Refinancing arithmetic: when a longer, larger, cheaper-looking deal costs more

The offer that always sounds good

You are eight weeks into an advance. A funder offers to pay it off, put more cash in your account, lower the factor and cut the weekly payment. Every visible number improves.

The visible numbers are the wrong ones. What you are being sold is new money, and the only honest question is what the new money costs.

The starting position

Illustrative only — an advance of $60,000 at a 1.38 factor, repaying $82,800 in 24 weekly payments of $3,450. You have made eight. You have paid $27,600 and the balance is $55,200 across the remaining 16 weeks.

Look closely at that balance. Of the $60,000 advanced, 16/24 remains unrepaid on a straight-line basis, which is $40,000. The other $15,200 of the payoff figure is cost that has not been earned yet — it exists because the total was fixed at signing, not because you have had the money for that long.

That $15,200 is the pivot of the whole transaction.

The refinance offer

A new advance of $100,000 at 1.32, repaying $132,000 in 48 weekly payments of $2,750, with a 3% origination fee.

The mechanics: $55,200 goes to pay off the old balance, $3,000 goes to the fee, and $41,800 reaches your account.

What improved: the factor fell from 1.38 to 1.32, the weekly payment fell from $3,450 to $2,750, and you got $41,800 in cash.

The arithmetic on the new money

Compare the two futures rather than the two contracts.

Without the refinance you owe 16 payments of $3,450: $55,200 in total.

With it you owe 48 payments of $2,750: $132,000 in total.

The extra you pay is $76,800. What you got for it is $41,800. So the new money costs $35,000 — a factor of 76,800 / 41,800 = 1.8373 on the cash that reached your account, against a headline factor of 1.32.

For a rate, take the incremental cash flows and solve. You receive $41,800 today. For 16 weeks you pay $700 a week less than you would have — that is the relief, and it is real money. From week 17 to week 48 you pay $2,750 a week you would not otherwise have owed. Solving for the weekly rate that sets those flows to zero gives 1.6977% a week, which is 88.3% annualised on a nominal basis and 140.0% as an effective annual rate.

Check the totals: 32 payments of $2,750 is $88,000, less 16 weeks of $700 relief, which is $11,200. Net extra $76,800. The arithmetic closes.

Where the money went

Three things happened at once, and the term sheet describes only the first.

The questions that settle it

1. What is the exact payoff figure today, and what discount, if any, applies for early payoff? A funder that will discount the unearned portion changes this entire calculation. Ask in writing.
2. How much cash actually reaches my account? That is the only amount being bought.
3. What is the total of all future payments under each option? The difference is what the new money costs.
4. What is the weekly outflow in weeks 1 to 16, and in weeks 17 to 48?
5. Is the relief in the early weeks worth the cost in the later ones — and is there anything specific it buys?

What a discount on the unearned cost is worth

Question one above is worth putting a number on, because it is the only lever in the transaction that moves the price rather than the schedule.

Illustrative only, on the same deal. The payoff is $55,200, of which $15,200 is cost that has not been earned.

• No discount. Payoff $55,200, cash to you $41,800. The new money costs $76,800, a factor of 1.8373, and solving the incremental cash flows gives 1.6977% a week — 88.3% annualised.
• Half the unearned cost discounted. Payoff $47,600, cash to you $49,400. The extra you pay is unchanged at $76,800, but it now buys $49,400. Factor 1.5547, and 1.2308% a week, or 64.0% annualised.
• All of it discounted. Payoff $40,000, cash to you $57,000. Factor 1.3474, 0.8309% a week, 43.2% annualised.

The same contract, the same payments, the same total. A $7,600 concession that nobody volunteers moves the cost of the new money by twenty-four percentage points a year. It is one email, sent before you agree to anything, to the funder being paid off rather than the one doing the paying.

The variant to watch for

Some offers do not pay the old positions off at all. A reverse consolidation deposits money into your account each week to cover the existing debits while collecting a larger amount back. The old agreements stay live, the old filings stay in place, and you now have one more obligation than you started with. Whatever it is called, test it against the same question: are my total outstanding obligations lower the day after funding than the day before?

When a refinance is the right call

If the business cannot make the current payment, a lower payment has value that the incremental rate does not capture. Buying sixteen weeks of $700 relief and $41,800 of cash for $35,000 may be the least bad option available on the day. That is a real decision, and it should be made with the $35,000 written down.

The version to refuse is the one presented as a saving. Nothing was saved. The payment got smaller, the term got longer, the balance got bigger, and the cost of the new money was 1.8373 per dollar received. Run your own figures through the calculators before you agree to anything, and run them on incremental cash flows rather than on the two term sheets.