CA Intermediate · Financial Management and Strategic Management

Management of Receivables: formula sheet

Full chapter guide

Key formulas

Receivables (average debtors): Average receivables = Credit sales per day × Average collection period; Use sales per day on a 365-day or 360-day year as the question states. Use only credit sales.
Investment in receivables: Investment in receivables = Average receivables × (Variable cost ÷ Sales); Use cost-based investment when the question asks for funds actually blocked. Use selling price only if told to.
Cost of carrying receivables: Carrying cost = Investment in receivables × Required rate of return; This is the capital or opportunity cost. Add administration and collection costs separately.
Bad debt cost: Bad debts = Credit sales × Bad debt %; Apply the percentage to the sales figure the question gives, usually credit sales.
Net benefit of credit: Net benefit = Additional contribution − (Carrying cost + Bad debts + Other credit costs); Contribution = Sales − Variable cost. Fixed cost is ignored if it does not change.
Credit terms notation: a/b, net c means a% discount if paid within b days, otherwise full amount by day c; Example: 2/10, net 45 means 2% discount within 10 days, full payment by day 45.
Average receivables: Average receivables = Credit sales per day × Average collection period; Use credit sales, not total sales, unless told all sales are on credit. Use 360 or 365 days as the question states.
Cost of carrying receivables: Carrying cost = Investment in receivables × Required rate of return; Investment in receivables is usually taken at cost (variable cost, or total cost as the question directs), not at sales value.
Incremental analysis of a policy change: Net benefit = Incremental contribution − Incremental bad debts − Incremental carrying cost − Incremental collection cost − Discount cost; Accept the change only if net benefit is positive. Add or drop terms as the question gives them.
Cost of giving up a cash discount (approximate): Cost = [Discount % ÷ (100 − Discount %)] × [360 ÷ (Credit period − Discount period)]; Used to judge whether a discount is worth offering or taking.
Incremental contribution: Increase in sales × P/V ratio (or contribution per unit × extra units); Use when fixed costs stay constant. If the question gives only profit margin on sales and says fixed costs are unchanged, convert carefully to contribution.
Average receivables: Credit sales ÷ Receivables turnover = Credit sales × Collection period ÷ 365 (or 360 as stated); Use the day count given in the question.
Investment in receivables: Average receivables × (Variable cost ÷ Sales), or total cost basis if the question says so; Follow the question's wording. The commonly used base is the cost of sales, not the sales value.
Cost of funds locked in receivables: Investment in receivables × Required rate of return; Compute for the present and the proposed policy, then take the difference.
Bad debts: Credit sales × Bad debt %; Bad debts are on sales value. Use the rate given for each policy.
Cash discount cost: Sales × % of customers availing × Discount %; Discount is on sales value of the customers who take it.
Net incremental benefit: Incremental contribution − Incremental cost of funds − Incremental bad debts − Incremental other costs − Discount cost; Accept the proposal if positive.
Annualised cost of cash discount: [Discount % ÷ (100 − Discount %)] × [365 ÷ (Credit period − Discount period)]; Compare this with the firm's cost of funds or return. A simple (non-compounded) approximation.
Average collection period / DSO: DSO = (Average receivables ÷ Credit sales) × Number of days; Use credit sales only. Use 365 days unless the question says 360. If only one receivables balance is given, use that balance.
Receivables turnover ratio: Receivables turnover = Credit sales ÷ Average receivables; Number of times receivables are collected in the year.
DSO from turnover: DSO = Number of days ÷ Receivables turnover; Gives the same answer as the direct formula.
Ageing schedule share: Share of a band (%) = Receivables in band ÷ Total receivables × 100; Compare the older bands with the credit terms.
Collection matrix: Collection in a month = Σ (Sales of month t−k × % collected after lag k), with k = 0, 1, 2, ...; Lag 0 is the share of the month's own sales collected in the month of sale. Add collections from each month's sales falling in the month asked.
Receivables balance from DSO: Receivables = (DSO × Credit sales) ÷ Number of days; Use when DSO is given and you need the investment in receivables.
Advance by factor: Advance = (Receivables × Advance %) − Factoring commission − (sometimes) interest deducted upfront; Read the question: advance % is usually applied on invoice value, then commission is deducted. Check whether interest is deducted in advance or paid later.
Factoring commission: Commission = Invoice value × Commission rate; Applied on the total receivables factored, not only on the advance.
Interest on advance: Interest = Advance × Rate × (Days ÷ 365 or 360); Use the day count given. If the interest rate is annual and the period is the average collection period, convert it to days. For a yearly net benefit, charge a full year of interest on the advance balance.
Net benefit of factoring: Net benefit = Savings (admin cost + bad debts avoided + interest saved on funds released) − Cost (commission + interest on advance); Accept the offer if net benefit is positive. Interest on the advance is always a cost. The interest saved on funds released from receivables is a separate saving. Show both lines.
Effective cost of factoring (annual): Effective cost = [(Commission + Interest − Savings, if the question gives any) ÷ Net advance received] × 100, annualised; If the question gives savings, deduct them from the cost before dividing. If it gives none, use gross cost (commission + interest). Divide by the net advance actually received, then annualise for the period. State clearly which version you used.
Recourse vs non-recourse: Non-recourse: factor bears bad debt. Recourse: client bears bad debt.; Non-recourse commission is higher because the factor takes credit risk.
Discount on a bill: Discount = Bill amount × Discount rate × (Days to maturity ÷ 365); Use 360 days only if the question says so. Days run from the discounting date to the due date.
Net cash received: Net proceeds = Bill amount − Discount − Other charges; Other charges include processing fees, if given.
Effective annual cost of discounting: Cost = (Discount + Charges) ÷ Net proceeds × (365 ÷ Days); This simple form divides by net proceeds, not the bill amount. If asked for compounded cost, use (1 + Cost per period)^(365 ÷ Days) − 1.
Advance under invoice discounting: Advance = Invoice value × Advance percentage; Interest is then charged on the advance, not on the full invoice.
Net benefit of credit insurance: Net benefit = Expected bad debt loss covered − Premium (plus any interest or admin savings); Cover applies only to the insured percentage of the loss.

