Cost of payment terms: a share of the unit price

What 30/70 with an at 90 days is actually worth, expressed as a percentage of unit price.

Live result

Your schedule is worth 2.10 points of price more than theirs at 12% a year.

Present value, your offer97.90%
Present value, their offer100.00%
Worth to you2.10%
Cost to the supplier2.10%

Conceding their structure is worth it only if the price moves by more than that gap.

Their offer

Fast counteroffer

A preset changes their schedule only. Reset returns both offers, the rate and the two optional lenses to their opening values.

Schedule detailTheir offer100

Payment legs

Leg 1100%

paid on day

on order, fixed

Leg 20%

paid on day90days

100% allocated

Letter of credit

Your offer

Schedule detailYour offer30 / 40 / 30

Payment legs

Leg 130%

paid on day

on order, fixed

Leg 240%

paid on day60days

Leg 330%

paid on day150days

100% allocated

Letter of credit

What your money costs

Your annual cost of money12%

What it costs you to borrow, or what your cash earns elsewhere. Everything on this page moves with it.

The rest of your cycle

Days the goods sit as stock45days

Days your customer takes to pay60days

Prepay a deferred paymentOpen

A deferred payment undertaking has a maturity, and a bank may agree to pay before it. This works out what the early money costs, from a face amount, a maturity, a discount rate and the fees.

Face amount of the undertaking

Days to maturity90days

Rate the discounting bank quotes7.50%

Fees, all in

$250,000 at maturity in 90 days produces $244,381 today, once $4,419 of discount and $1,200 of fees come off. That is 2.2% of the face, or 9.1% a year on the money you brought forward.

Whether a bank will do this is not arithmetic. A bank named in a credit is not obliged to advance anything, prepayment is a matter of agreement, and the rate above is the one you were quoted rather than one this page knows.

What each structure is worth

97.90% faces 100.00%. The negotiable difference is 2.10 points of invoice price.

Structure: Your offer30 / 40 / 30
Their offer100
Present value: Your offer97.90%
Their offer100.00%
Worth to you: Your offer2.10%
Their offer0.00%
Cost to the supplier: Your offer2.10%
Their offer0.00%

Measure	Your offer	Their offer
Structure	30 / 40 / 30	100
Present value	97.90%	100.00%
Worth to you	2.10%	0.00%
Cost to the supplier	2.10%	0.00%

The same figure, read from each side of the table.

Trade price against termsOpen

Test the exact price move that balances their invoice against the two payment schedules already entered.

Price change on their offer0.00%

Negative lowers their invoice. Positive raises it. Payment dates and LC costs stay as entered below.

At an unchanged price, their price and terms cost 2.10 points more than your offer.

Invoice price: Your offer100.00%
Their offer100.00%
Terms PV: Your offer97.90%
Their offer100.00%
Price with terms: Your offer97.90%
Their offer100.00%
Gap against yours: Your offer0.00 pts
Their offer+2.10 pts

Measure	Your offer	Their offer
Invoice price	100.00%	100.00%
Terms PV	97.90%	100.00%
Price with terms	97.90%	100.00%
Gap against yours	0.00 pts	+2.10 pts

At the current schedules, their invoice needs to be 2.10% lower to balance your offer.

If the rate moves

Same schedules, priced at three annual rates three points apart.

1.61 pts

higher PV

Their price 1.61% lower

12%

current

2.10 pts

higher PV

Their price 2.10% lower

15%

2.58 pts

higher PV

Their price 2.58% lower

When the cash moves

Your offer moves 70% of the invoice beyond order and finishes on day 150. Theirs moves 0% beyond order and finishes on day 0.

Horizontal: days from order
Assumptions: Inventory and customer credit use the values entered above. Payable days come from each payment schedule.

Your offer pays on a weighted day 69 and their offer on day 0. With 45 days of stock and 60 days of customer credit, your cash is out for 36 days against 105 days, and the 69 days between them is the whole of what the schedule is worth in days.

Inspect who carries the invoiceOpen

Read the nominal schedule one week at a time. LC costs stay in the value calculation and are not added to these payment bars. This is schedule arithmetic, not a credit judgement.

Peak across the schedule

The largest gap is 70 points from day 0 until day 60. The supplier carries that much more of the invoice under your offer for 60 days.

Week in the scheduleWeek 8

Week 0 includes payments due on order. Each later week includes payments due by the end of its seventh day.

By week 8, your offer has paid 30% and theirs has paid 100%. Under your offer, the supplier carries 70 more points of the invoice at that point.

Paid by this week: Your offer30%
Their offer100%
Still unpaid: Your offer70%
Their offer0%
Next payment: Your offer40% · day 60
Their offerschedule complete

Measure	Your offer	Their offer
Paid by this week	30%	100%
Still unpaid	70%	0%
Next payment	40% · day 60	schedule complete

Here is the maths

Model version: 1.0

The formula, in words

Money paid later is worth less than money paid today, by the rate at which money costs you. Discounting each leg back to day zero and adding them up gives what the whole structure is worth as a share of the invoice.
Annual compounding is used rather than simple interest, because the rate on the slider is an annual rate and legs often run beyond a year. $(1+r)^{-d/365}$ is the same convention a treasury team would use, where $r$ is the annual rate and $d$ the payment day.
An LC you pay for is a cost at day zero, so its full percentage comes straight off what the terms were worth. An LC the supplier pays for is their cost, and it appears in their column, not yours.
The result reads two ways from one number, and that is the point. If your structure is worth 97.9%, the terms are worth 2.1% to you and cost the supplier 2.1%. A supplier asking 3% to change them is asking for more than the change is worth.
The rate check prices the same two schedules at three annual rates, spaced three points apart and kept within the slider range. At each rate, the equal price on their offer is $\frac{100 PV_A}{PV_B}$ , where $PV_A$ is the present value of your schedule and $PV_B$ that of their schedule, in percentage points.
The peak carry is the largest absolute difference between the two cumulative paid percentages immediately after a payment date. Its window ends at the next payment date, when that difference can change.
The weighted payment day multiplies each payment day by its share of the invoice. Stock days and customer credit days extend the cash cycle, while the weighted payment day shortens it.
Prepayment discounts the face amount from maturity back to today, then removes the entered fees. The annualised figure scales that cost by the entered maturity.

