Working Capital and Liquidity: formula sheet

Key formulas

Net working capital

Net working capital = Current assets − Current liabilities

A positive value means current assets exceed short-term obligations. It is not the same as cash.

Operating working capital

Operating working capital = (Receivables + Inventory) − (Payables + Accruals)

Excludes cash, securities and short-term debt. Definitions vary, so follow the question's wording.

Current ratio

Current ratio = Current assets ÷ Current liabilities

A basic liquidity measure. Higher means more cover, not necessarily better management.

Liquidity trade-off

More liquidity → lower expected return; less liquidity → higher return but more risk

The core idea behind working capital decisions.

Days of inventory on hand (DIO)

DIO = Inventory ÷ (Cost of goods sold ÷ 365)

Uses COGS, not sales. Use average inventory if the question gives it. Use the number of days the question states, normally 365.

Days sales outstanding (DSO)

DSO = Accounts receivable ÷ (Revenue ÷ 365)

Uses revenue (credit sales if given).

Days payables outstanding (DPO)

DPO = Accounts payable ÷ (Purchases ÷ 365)

Uses purchases. If purchases are not given, the exam usually says to use COGS. Purchases = COGS + ending inventory − beginning inventory.

Operating cycle

Operating cycle = DIO + DSO

Days from acquiring inventory to collecting cash.

Cash conversion cycle

CCC = DIO + DSO − DPO

Also called the net operating cycle. Can be negative.

Turnover to days

Days = 365 ÷ Turnover ratio

Inventory turnover = COGS ÷ inventory; receivables turnover = revenue ÷ receivables; payables turnover = purchases ÷ payables.

Current ratio

Current assets ÷ Current liabilities

Broadest measure. Inventory counts, so it can flatter a firm with slow stock.

Quick ratio

(Cash + Short-term marketable securities + Receivables) ÷ Current liabilities

Some texts use (Current assets − Inventory) ÷ Current liabilities. Use the version the question implies.

Cash ratio

(Cash + Short-term marketable securities) ÷ Current liabilities

Strictest ratio. Excludes receivables.

Defensive interval ratio

(Cash + Short-term marketable securities + Receivables) ÷ Daily cash expenditures

Answer is in days. Daily cash expenditures = (Cash operating expenses, such as COGS + SG&A, excluding non-cash charges like depreciation) ÷ 365.

Order of strictness

Cash ratio ≤ Quick ratio ≤ Current ratio

Holds because each ratio uses the same denominator and fewer assets in the numerator.

Current ratio

Current ratio = Current assets ÷ Current liabilities

A higher ratio means more liquidity on paper, but it ignores asset quality.

Quick ratio

Quick ratio = (Cash + Short-term marketable securities + Receivables) ÷ Current liabilities

Excludes inventory, so it is a tougher test of liquidity.

Cash ratio

Cash ratio = (Cash + Short-term marketable securities) ÷ Current liabilities

The strictest of the three static ratios.

Net working capital

Net working capital = Current assets − Current liabilities

A currency amount, not a ratio.

Cash conversion cycle

CCC = Days of inventory on hand + Days of sales outstanding − Days of payables outstanding

A shorter cycle usually means less cash tied up and better liquidity.

Source classification rule

Primary = readily available in the normal course of business without significantly affecting operations; Secondary = may reduce or change normal operations or the financial and capital structure, or signal distress

Use this rule to sort any listed source. A drawn line of credit adds debt but is still primary.

Policy priority order

Safety of principal > Liquidity > Yield

Default order for corporate short-term cash. If a question states different priorities, follow the question.

Discount-basis pricing

Price = Face value × (1 − Discount rate × Days ÷ 360)

Used for T-bills and commercial paper quoted on a bank discount basis. Uses a 360-day year.

Holding period yield

HPY = (Face value − Price) ÷ Price

Return earned over the life of the instrument, measured on the price paid.

Money market yield

MMY = HPY × (360 ÷ Days)

Annualizes on a 360-day year without compounding.

Bond equivalent yield

BEY = HPY × (365 ÷ Days)

Annualizes on a 365-day year without compounding; comparable with bond yields.

Yield ranking logic

More credit risk + less liquidity + longer maturity = higher yield

Use this to rank T-bills, CDs and commercial paper.

Cost of trade credit (effective annual rate)

Cost = (1 + discount ÷ (1 − discount))^(365 ÷ (days credit − discount days)) − 1

Use for terms like d/x net y. Days credit = y, discount days = x. This compounds the periodic cost; it is the form the curriculum emphasizes.

Periodic cost of trade credit

Periodic cost = discount ÷ (1 − discount)

Example: 2% discount gives 0.02 ÷ 0.98 = 2.0408%. Always divide by (1 − discount), not by 1.

Number of days you borrow

Extra days = net due day − discount day

For 2/10 net 30 it is 30 − 10 = 20 days. The compounding exponent is 365 ÷ 20.