Quick revision

Receivables arise from credit sales and tie up funds, so every extra rupee of credit has a financing cost.
Credit policy variables: credit standards, credit period, cash discount and collection effort.
Accept a policy change only if incremental contribution exceeds incremental costs.
Investment in receivables is usually measured on cost, not sales value, when the question gives cost data.
Cost of extra receivables = extra investment × required rate of return.
Cash discount cuts the average collection period but costs the discount given.
DSO = (Receivables ÷ Credit sales) × number of days in the period.
Ageing analysis groups debtors by how long they are overdue, so it shows where collection is slipping.
Factoring: a factor buys receivables and may offer finance, collection and credit protection; with non-recourse the factor bears bad debt risk.
Forfaiting: non-recourse discounting of medium-term export receivables, usually backed by a bank guarantee or similar.
Bills discounting turns a bill of exchange into cash before maturity at a discount charge.
Credit insurance covers loss from customer default and is a protection tool, not a collection tool.

Common mistakes

Using total sales instead of credit sales to find receivables. Fix: Underline the credit sales figure or percentage. Cash sales never create debtors.
Charging the required return on sales value of receivables instead of cost. Fix: Multiply by variable cost ÷ sales when the question asks for investment, unless it says to use sales value.
Valuing the investment in receivables at sales value Fix: Convert to cost (variable cost or total cost, as directed) before applying the required return, because only the cost is actually blocked.
Charging bad debts or carrying cost on the whole sales, not the incremental part Fix: Take the difference between proposed and present for every cost line.
Using full sales value instead of cost to compute investment in receivables. Fix: Convert receivables to the cost invested (variable or total cost as stated) before applying the required return.
Treating extra sales as extra profit. Fix: Take only incremental contribution. Fixed costs are added only if the question says they change.
Using total sales instead of credit sales in the DSO formula. Fix: Scan for cash sales or the percentage of credit sales. Deduct cash sales before computing.
Using the wrong number of days, such as 365 when the question says 360. Fix: Underline the days basis in the question and use it throughout.
Applying commission on the advance instead of the invoice value. Fix: Commission is on the total invoice value unless the question states otherwise. Interest is on the advance.
Forgetting to deduct the reserve and commission to get the actual cash received. Fix: Always show Invoice value, less reserve, less commission, less interest (if upfront) to reach net advance.

Exam tips

Learn the five costs (capital, administration, collection, delinquency, default) as a list. Questions often ask you to name or explain them.
In theory answers, always mention the trade-off between profitability and liquidity or risk.
In numerical questions, state your assumption on the 360 or 365-day year if the question is silent.
Read for words like 'investment at cost' versus 'at sales value' before you start.
MCQs carry no negative marking, so always attempt every one.
In theory answers, use the headings credit standards, credit period, cash discount and collection policy, and give effect on sales, receivables and bad debts for each.
For the 5 Cs, write the name and a one-line meaning for each. If a case is given, link each C to a fact in it.
Always state the day basis (360 or 365) and whether investment is at sales or cost value. Follow the question's instruction.