PV = \sum_i p_i(1+r)^{-d_i/365}

where

PV

is the present value in percentage points,

i

indexes payments,

p_i

the payment share in percentage points, and

d_i

its day.

V = 100-PV

where

V

is the value of the terms to you in percentage points.

The cost to the supplier is the same figure, from the other side.

The LC you pay for is added straight back onto what you effectively pay.

P = \frac{P_0 PV}{100}

where

P

is the price with terms and

P_0

the invoice price.

P_B = \frac{100 PV_A}{PV_B}

where

P_B

is the equal price for offer B.

A(d) = \sum_{d_i\le d}p_i

where

A(d)

is the cumulative share paid by the specified day.

\Delta P = \frac{100 PV_A(r\prime)}{PV_B(r\prime)}-100

where

\Delta P

is the price move and

r\prime

the rate checked.

C_{\max}=\max_{d_i}|A_B(d_i)-A_A(d_i)|

where

C_{\max}

is peak cash carry,

A_B(d_i)

the cumulative share paid by B, and

A_A(d_i)

that paid by A at each payment date.

d_w = \sum_i\frac{p_i d_i}{100}

where

d_w

is the weighted payable day.

d_c = d_s+d_b-d_w

where

d_c

is the cash cycle,

d_s

stock days, and

d_b

customer credit days.

f=(1+q)^{-d_m/365}

where

f

is the discount factor,

q

the discount rate, and

d_m

maturity days.

N=Ff-C

where

N

is net proceeds,

F

the face amount, and

C

fees.

r_a=\frac{C_t}{F}\frac{365}{d_m}

where

r_a

is the annualised cost and

C_t

the total cost.

A worked example

30% on order, 40% on day 60, 30% on day 150, at 12% a year. The first leg is paid today, so it is worth its full 30%. The second is discounted by $1.12^{-60/365} = 0.9815$ , so 40% becomes 39.26%. The third is discounted by $1.12^{-150/365} = 0.9545$ , so 30% becomes 28.63%. Adding them gives 97.90%. The terms are worth 2.10% of the price, which is the number to put on the table when the supplier asks for cash up front, and the number to compare against whatever discount they offer for it.

Their default structure is worth 100.00%, so an equal invoice price is $100 \times 97.8966 \div 100 = 97.8966$ . That is a 2.10% lower price. At week 8, which is day 56, your offer has paid 30% while theirs has paid 100%. The supplier is carrying the 70 point difference under your schedule at that week.

With the schedules held still, the gap is 1.61 points at 9%, 2.10 points at 12%, and 2.58 points at 15%. Their equal-value invoice is therefore 1.61%, 2.10%, or 2.58% lower at those rates. Across the nominal schedule, the largest cumulative payment gap is 70 points from day 0 until day 60: 100% has been paid under their offer and 30% under yours.

What this does not model

Currency movement between the legs, counterparty risk (which is usually the actual reason a structure exists), the credit line the LC consumes, bank charges beyond the single percentage entered, confirmation and discrepancy fees, the difference between a sight LC and a usance LC, tax timing, and any covenant that makes a payment date less flexible than a slider suggests. Discounting a schedule tells you what a structure is worth on paper. It says nothing about whether the counterparty will be there in 150 days, and that judgement is not arithmetic.

The cash cycle treats the entered stock days, customer credit days and weighted payment day as fixed. It does not model changes in demand, customer payment behaviour or bank availability. The prepayment arithmetic prices only the entered face, maturity, rate and all in fees, and does not say that a bank will make the advance.

Where this comes from

The prepayment structure is described from UCP 600 and from the ICC's practitioner collection on it, ICC Publication 682. Both are named and neither is reproduced: no article text, no definition and no time limit is quoted here, and where a credit or a bank's own undertaking says something different, that governs and not this page.

The whole record prints. Your browser can save it as a PDF instead of printing it.

Negotiation arithmetic for comparing two offers on your own cost of money. It does not recommend accepting or refusing any structure. Letter of credit costs vary by bank, tenor and country risk. The figure here is whatever you enter. Discounting a payment schedule tells you what a structure is worth on paper; it says nothing about counterparty risk, which is usually the reason the structure exists in the first place.

Cash timeline sheet

Their offer

Leg 1: 100% · day 0 · on order, fixed
Leg 2: 0% · day 90

Your offer

Leg 1: 30% · day 0 · on order, fixed
Leg 2: 40% · day 60
Leg 3: 30% · day 150

Present value

Your annual cost of money: 12%
Their offer: 100.00%
Your offer: 97.90%
Gap: 2.10 points of price

Cash cycle

Their weighted payable day: 0 days
Your weighted payable day: 69 days
Days the goods sit as stock · assumption: 45 days
Days your customer takes to pay · assumption: 60 days
Their cash cycle: 105 days
Your cash cycle: 36 days

Their offer

Your offer

What your money costs

The rest of your cycle

What each structure is worth

When the cash moves

Here is the maths

The formula, in words

A worked example

What this does not model

Where this comes from

Related

Their offer

Your offer

Present value

Cash cycle