CMA Intermediate · Financial Management and Business Data Analytics

Receivable Management: formula sheet

Full chapter guide

Key formulas

Average receivables: Average receivables = Credit sales per day × Average collection period (days); Use credit sales only. Cash sales do not create receivables. Use 365 days unless the question says 360.
Receivables turnover: Receivables turnover = Net credit sales ÷ Average trade receivables; Average collection period = Days in year ÷ Receivables turnover.
Investment in receivables: Investment in receivables = Average receivables × (Variable cost ÷ Sales); Use cost-based investment when the question asks for funds actually blocked. Use the sales value only if the question says so.
Cost of carrying receivables: Carrying cost = Investment in receivables × Required rate of return; The rate is the firm's cost of funds or required return, as given.
Incremental profit from credit: Incremental contribution = Extra sales × (Contribution ÷ Sales); Fixed costs are ignored if they do not change. Bad debts and extra costs are deducted from this.
Net benefit of a credit policy: Net benefit = Incremental contribution − Carrying cost − Bad debts − Administration and collection costs; Accept the policy if the net benefit is positive.
Incremental contribution: Incremental sales × Contribution margin ratio (P/V ratio); Contribution ratio = 1 − variable cost ratio. Fixed costs are ignored if they stay unchanged.
Average collection period (weighted): Σ (% of customers in each group × days taken by that group); Used when some customers take the discount and others pay on the due date.
Investment in receivables: (Annual credit sales ÷ days in year) × Average collection period × Cost ratio; Use the variable cost ratio for incremental decisions unless the question says otherwise. Use 360 or 365 days as the question specifies.
Carrying cost of receivables: Investment in receivables × Required rate of return; Take the incremental or reduced investment, depending on the question.
Incremental bad debts: Bad debts under new policy − Bad debts under old policy; Apply each policy's bad debt rate to the sales it relates to, as the question states.
Cost of cash discount: Sales × % of customers taking the discount × Discount rate; Apply the discount only to sales paid by customers who actually take it.
Net benefit of a policy change: Incremental contribution − Incremental bad debts − Incremental carrying cost − Incremental collection cost − Discount cost; Accept the change if the net benefit is positive. Where a policy reduces receivables, the carrying cost saved is added.
Credit score: Score = Σ (weight × rating) for all factors; Weights usually add to 100% or 1. Compare the total with the cut-off score given in the question.
Expected bad debt: Expected bad debt = Credit sales × Probability of default; If the question gives a percentage of sales as bad debt, use it directly. Use sales value, not cost, unless told otherwise.
Carrying cost of receivables: Cost = Average receivables at cost × Required rate of return, where Average receivables = Credit sales × Collection period ÷ 365; Use cost of sales (variable cost) as the investment base if the question says so. Use 360 days only if the question says so.
Net benefit of granting credit: Net benefit = Contribution (or profit) on extra sales − Bad debts − Carrying cost − Collection cost; Grant credit if the net benefit is positive. For expected value problems, weight each outcome by its probability.
Expected profit on a credit order: Expected profit = p × (Sales − Cost) − (1 − p) × Cost, where p = probability of payment; This applies when a non-paying customer pays nothing and the firm loses the whole cost. Adjust if part payment is expected.
Cost of cash discount (annualised, simple): [d ÷ (100 − d)] × [365 ÷ (credit period − discount period)]; d is the discount percentage. For 2/10 net 30: 2/98 × 365/20 = 37.24%. Use 360 days if the question says so.
Cost of cash discount (effective, compound): (1 + d ÷ (100 − d))^(365 ÷ (N − D)) − 1; N is the credit period and D the discount period. Use only if the question asks for the effective rate. For 2/10 net 30 it is about 44.6%.
Average receivables: (Credit sales ÷ days in year) × average collection period; This gives receivables at selling price.
Investment in receivables: Average receivables × variable cost ratio; Use the total cost ratio only if the question tells you to.
Cost of carrying receivables: Investment in receivables × required rate of return; Compute it for both policies and take the difference.
Bad debts: Bad debt % × credit sales; Check whether the percentage applies to all sales or only to the incremental sales.
Cost of discount allowed: Discount % × proportion of customers availing × credit sales; Applied to the sales figure of the proposed policy.
Net incremental profit: Incremental contribution − incremental carrying cost − incremental bad debts − discount cost; Positive means accept the proposal. Savings in carrying cost or bad debts are added.
Receivables turnover ratio: Receivables turnover = Net credit sales ÷ Average receivables; Use credit sales only. If only closing receivables are given, use them.
Average collection period (ACP): ACP = (Receivables ÷ Net credit sales) × Number of days in the year; Equals Days ÷ Receivables turnover. Use 365 days unless the question says 360.
Average daily credit sales: Credit sales per day = Annual credit sales ÷ 365; Receivables = ACP × credit sales per day.
Bad debt ratio: Bad debt ratio = (Bad debts ÷ Credit sales) × 100; Compare with the target set in the credit policy.
Ageing percentage: % of age group = (Amount in group ÷ Total receivables) × 100; Used in the ageing schedule. The percentages should add up to 100.
Expected bad debts from ageing: Provision = Σ (Amount in each age group × Expected default %); Default rates rise with age of the debt.
Advance by factor: Advance = Invoice value × Advance % (after any reserve/factor holdback); The reserve (balance) is paid to the client on collection, less charges.
Factoring commission: Commission = Invoice value × Commission rate %; Charged on the full invoice value, not only on the advance.
Interest on advance: Interest = Advance × Rate % × Days ÷ 365; Charged on the advance actually drawn. If commission is deducted upfront, charge interest on the advance left after that deduction. Interest deducted upfront is not itself charged with interest unless the question says so. Use the days or rate the question gives.
Net benefit of factoring: Net benefit = Savings (admin cost + bad debts avoided + financing cost saved) − Factoring cost (commission + interest); Positive means accept factoring. Compare on the same annual basis. Financing cost saved is on the fall in the firm's own investment in receivables, that is, old receivables less (new receivables − advance).
Effective cost of factoring: Effective cost % = (Commission + Interest − Savings in administration and bad debts) ÷ (Advance − Interest if deducted upfront) × 100; Savings of financing cost are not deducted, because the advance is the financing being costed. Use annual figures and compare with the bank borrowing rate.
Average receivables: Receivables = Credit sales × Collection period ÷ 365; Use 360 if the question says so.

