Payable Management: formula sheet

Key formulas

Payables deferral period (PDP)

PDP = Average trade payables ÷ Credit purchases per day = (Average payables ÷ Annual credit purchases) × 365

Use credit purchases, not total purchases. If only cost of goods sold is given, state that you are using it as a proxy for purchases. Use 360 days if the question says so.

Payables turnover ratio

Payables turnover = Annual credit purchases ÷ Average trade payables

PDP = days in year ÷ payables turnover. Average payables = (opening + closing) ÷ 2 when both are given.

Cash conversion cycle

CCC = Inventory period + Receivables period − Payables deferral period

Operating cycle = inventory period + receivables period. CCC = operating cycle − PDP.

Net working capital

NWC = Current assets − Current liabilities

Higher payables raise current liabilities and lower NWC for the same current assets. This means less funding is needed.

Cost of foregoing a cash discount (approximate, annualised)

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

Example terms: 2/10 net 30. Covered in detail in the cash discount topic.

Cost of not taking the cash discount (simple)

Cost = [D ÷ (100 − D)] × [365 ÷ (Credit period − Discount period)] × 100

D is the discount in % of invoice price. Credit period is the net period in days. Some questions use 360 days; follow the question.

Effective (compound) annual cost

Effective cost = [1 + D ÷ (100 − D)]^(365 ÷ N) − 1

N is credit period minus discount period. Use this when the question asks for the effective or compounded rate.

Amount payable if discount is taken

Payment = Invoice price × (1 − D ÷ 100)

This is the true amount borrowed if you do not take the discount.

Decision rule

Take the discount if cost of forgoing > cost of alternative short-term finance

If equal, you are indifferent. If lower, pay on the last day of the net period.

Cost of foregoing discount (simple, annualised)

[d ÷ (100 − d)] × [365 ÷ (N − D)]

d = discount %, N = credit period in days, D = discount period in days. Use 360 days if the question says so.

Cost of foregoing discount (compound, effective)

[1 ÷ (1 − d)]^(365 ÷ (N − D)) − 1

d as a decimal. Use it only when the question asks for the effective or compounded rate.

Amount paid if discount is taken

Invoice value × (1 − d)

This is the amount you need to arrange (or borrow) on day D.

Net benefit of taking discount with borrowing

Discount amount − Interest on (invoice − discount) for (N − D) days

Interest = Amount borrowed × bank rate × (N − D) ÷ 365. A positive result means take the discount.

Decision rule

Cost of foregoing > Cost of funds → take discount; otherwise forgo and pay on day N

Compare like with like: both rates annual, both on the same day basis.

Days payable outstanding (DPO)

DPO = (Average trade payables ÷ Credit purchases) × 365

Use cost of goods sold if credit purchases are not given. State the basis you use. Use 360 days if the question says so.

Payables turnover ratio

Payables turnover = Credit purchases ÷ Average trade payables

DPO = 365 ÷ payables turnover. A lower turnover means slower payment.

Cost of foregoing cash discount

Cost = [d ÷ (100 − d)] × [365 ÷ (Credit period − Discount period)]

d is the discount percentage. Credit period is the final due date in days. Simple annual cost.

Cost of foregoing discount when payment is delayed to a later day

Cost = [d ÷ (100 − d)] × [365 ÷ (Days actually taken − Discount period)]

This gives only the implicit cost of the supplier credit when the discount is forgone. Paying later spreads the same discount over more days, so the annual percentage falls. Late-payment penalties, lost goodwill and other costs of stretching are not included and must be added separately.

Cash released by stretching

Cash released = (Daily credit purchases) × (Extra days taken)

Daily purchases = annual credit purchases ÷ 365.

Annualised cost of early payment or discounting

Cost % = (Discount ÷ Amount received) × (365 ÷ Days financed) × 100

Use this to compare the supplier's cost of early payment. The amount received is the invoice value less the discount. This simple form ignores compounding.

