches L: sell securities to return to Z. When cash reaches H: invest excess to return to Z. Within [L, H], let cash fluctuate naturally.

Z	=	L + (3Fσ² / 4K)^(1/3)
H	=	3Z − 2L (upper limit)
Average cash balance	=	(4Z − L) / 3

Where:

F = transaction cost of converting securities/cash
σ² = variance of daily cash flows
K = daily interest rate (opportunity cost)

Example: Variance of daily cash flows £500,000 (so σ = £707). Transaction cost £25. Annual interest rate 5%, so daily K ≈ 0.000137. Lower limit L = £5,000.

Spread (Z − L) = (3 × 25 × 500,000 / (4 × 0.000137))^(1/3) = (6.84 × 10¹⁰)^(1/3) ≈ £4,091
Z = £5,000 + £4,091 = £9,091
H = 3 × £9,091 − 2 × £5,000 = £27,273 − £10,000 = £17,273
Average cash balance = (4 × £9,091 − £5,000) / 3 = £31,364 / 3 = £10,455

Intuition: Miller-Orr gives a range [£5,000 − £17,273] within which cash fluctuates. Outside this range, trigger a transaction to return to £9,091. Unlike Baumol, this handles UNPREDICTABLE cash flows.

Factors affecting the limits:

Higher volatility (σ²) → wider spread (more uncertainty)
Higher transaction cost → wider spread (fewer transactions)
Higher interest rate → narrower spread (more incentive to invest idle cash)

Financial Management