Points math under uncertainty: break-even vs. the refi you'll probably do

The standard advice on discount points is a break-even calculation: divide the upfront cost by the monthly savings, and if you'll keep the loan longer than that many months, buy the points. It's clean, it's everywhere, and it's subtly wrong — because it treats 'how long you'll keep this loan' as a number you know. You don't. You hold a probability distribution over moving, refinancing, and rate paths, and the moment you model points that way, the answer changes: points are a bet that rates won't fall and you won't move, and in most environments that's a worse bet than the simple break-even suggests.

The naive math, stated fairly

One point costs 1% of the loan and typically buys the rate down about 0.25% (this varies with the rate sheet — always ask for the actual buydown schedule, because the first point often buys more than the third). On a $400,000 loan at 6.75%, one point costs $4,000 and drops the rate to roughly 6.5%, cutting the payment from $2,594 to $2,528 — $66 a month. Break-even: $4,000 ÷ $66 ≈ 61 months. Keep the loan five years and you're ahead; hold it 30 and you save nearly $20,000. On these numbers, points look great for anyone 'planning to stay.'

What the naive math ignores

• Refinance probability: if rates fall enough to justify a refi, your points evaporate — you paid upfront for a rate you abandoned. In a high-rate environment, refinancing within 3–5 years is not a tail risk; it's often the base case.
• Move probability: the median owner moves well before year 13; first-time buyers move sooner. Every path where you sell early truncates the payoff.
• Opportunity cost: the $4,000 could earn a return elsewhere, or reduce the loan balance, or stay liquid as reserves. Break-even at 61 months against a 0% alternative is really break-even at 70+ months against invested cash.
• Asymmetry: if rates rise, you didn't need the points to keep your loan — you'd keep it anyway. Points pay off only in the narrow middle world where rates stay flat-to-slightly-down and you stay put.

Expected value with a refinance probability

Put a probability on the truncating events. Suppose there's a 40% chance you refinance or sell within 3 years (36 months x $66 = $2,376 recovered), a 30% chance within 5 years (~$3,960 — roughly break-even), and a 30% chance you hold 10+ years (cap it at 120 months = $7,920). Expected recovery: 0.4 x $2,376 + 0.3 x $3,960 + 0.3 x $7,920 = $950 + $1,188 + $2,376 = $4,514 against a $4,000 cost. That's an expected profit of about $514 — barely positive, before opportunity cost on the upfront $4,000, which at 5% over the average holding period eats most of it. The same purchase that looked like '$20,000 of savings' is approximately a coin flip once you price the exits honestly.

When points genuinely make sense

• You're borrowing at rates you'd celebrate keeping — near cycle lows — so refinance probability is genuinely small.
• The buydown schedule is unusually rich (e.g., a point buys 0.375%+ because the lender is managing pipeline), shortening true break-even below ~40 months.
• You need the lower rate to qualify on DTI — points as a qualification tool, not an investment.
• Seller or builder credits must be spent on closing costs anyway: points bought with other people's money have no opportunity cost and skip most of this analysis.
• You have maximal staying power: long horizon, stable household, and enough liquidity that $4,000–8,000 upfront doesn't thin your reserves.

1. 1
   Get the real buydown schedule

   Ask for pricing at 0, 1, and 2 points. Rate sheets are lumpy; sometimes one specific point is cheap and the rest are poor value.

2. 2
   Write down three holding scenarios

   Early exit, medium, long — with honest probabilities. If you can't defend a probability, that itself argues against paying upfront.

3. 3
   Compute weighted recovery

   Months held x monthly savings per scenario, probability-weighted, against the upfront cost.

4. 4
   Subtract opportunity cost

   What the cash earns in your actual alternative (reserves, index fund, extra principal) over the average holding period.

5. 5
   Check the credit side too

   Run the mirror-image math on lender credits before deciding the zero-point loan is the default.

The bottom line

Break-even months answer the wrong question. The right question is: across the realistic futures — you move, you refinance, you stay — what is the probability-weighted value of this upfront payment against its opportunity cost? Framed that way, points are usually a mediocre bet in high-rate environments (where the refi you'll probably do erases them) and a decent one near rate lows for long-horizon owners. Buy points with seller credits freely, buy them with your own cash skeptically, and remember that the lender selling you the point has already priced the same probabilities — from the other side of the table.