Working Capital Management: formula sheet

Key formulas

Gross working capital

Gross working capital = Total current assets

Includes inventory, receivables, cash, bank and short-term investments.

Net working capital

Net working capital = Current assets − Current liabilities

A negative figure means current liabilities exceed current assets.

Raw material storage period

Average raw material stock ÷ Average daily raw material consumption

Daily consumption = annual consumption ÷ number of days in the year (365 or as given).

Work-in-progress period

Average WIP stock ÷ Average daily cost of production

Adjust for the degree of completion if the question gives it.

Finished goods storage period

Average finished goods stock ÷ Average daily cost of goods sold

Use cost of goods sold, not sales.

Receivables collection period

Average receivables ÷ Average daily credit sales

Use credit sales. Use the basis the question specifies (sales or cost of sales).

Creditors payment period

Average trade creditors ÷ Average daily credit purchases

Use credit purchases.

Operating cycle

Operating cycle = R + W + F + D

R = raw material period, W = WIP period, F = finished goods period, D = receivables period.

Cash conversion cycle

Cash conversion cycle = R + W + F + D − C

C = creditors' payment period. This is the net operating cycle.

Net working capital

Net working capital = Current assets − Current liabilities

This is the final figure in the estimate statement.

Raw material stock

Annual raw material consumption ÷ 12 × months of stock held

Use weeks and 52 if the question gives weeks.

Work-in-progress

(Material % × material cost + Labour % × labour cost + Overhead % × overhead cost) per unit × units in process

Use the completion percentage given for each element. If none is given, assume 100%.

Finished goods stock

Annual cash cost of production ÷ 12 × months of stock held

Exclude depreciation unless told otherwise.

Debtors

Annual cost of sales (or sales) ÷ 12 × months of credit given

Use cost of sales unless the question says to use selling price. State your assumption.

Creditors and outstanding expenses

Annual purchases (or expense) ÷ 12 × months of credit or payment lag

Wages and overheads paid after a lag create outstanding expenses.

Safety margin

Net working capital × margin % (added to net working capital)

Apply it only if the question gives it. A margin on sales or cost needs a different base, so read the wording.

Total working capital financing

Total current assets = Permanent current assets + Temporary current assets

Permanent is the minimum level always held. Temporary is the seasonal or peak part.

Matching rule

Long-term funds = Fixed assets + Permanent current assets; Short-term funds = Temporary current assets

This is the textbook split under the matching approach.

Net working capital

Net working capital = Current assets − Current liabilities

Useful for judging how much of current assets is funded by long-term sources.

Cost of forgoing cash discount (approx.)

[Discount % ÷ (100 − Discount %)] × [365 ÷ (Credit period − Discount period)] × 100

Use it to compare trade credit with bank borrowing. Credit period and discount period are in days.

Effective cost of commercial paper (approx.)

[(Face value − Issue price) ÷ Issue price] × [365 ÷ Days to maturity] × 100

Add issue costs, such as issuing and paying agent fees, if given.

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.

Receivables turnover and average collection period

Receivables turnover = Credit sales ÷ Average receivables Average collection period (ACP) = Days in year ÷ Receivables turnover

Use the number of days (360 or 365) that the question specifies. If it says nothing, state your assumption and stay consistent.

Average receivables

Average receivables = (Credit sales ÷ Days in year) × ACP

This is the amount of receivables at selling price.

Investment in receivables

Investment = Average receivables × (Variable cost ÷ Sales)

Use variable cost when fixed costs do not change. Use total cost only if the question says so. Never use the selling price unless told.

Carrying cost of receivables

Carrying cost = Investment in receivables × Required rate of return

The required rate is the cost of funds or the opportunity cost given in the question.

Bad debts

Bad debts = Bad debt % × Credit sales

Apply the percentage to the sales of that policy, then take the difference between policies.

Net benefit of a credit policy

Net benefit = Contribution − Carrying cost − Bad debts − Collection cost − Cash discount

Compute for each policy and compare. Or compute only the incremental items. Both give the same answer.

Annualised cost of cash discount

Cost = [Discount % ÷ (100 − Discount %)] × [Days in year ÷ (Credit period − Discount period)]

For 2/10 net 30 this is (2 ÷ 98) × (365 ÷ 20) ≈ 37.24%. Compare with the cost of bank borrowing.

Factoring advance and cost

Advance = Invoice value − Reserve − Commission − Interest on advance Effective cost = Annual factoring charges ÷ Net funds received

Reserve is the part held back by the factor. Commission is usually charged on the invoice value. Interest is on the advance for the period. Read the question for the order of deductions.