Discount charge on a bill

Discount = Bill amount × Discount rate % × Days to maturity ÷ 365

Net proceeds = Bill amount − Discount (less any other fee). Use the day count given in the question.

Cost of foregoing a cash discount

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

d is the discount percentage. Compare it with the cost of bank borrowing before deciding whether to take the discount.

Key distinction

Factoring = supplier-led, receivables sold, priced on the credit risk of the supplier's customers and the arrangement | Reverse factoring = buyer-led, approved invoices, priced on the buyer's (stronger) credit rating

Write this in theory answers on the difference.

Quick revision

• Payables are a spontaneous, usually low-cost source of short-term finance.
• Credit terms 2/10 net 30 mean 2% discount if paid by day 10, otherwise pay in full by day 30.
• Cost of foregoing discount = [d ÷ (100 − d)] × [365 ÷ (N − D)], with d as discount % and N − D as days of extra credit.
• Take the discount if the cost of foregoing it is higher than your borrowing cost.
• Forgo the discount only if the cost of foregoing it is lower than the cheapest alternative finance.
• A longer credit period with the same discount lowers the annual cost of foregoing the discount.
• Stretching payables means paying after the due date, and it can cost you supplier trust, credit rating and future discounts.
• A longer payables period shortens the cash conversion cycle.
• Reverse factoring is buyer-led: the supplier gets early payment against the buyer's approved invoices.
• In reverse factoring, the financier relies on the buyer's credit strength, so the supplier can get cheaper finance.
• Write the comparison and the decision line in every numerical answer, since it earns marks.
• Use the number of days stated in the question, 360 or 365, and do not mix them.

Common mistakes

• Using sales or total purchases instead of credit purchases to compute PDP. Fix: Payables relate to credit purchases. Use cost of goods sold only when purchases are not given, and say so.
• Adding PDP to the operating cycle instead of subtracting it. Fix: Remember that payables are a source of finance, so they reduce the cycle: CCC = inventory + receivables − payables.
• Dividing the discount by the invoice price instead of by the discounted price (using D ÷ 100). Fix: The amount you actually owe if you pay early is 100 − D. Always use D ÷ (100 − D).
• Using the full net period (30 days) instead of the extra days (20 days) for annualising. Fix: Subtract the discount period from the net period. Use N = net days − discount days.
• Using d ÷ 100 instead of d ÷ (100 − d). Fix: Always write the fraction as 2/98, 3/97 and so on. The base is what you pay on the discount date.
• Using the full credit period N in the annualising factor. Fix: The extra credit starts after the discount period. Use N − D, here 45 − 10 = 35 days.
• Treating stretched payables as free finance. Fix: Always list lost discount, penalty, price rise and rating impact, and cost them where numbers are given.
• Using the wrong denominator for DPO. Fix: Use credit purchases where given. Otherwise use cost of goods sold and say so.
• Saying reverse factoring is the same as factoring with a different name. Fix: Remember the initiator and pricing basis: buyer-led and buyer's credit in reverse factoring.
• Calculating the cost on the invoice amount instead of the amount received. Fix: Divide the discount by the net amount actually received when computing financing cost.

Exam tips

• For a 'discuss' question, structure the answer as meaning, objectives, benefits and risks. This earns step marks even without numbers.
• In MCQs, check whether the question wants the effect on CCC. A longer payables period always shortens CCC when other periods are unchanged.
• Write the formula before substituting. Show average payables and purchases per day as separate lines.
• State the day basis (365 or 360) that you used, so a marker can follow your working.
• Add a one-line interpretation to every numerical answer. ICMAI expects comment, not just the figure.
• In MCQs, spot the terms first. Many questions give 2/10 net 30 and ask for the cost. Remember that the answer for this common term is about 37.24% with 365 days, or 36.73% with 360 days.
• Always show the formula, the value of N and the comparison with the borrowing rate. Step marks are given for each, even if the final figure slips.
• State your assumption on 360 or 365 days in one line when the question does not say.