ACCA Applied Skills · Financial Management

Management of inventories, accounts receivable, accounts payable and cash: formula sheet

Full chapter guide

Key formulas

Inventory days: Inventory days = (Inventory ÷ Cost of sales) × 365; For a manufacturer you may split into raw materials (÷ purchases or material usage), WIP (÷ cost of production) and finished goods (÷ cost of sales).
Receivable days: Receivable days = (Trade receivables ÷ Credit sales) × 365; Use credit sales, not total sales, if the data gives both. Use revenue only if no split is given.
Payable days: Payable days = (Trade payables ÷ Credit purchases) × 365; Use credit purchases if given. Otherwise use cost of sales as an approximation and state the assumption.
Cash operating cycle: Cycle = Inventory days + Receivable days − Payable days; For a manufacturer, add raw material, WIP and finished goods days, then add receivable days and subtract payable days.
Working capital: Working capital = Current assets − Current liabilities; An amount at a point in time, not a period.
Current ratio and quick ratio: Current ratio = Current assets ÷ Current liabilities; Quick ratio = (Current assets − Inventory) ÷ Current liabilities; Rules of thumb such as 2:1 and 1:1 vary by industry. Do not treat them as fixed targets.
Total working capital: Net working capital = Current assets − Current liabilities; Used to compare the level of investment under different policies.
Split of current assets: Total current assets = Permanent current assets + Fluctuating current assets; Permanent is the minimum level needed all year; fluctuating is the seasonal or cyclical extra.
Matching policy: Long-term finance = Non-current assets + Permanent current assets; Short-term finance = Fluctuating current assets; A benchmark. Aggressive uses more short-term finance than this; conservative uses more long-term finance.
Current ratio: Current ratio = Current assets ÷ Current liabilities; A higher ratio normally suggests a more conservative position.
Cost of a financing mix: Annual finance cost = Σ (amount of funds × interest rate); Use this to compare policies in numerical questions. Cost of each source depends on the rates given.
Economic order quantity: EOQ = √(2 × Co × D ÷ Ch); Co = cost per order, D = annual demand in units, Ch = holding cost per unit per year. D and Ch must use the same time period (annual).
Total annual ordering and holding cost: Total cost = (D ÷ Q) × Co + (Q ÷ 2) × Ch; Q is the order size. Average stock is Q ÷ 2 because stock falls steadily from Q to zero.
Total annual cost including purchases: Total cost = D × P + (D ÷ Q) × Co + (Q ÷ 2) × Ch; P is the price per unit at that order size. Use this form for bulk discount decisions.
EOQ cost balance: At EOQ: (D ÷ Q) × Co = (Q ÷ 2) × Ch; A quick check on your answer. If the two costs differ at EOQ, something is wrong.
Reorder level (no buffer): Reorder level = usage per period × lead time; With uncertain demand or lead time, many questions use maximum usage × maximum lead time.
Reorder level with buffer stock: Reorder level = average usage × average lead time + buffer stock; Use whichever approach the question's data points to.
Receivable days: Receivable days = (Trade receivables ÷ Credit sales) × 365; Use credit sales if given, otherwise revenue. Use the days in the year the question uses (365 unless told otherwise).
Average receivables from days: Receivables = Annual credit sales × days ÷ 365; Used to find the change in receivables when a policy changes. Work out each customer group separately.
Financing cost or saving of receivables: Finance cost = Receivables × interest rate; Use the rate at which the company borrows (or earns if cash is surplus). A fall in receivables saves interest.
Annual cost of early settlement discount (compound): Annual cost = [100 ÷ (100 − d)]^(365 ÷ t) − 1, where d = discount % and t = days of credit given up; t = normal credit period − discount period. Compare with the company's cost of short-term finance.
Approximate (simple) annual cost of discount: Approx. cost = [d ÷ (100 − d)] × (365 ÷ t); Quicker but lower than the compound figure. Use compound unless the question says otherwise.
Cost of discount in money: Discount cost = Discount % × sales paid early; Only sales that take the discount count.
Factoring net benefit: Net benefit = admin savings + bad debt savings + finance saving − factor fees − extra finance charges; Finance saving comes from lower receivables and from replacing overdraft with cheaper or dearer factor finance.
Simple cost of forgoing the discount (per period): d ÷ (100 − d); d is the discount % . For 2% this is 2 ÷ 98 = 2.04%. This is the cost over the extra credit period, not a year.
Annualised cost (compound): (1 + d ÷ (100 − d))^(365 ÷ N) − 1; N is the days of extra credit gained by not taking the discount (final due date minus discount date). This is the preferred and more accurate method.
Annualised cost (simple): d ÷ (100 − d) × 365 ÷ N; Quick approximation. It gives a lower figure than the compound method and understates the true cost. Use compound unless the question asks for simple.
Payables days: Trade payables ÷ Cost of sales (or credit purchases) × 365; Use purchases if given. Use year-end payables unless an average is requested.
Decision rule: Take the discount if annualised cost of forgoing it > cost of short-term finance; If the cost of finance is higher, it is cheaper to forgo the discount and pay later.
Baumol optimal sale size: Q = √(2 × C × S ÷ i); C = cost per transaction, S = total cash needed for the period, i = interest rate for the same period (the opportunity cost of holding cash). Q is the amount of securities to sell each time.
Baumol total cost: Total cost = (Q ÷ 2) × i + (S ÷ Q) × C; Holding cost on the average balance (Q ÷ 2) plus transaction costs. At the optimum Q the two parts are equal, which is a quick check.
Number of transactions: Transactions = S ÷ Q; Use it to find the transaction cost part of the total cost.
Miller-Orr spread: Spread = 3 × (¾ × transaction cost × variance of daily cash flows ÷ daily interest rate)^(1/3); Use a daily interest rate when the variance is of daily flows. Variance = (standard deviation)². The cube root is the 1/3 power.
Miller-Orr upper limit: Upper limit = lower limit + spread; The lower limit is set by management, for example a safety buffer or overdraft facility. It is a given in the question.
Miller-Orr return point: Return point = lower limit + (spread ÷ 3); At the upper limit, buy securities to bring cash back to the return point. At the lower limit, sell securities to return to it.
Annual rate to daily rate: Daily rate = annual rate ÷ 365 (simple), or (1 + annual rate)^(1/365) − 1 (compound); Follow the question's instruction. If none is given, state the method you use.
Simple interest for part of a year: Interest = Amount × annual rate × (months ÷ 12); Use for deposits, overdrafts and loans of less than a year. Use days ÷ 365 if days are given.
Treasury bill yield (discount instrument): Return over the period = (Face value − Price paid) ÷ Price paid; Divide by the price paid, not the face value. Annualise by scaling with 12 ÷ months, or compound if the question asks for the effective rate.
Effective annual rate (EAR): EAR = (1 + r)^n − 1, where r is the return per period and n is the number of periods in a year; Use it to compare instruments with different terms or compounding.
Net benefit of investing: Net gain = Interest earned − Costs (fees, lost interest or higher borrowing cost); Compare with the alternative of simply holding cash or repaying an overdraft.
Risk, return and liquidity rule: Higher return ⇒ usually lower liquidity and/or higher risk; A general tendency, not a law. Use it to justify a choice in written answers.

