A ratio cannot answer a question about time
The familiar rule is that a repair costing more than half the price of a replacement is not worth doing. It survives because it is easy, and it fails because it never asks the only question that decides the matter: how many more years does the repair buy?
A $250 repair on a machine that costs $1,300 to replace is 19 percent, which the rule waves through. If that repair holds for one year it costs $250 a year, and a $1,300 replacement lasting twelve years costs $108 a year. The rule just approved the more expensive option. Run it the other way: a $600 repair on the same machine is 46 percent and still passes, and if it buys six years it costs $100 a year and genuinely wins. The ratios were similar. The durations decided everything.
Both sides converted to cost per year
The repair side is the quote divided by the years it buys, plus any running-cost penalty from keeping the older machine. That last term belongs on the repair side because an inefficient machine costs you that difference every year you keep it, which is precisely the period the repair extends.
The replacement side is the price plus delivery, installation and disposal, less whatever the old one fetches, divided by the expected life of the new one. Both sides come out in dollars per year and can be compared directly.
Rearranging gives the number the calculator leads with. Divide the quote by the annual cost of replacing minus the running-cost penalty, and you get the years the repair must deliver to break even. If the technician says four and the calculator says two and a half, repair. If the technician says maybe a year and the calculator says three, do not.
The second failure
Old machines rarely fail once. Components age together, so the pump that goes this year sits beside a bearing and a control board of exactly the same age. Ignoring that overstates the repair case, and the allowance field handles it by raising the quote to an expected value: a 20 percent chance of one more repair of similar size turns a $250 quote into $300.
Nobody knows the true probability. What you do know is the direction of the adjustment. Raise it if the machine is past its expected life, if you have already had it fixed once or twice, or if the technician mentioned other parts looking tired. Then re-run at 30 and 50 percent — a conclusion that holds across all three is one you can act on.
Residual value, and what it is good for
The straight-line residual is the purchase price reduced in proportion to how much of its expected life is gone. An eight-year-old machine that cost $1,200 with a twelve-year life shows $400 of book value. It is worth knowing and it is not a decision rule: what you paid years ago is gone either way, and a repair costing more than the residual can still be the cheaper path if it buys enough time. The figure is here because people reach for it, and it works better as a sanity check than as an argument.
The things with no price on them
Days without a working machine. A week waiting for a part. A second visit and a second afternoon spent at home. The features on a newer one that you would actually use. And the disposal of something that mostly still works, which carries a real environmental cost that appears in neither column and pulls consistently toward repair.
None of these are in the arithmetic, and they are exactly what should settle a close call. Where the two annual costs land within about ten percent of each other, the calculation has told you what it can, and the rest is a judgement about your week rather than about your money.
One question to ask the technician
Before agreeing to anything, ask how long the repair is expected to hold and whether anything else is close to failing. That answer feeds the single most sensitive input on this page, and the sensitivity table exists to show how much rides on it. A technician who says the machine has years in it is handing you a different calculation from one who shrugs, and the shrug is information too.
Questions people ask
Is the 50 percent rule wrong?
It is a shortcut that ignores duration, which is the deciding variable. It happens to be right when repairs buy an average amount of extra life and wrong at both extremes: a cheap repair that lasts a year is a bad deal it approves, and an expensive one that lasts six years is a good deal it rejects.
How do I estimate the extra life a repair buys?
Ask the person doing the repair, and treat the expected total life for the type as an upper bound. If the machine is already at or past that figure, treat any number over two or three years with suspicion and raise the second-failure allowance instead.
Should the running cost difference really count against the repair?
Yes, because you pay it every year you keep the older machine, which is exactly the period the repair extends. Use the annual consumption figures for the two units and your own rate rather than a label estimate, which assumes a usage pattern that is probably not yours.
What if the machine is already past its expected life?
Then failures tend to come in sequence and a single repair quote understates what the next two years will cost. Raise the second-failure allowance sharply, and check whether parts are still available at all, because that limit ends the argument regardless of the numbers.