How the calculation works
Four lines, no hidden model
Net cash today = price - resale. What actually leaves your account.
Buy cost per year = (price - end value) / years. The new machine's depreciation spread over the period you keep it.
Keep cost per year = repairs + (resale today / years). Repairs are cash; the second term is the value of the old machine that disappears because you did not sell it.
Difference = keep per year - buy per year. Positive means buying is cheaper per year. Break-even, when it exists, is net cash divided by that difference.
Worked example, default numbers
New machine 1999, current one sells for 650, five-year horizon, 120 a year in repairs, new machine worth 600 at the end.
- Net cash today: 1349.
- Buy per year: (1999 - 600) / 5 = 279.80.
- Keep per year: 120 + 650 / 5 = 250.00.
- Difference: -29.80. Buying costs about 30 a year more.
- Break-even: none, because buying is not cheaper per year.
So the honest conclusion is that the upgrade is a capability purchase, roughly 150 more expensive over five years. If that is what you want, it is a fine purchase. It is just not a saving.
Same example, expensive repairs
Change one number: repairs of 480 a year instead of 120.
- Keep per year: 480 + 130 = 610.
- Difference: 610 - 279.80 = 330.20 in favour of buying.
- Break-even: 1349 / 330.20 = 4.1 years, inside the five-year horizon.
Now the upgrade pays for itself before the period ends. One input moved the verdict, and it was the one people estimate worst.
When payback exists at all
Payback is not always defined. The new laptop only wins per year when the old laptop burns more value than the new one, which happens when:
repairs > (price - new machine end value - current resale) / years
With the defaults that line sits at 150 per year: (1999 - 600 - 650) / 5. Repair spend of 120 is below it, so keeping is cheaper per year and there is nothing to pay back. The page therefore says "none" and prints the threshold beside it, because a bare "none" hides the only number that would change the decision.
Move the years to 10 and the line drops to 75, because the same value gap is now spread over twice as long. Same laptop, same prices, different verdict.
Sensitivity
Break-even is linear in net cash and inverse in the annual difference. A repair estimate that doubles does not double the break-even, it halves it. A resale value you overstate by 200 shortens the break-even noticeably, because that number is subtracted from the cost and added to the keep side at the same time.
If moving an input by 20 percent does not change the verdict, that input is not your decision. If it flips the verdict, that is the number to go and research before buying.
Why the old version of this page was wrong
The first version compared buy cost per year (capital plus repairs) against keep cost per year (repairs only). Those are not the same quantity, so the comparison always flattered keeping, and it produced break-evens of eleven years against a five-year horizon. The model now charges both sides for the value they consume. The formula changed; the arithmetic was never the problem.