Quick revision

Receivables arise from credit sales; the aim is higher value, not the highest sales.
Credit policy variables: credit standards, credit period, cash discount and collection effort.
Looser standards raise sales but also bad debts and investment in receivables.
Investment in receivables is measured at cost (or variable cost for extra sales), not at sales value, unless the question says otherwise.
Average collection period = Receivables ÷ Credit sales per day.
Receivables turnover = Credit sales ÷ Average receivables.
Carrying cost = Investment in receivables × Required rate of return.
Decide by incremental benefit: accept a policy only if net benefit is positive.
Cost of forgoing a cash discount, approx. = Discount % ÷ (100 − Discount %) × 365 ÷ (Credit period − Discount period).
Ageing schedule groups dues by how long they are outstanding, to spot slow payers.
Factoring: with recourse leaves bad-debt risk with you; without recourse transfers it to the factor.
Compare factoring cost (fee plus interest) with savings in collection cost, bad debts and funding.

Common mistakes

Taking receivables at sales value when asked for the funds blocked Fix: Multiply by the variable cost ratio when cost data is given, because the firm has invested only its cost, not its profit.
Including cash sales in receivables calculations Fix: Use only credit sales. Remove cash sales before computing average receivables.
Calculating receivables investment on sales value when the question calls for variable cost. Fix: Multiply sales by the variable cost ratio before applying days ÷ 360, unless the question states that sales value should be used.
Applying the new bad debt percentage only to incremental sales when it applies to all sales. Fix: Read the wording. If the new rate applies to total sales, compute total new bad debts and subtract total old bad debts.
Listing the 5 Cs without explaining them Fix: Write one line per C saying what is judged and how, for example Capacity is judged from cash flows and liquidity ratios.
Using sales value instead of cost to compute carrying cost Fix: Check if the question gives variable cost or cost of sales. The firm's investment in receivables is at cost, so use it when given.
Measuring investment in receivables at selling price Fix: Multiply average receivables by the variable cost ratio unless the question says otherwise. Then apply the required return.
Applying the discount to all customers Fix: Discount cost = discount % × share of customers availing × credit sales.
Using total sales instead of credit sales in ACP Fix: Read the question for cash sales and deduct them. Receivables arise only from credit sales.
Mixing 360 and 365 days Fix: Use the number of days stated. If none is stated, use 365 and say so.

Exam tips

For theory questions, use headed points: meaning, benefits, costs, factors, objective. This gets step marks easily.
In MCQs, remember that carrying cost is a cost of funds, so it depends on investment in receivables and the required return.
Check whether the question wants receivables at sales value or at cost before you calculate.
State the days in the year you have used. This protects marks if the examiner uses a different basis.
End a numerical answer with a one-line decision and reason.
MCQs often test the 5 Cs (Character, Capacity, Capital, Collateral, Conditions) or the direction of change. Learn that tight standards mean lower sales and lower bad debts, and loose standards mean the opposite.
In written answers, always show a clear incremental statement with a decision line. Step marks are given for each component such as contribution, bad debts and carrying cost.
State your assumptions at the top: 360 or 365 days, cost basis for receivables and treatment of fixed costs. This protects marks if the examiner expects a different convention.