Quick revision

Cash operating cycle = inventory days + receivable days − payable days.
Inventory days use average or closing inventory ÷ cost of sales × 365; receivable days use receivables ÷ credit sales × 365; payable days use payables ÷ credit purchases (or cost of sales) × 365.
EOQ = √(2 × Co × D ÷ Ch); at the EOQ, annual ordering cost equals annual holding cost.
With a bulk discount, compare total annual cost (purchase + ordering + holding) at the EOQ and at each discount quantity.
A conservative policy holds high working capital and uses long-term finance; an aggressive policy holds low working capital and uses more short-term finance.
Annual cost of forgoing a discount = (1 + d ÷ (100 − d))^(365 ÷ n) − 1; take the discount if this is higher than your cost of borrowing.
Factoring can speed up cash and cut admin costs, but it costs fees and interest and may affect customer relationships.
Reducing receivable days frees up cash; the saving is the reduction in receivables × the cost of finance.
Cash forecasts show timing only: leave out non-cash items such as depreciation.
Overtrading means growth without enough finance, so look for a rising need for cash and a strained overdraft.
Surplus cash should be placed with attention to liquidity, risk and return; shortfalls can be met by overdrafts, loans or tighter working capital.
In a Section C answer, state the calculation, then give a recommendation and one or two risks.

Common mistakes

Adding payable days instead of subtracting them. Fix: Remember payables are cash you have not paid yet. They shorten the cycle, so subtract.
Using revenue for inventory days and payable days. Fix: Use cost of sales (or purchases) for inventory and payables. Revenue is for receivables only.
Mixing up investment policy and financing policy. Fix: Ask first: is this about how much is held, or how it is paid for? Answer only that part, and treat the other separately.
Saying conservative financing means less long-term finance. Fix: Conservative financing means more long-term finance, which is safer but costlier. Aggressive means more short-term finance.
Using Q instead of Q ÷ 2 for holding cost. Fix: Always write (Q ÷ 2) × Ch. Then check that ordering cost equals holding cost at EOQ.
Mixing time periods, such as monthly demand with annual holding cost. Fix: Convert everything to annual figures before using the formula, and say so in your working.
Calculating the discount cost as d ÷ 100 without annualising. Fix: Divide by (100 − d), then scale by 365 ÷ t. Always compare annual with annual.
Using the wrong number of days saved, for example using the full credit period instead of the credit period minus the discount period. Fix: Write t = normal days − discount days before you start. For 2/10 net 30, t = 20.
Using d ÷ 100 instead of d ÷ (100 − d). Fix: The discount is based on the invoice price. You actually pay 100 − d if you pay early, so the cost is measured on that smaller amount.
Using the full credit period as N. Fix: N is only the extra time gained by not taking the discount. For 2/10 net 30, N is 20 days, not 30.

Exam tips

In objective tests, read which figure each ratio needs. Wrong denominators are the usual trap.
Use 365 days unless told otherwise and keep decimals until the final answer.
In written answers, give the calculation first, then comment on causes, effects and actions. Calculation alone scores little on the discussion marks.
For overtrading, link each symptom to the data given, and give remedies as well as symptoms.
Remember that industry context matters. Say whether a change is good or bad for that type of business.
Always define permanent and fluctuating current assets before classifying a policy. It earns marks in written answers and helps you in objective tests.
In objective questions, work out the matching level of long-term finance first. Then compare it with the actual figure.
In Section C, give both sides: return and cost against risk and flexibility. Then apply it to the scenario, such as seasonal sales.