Days sales outstanding (DSO)

DSO = 365 ÷ receivables turnover = (average receivables ÷ credit sales) × 365

Higher DSO means slower collection.

Days of inventory on hand (DOH)

DOH = 365 ÷ inventory turnover = (average inventory ÷ COGS) × 365

Uses cost of goods sold, not sales.

Days payable outstanding (DPO)

DPO = (average payables ÷ COGS) × 365

Higher DPO means more supplier financing, but beyond terms it creates risk.

Cash conversion cycle

CCC = DSO + DOH − DPO

Shorter is generally better for liquidity.

Interest on a borrowing

Interest = Amount borrowed × Annual rate × (Days ÷ Day-count basis)

Use the basis the question gives (360 or 365). If none is stated, follow the question's own convention.

Commitment fee

Fee = Fee rate × Unused amount × (Days ÷ Basis)

Charged on the part of a committed line not drawn. Include it in total cost.

Periodic cost of borrowing

Periodic cost = (Interest + Fees) ÷ Usable funds received

Divide by the cash the firm actually gets, not the face amount, when fees or discounts are taken upfront.

Effective annual cost

EAC = (1 + Periodic cost)^(365 ÷ Days) − 1

Compounds the periodic cost over a year. Simple annualizing is Periodic cost × (365 ÷ Days).

Discount (commercial paper) proceeds

Proceeds = Face value − Discount, and Periodic cost = (Face − Net proceeds) ÷ Net proceeds

Net proceeds are proceeds minus dealer fees and backup line costs.

Quick revision

• Operating cycle = days of inventory on hand + days of sales outstanding.
• Cash conversion cycle = operating cycle − days of payables outstanding.
• A shorter cash conversion cycle generally means less cash tied up in operations.
• Current ratio = current assets ÷ current liabilities.
• Quick ratio = (cash + short-term marketable securities + receivables) ÷ current liabilities.
• Cash ratio = (cash + short-term marketable securities) ÷ current liabilities.
• Primary liquidity sources include cash balances and operating cash flow; secondary sources include credit lines and asset sales.
• Short-term investments trade off safety and liquidity against yield.
• Skipping a trade discount is often a costly form of borrowing; compute its effective annual rate.
• Commercial paper is often cheaper than a bank line for strong issuers but is less flexible.
• Check whether a question wants averages or period-end balances before computing day counts.
• Read the units: days, years and percent are easy to mix up.

Common mistakes

• Treating net working capital as the same as cash. Fix: Remember it is current assets minus current liabilities. It includes receivables and inventory, which are not cash.
• Including long-term debt or fixed assets in the calculation. Fix: Only current items count. Use the current portion of long-term debt, not the full amount.
• Using revenue instead of COGS for DIO or DPO Fix: Remember the match: inventory and payables relate to costs (COGS or purchases); receivables relate to revenue.
• Adding DPO instead of subtracting it Fix: DPO is financing from suppliers. It shortens the cycle, so it is subtracted.
• Including inventory in the quick ratio. Fix: Quick ratio excludes inventory and prepaid items. Start from cash, securities and receivables.
• Using total expenses, including depreciation, in the defensive interval. Fix: Use cash expenses only. Remove depreciation and amortization before dividing by 365.
• Labelling a bank line of credit as a secondary source. Fix: Lines of credit are listed as a primary source because they are readily available in the normal course of business without significantly affecting operations. Drawing on one does add debt, but it is still primary. Negotiating debt terms is secondary.
• Mixing up drags and pulls. Fix: A drag slows or cuts inflows (slow-paying customers, obsolete inventory). A pull speeds or forces outflows (suppliers cutting credit terms).
• Choosing the highest-yielding instrument for a safety-first policy. Fix: Find the stated objective first. Eliminate options that add credit or liquidity risk beyond the policy.
• Treating commercial paper as secured or government-backed. Fix: Remember that commercial paper is unsecured corporate debt. It carries credit risk and yields more than T-bills.

Exam tips

• Questions often test the classification of liquidity sources. Memorise the primary list and treat asset sales, debt renegotiation and bankruptcy as secondary.
• Always list only current items before subtracting. Wrong options are often built from including long-term debt.
• Expect judgement items on the liquidity versus profitability trade-off. Excess cash lowers return; too little raises risk.
• There is no penalty for wrong answers. If unsure, eliminate the two options that contradict the trade-off and guess.
• Check which denominator each ratio uses before touching the calculator. Wrong denominators are the most common trap.
• Options are listed smallest to largest. Rule out any CCC option above DIO + DSO, since DPO reduces the cycle.
• Expect conceptual items too: which change shortens the CCC (faster collection, lower inventory, longer payment terms) and what a falling CCC signals.
• If the question gives turnover ratios, divide 365 by each one and skip the balance sheet work.