Abaque 14 · Downsizing

What the next house really costs

Selling a house to lower a monthly payment is arithmetic, not intuition — and the intuition is usually wrong, because a below-market mortgage is an asset that does not travel. This sheet prices that asset, then reads the corridor of replacement prices where a move actually pays.

Governing variableReplacement price
Hidden termOld loan value
Independent ofHome appreciation
Figures3
Sheet14 · Rev A
The term everyone omits. If your rate is below today's market, your mortgage is worth money — the payments you owe are worth less than the balance you owe them on. Sell, and you hand that value back. It never appears on a settlement statement, so it is invisible exactly when it matters. The readout below prices it, and Fig. 2 shows it is often larger than the realtor's commission.
Inputs

Your house as it stands

$450,000
$240,000
3.250%
25
Rate and remaining term are what give the loan its value.
6.75%
1.25%
Effective rate on market value. This one moves the answer more than you expect.
$150 / mo
8.0%
1.5%
$275,000
The one number you are really choosing.
20
Paying now
—
—
After the move
—
—
Your old loan is worth
—
—
Break-even price
—
—
Years to recover the move
—
—
Fig. 1

The corridor — where a move lowers the payment

Reading the chart
  1. Find the price of the house you are considering along the bottom.
  2. Read up to the solid line, then across: that is the change in your monthly payment.
  3. Below the zero rule you save; above it you pay more. The crossing is your break-even price.
  4. The dashed line is the same move if you could carry your old rate with you. The gap between the lines is what the rate difference alone costs.
Table view — Fig. 1
Fig. 2

The ledger — what moving costs before it saves anything

Table view — Fig. 2
Fig. 3

How long you must stay for the move to pay

Table view — Fig. 3
Notes

How the loan is valued, and what the sheet ignores

Pricing a mortgage you already have

A mortgage is a stream of payments you owe. Its economic value is not the balance on the statement — it is what that stream is worth at today's cost of money. Discount your remaining payments at the current market rate and compare against the balance:

loan advantage = balance − PV(your remaining payments @ market rate)

If your rate is below market the payments are small, the present value comes in under the balance, and the difference is yours — a real asset, earned by having borrowed at the right moment. If your rate is above market the sign flips and your loan is a liability worth escaping, which is what makes refinancing worthwhile in the other direction.

This is the same arithmetic a bank does when it buys a loan portfolio. Households almost never do it, which is why "I'll just sell and buy something smaller" so often disappoints.

Why the corridor slopes the way it does

Three things move together with the replacement price: the new loan, the property tax, and the insurance. Only the loan is affected by your equity, and it saturates — below the cash you walk away with, there is no loan at all and the line flattens into pure tax-and-insurance. That flat left end is the region where a move genuinely transforms your monthly cost, and it exists only if you buy for roughly what you clear on the sale.

The honest reading

  • A lateral move is always a loss. Same price, new loan at a higher rate, plus both sets of transaction costs. There is no version of this that wins.
  • You save in proportion to how much less house you accept. The transaction contributes nothing on its own; only the size difference does.
  • Check the payback against your own horizon. Fig. 3's curve goes vertical near the break-even price. A move that pays back in thirty years is not a plan, it is a hope.
  • Property tax rate deserves care. Many places reassess on sale, so the new house may be taxed on its purchase price while your current bill rests on a stale valuation. Set the rate to what the new house would actually pay.

What this sheet cannot see

  • Capital gains. A married couple may exclude up to of gain on a main home ( single) under 26 U.S.C. §121, having owned and lived in it . Most downsizers owe nothing — but a long-held or much-appreciated home can exceed it, and this sheet does not check.
  • What you do with leftover cash. Buy below your net proceeds and the remainder is investable. That return is not counted here, and it can exceed the monthly saving.
  • Condo and association fees, which routinely swallow the entire saving of moving to a smaller place. Add them to the replacement price's carrying cost yourself.
  • Maintenance, utilities and upkeep, which genuinely do fall with square footage — so the sheet understates the case for downsizing.
  • Moving costs, new furnishings, and the repairs a buyer will demand before closing.
  • Inflation and appreciation. Everything is in today's dollars, and both houses are assumed to appreciate alike — so appreciation cancels and never appears.
  • Whether you want to live there. Which, once the two columns are close, is the only thing left deciding it.
This is arithmetic, not advice. Mortgage mathematics is exact; every input feeding it is an estimate, and the property tax rate and selling cost in particular are worth confirming before you trust the third digit. The shape of the corridor is the durable part. Take a real decision to a fee-only planner, and get a broker's valuation rather than an online estimate.
Indexed figures are re-set every January and this snapshot will go stale. Get notified when they are re-verified → · All fifteen sheets