Economic Order Quantity

EOQ = √(2 × A × O ÷ C)

A = annual consumption in units, O = ordering cost per order, C = carrying cost per unit per year. If carrying cost is given as a percentage, C = percentage × purchase price per unit.

Number of orders per year

Orders = A ÷ EOQ

Time between orders = 12 months (or 365 days) ÷ number of orders.

Total inventory cost

Total cost = Purchase cost + Ordering cost + Carrying cost = (A × P) + (A ÷ Q × O) + (Q ÷ 2 × C)

Q = order quantity, P = price per unit. Use this to compare discount offers.

Reorder level

Reorder level = Maximum usage × Maximum lead time

Alternative when only normal usage is given: Normal usage × Lead time + Safety stock.

Minimum stock level

Minimum level = Reorder level − (Normal usage × Normal lead time)

Normal usage is the average of maximum and minimum usage unless stated.

Maximum stock level

Maximum level = Reorder level + Reorder quantity − (Minimum usage × Minimum lead time)

Reorder quantity is usually the EOQ.

Average stock level

Average level = (Minimum level + Maximum level) ÷ 2, or Minimum level + ½ × Reorder quantity

The two forms can differ slightly in theory; use the one the question implies.

Danger level

Danger level = Normal usage × Emergency lead time

Some texts use average usage; follow the data given.

Quick revision

• Gross working capital = total current assets; net working capital = current assets − current liabilities.
• Operating cycle = raw material days + work-in-progress days + finished goods days + debtors days.
• Net operating cycle = operating cycle − creditors days.
• Estimation sums: value stock, debtors and cash at the basis the question states.
• Conservative policy holds more current assets, so lower risk and lower return; aggressive policy does the opposite.
• Matching approach funds permanent needs with long-term funds and temporary needs with short-term funds.
• Cash management aims to balance liquidity and profitability; know the Baumol and Miller-Orr ideas.
• Receivables depend on credit policy, credit period, discount and collection effort.
• Judge a credit change by comparing extra profit with extra cost of funds and bad debts.
• EOQ = √(2AO ÷ C), where A is annual usage, O is ordering cost per order and C is carrying cost per unit.
• Reorder level = maximum usage × maximum lead time.
• ABC analysis gives tight control to high-value items and simple control to low-value items.

Common mistakes

• Using total sales for the receivables period even when credit sales are given. Fix: Read for the words credit sales. Cash sales never create receivables, so exclude them.
• Forgetting to subtract the creditors' period when asked for the cash conversion cycle. Fix: Remember that operating cycle ends at cash collection, while cash conversion cycle also deducts the credit taken from suppliers.
• Including depreciation in the cost used for stock and debtors. Fix: Remove depreciation from overheads before you value stock, WIP and debtors. Do this unless the question says to include it.
• Valuing work-in-progress at full cost. Fix: Use the completion percentage for labour and overheads. Take material at 100% if all material is issued at the start.
• Saying the conservative policy is cheaper because it is safe. Fix: Remember that conservative means low risk but higher cost, since long-term funds cost more and may lie idle.
• Treating matching and hedging as different approaches. Fix: Write that the matching approach is also called the hedging approach. Both match the maturity of funds with the life of the asset.
• Including depreciation or provisions as cash payments in the cash budget. 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. Fix: Shift each month's sales by the credit period. Note the timing before you start.
• Computing the investment in receivables at selling price and charging interest on it. Fix: Multiply average receivables by the variable cost ratio (or total cost ratio if the question says so) before applying the required return.
• Using 2 ÷ 100 instead of 2 ÷ 98 in the cost of cash discount. Fix: The customer pays 98 to get use of 98 for the extra days. Use Discount ÷ (100 − Discount).

Exam tips

• Write the definitions of gross and net working capital in the first two lines of any theory answer. Examiners look for the formula.
• In numerical questions, show the daily figure for each item. Marks are often given for each period even if the final total is wrong.
• Always state the days basis you used and the base for each period, especially when the question is silent.
• End numerical answers with one line of interpretation. A shorter cycle means less cash blocked.
• For classification questions, a neat list of permanent versus temporary working capital with one example each earns easy marks.
• Draw the statement format first: current assets on one side, current liabilities on the other, then net working capital. Fill each line with its working note.
• Always list your assumptions, such as even production, sales on credit, or debtors at cost. Examiners give marks for them when data is missing.
• In theory questions, link each factor to its effect. For example, a longer operating cycle raises the need, and longer supplier credit lowers it.