Should I buy the warranty?
Price, chance and cost: what each choice costs on average, the chance where the plan starts to pay, and when to buy it anyway.
Try it with your own numbers
$39.80 less on average if you skip the plan.
Two years of cover for $180. Say 1 in 5 phones break in that time. A new one costs $800; the plan still charges $99. Made-up numbers.
The chance is over the whole plan, not per year. What you still pay is the deductible, if there is one.
- Skip it, on average
- $160
- 20% × $800
- Buy it, on average
- $199.80
- $180 + 20% × the $99 you still pay
- Break-even chance
- 25.7%
- above this, the plan pays on average
- The plan's markup
- 1.28×
- you pay $1.28 for each $1 it pays out, on average
Skipping costs $39.80 less on average. The plan only pays if the chance is above 25.7%; you put it at 20%. You could cover $800 from savings, so skipping is a safe bet.
How this works, step by step
Two choices, two kinds of cost.
Skip the plan, and most of the time you pay nothing, but now and then you pay the whole bill. Buy it, and you pay a sure price every time, plus a deductible if something goes wrong. One is a small certain cost, the other a big uncertain one.
Average each one over many tries.
Picture 100 people with the same phone. If they all skip the plan, about 20 pay $800: $16,000 in all, or $160 each on average. If they all buy it, each pays $180, and 20 of them pay $99 more: $199.80 each. That average is the expected cost.
skip = chance × cost · buy = price + chance × deductible · 0.20 × $800 = $160 · $180 + 0.20 × $99 = $199.80
Find the break-even chance.
There is one chance where both choices cost the same. Above it the plan is the better deal on average; below it, skipping is. Compare it with your honest guess of the real chance.
break-even = price ÷ (cost − deductible) · $180 ÷ ($800 − $99) = 25.7%
The seller knows the chance better than you.
A company selling cover has records of how often things break. It sets the price above the average payout, because that gap pays its staff and its profit. So most plans cost more than they pay out on average, often far more. The markup shows by how much.
markup = price ÷ (chance × (cost − deductible)) · fridge: $150 ÷ (0.08 × $350) = 5.36×
Buy it anyway when the loss would hurt.
An average only helps if you can live through the bad case and many choices like this even out. A loss you can’t absorb breaks that: a car crash with no savings, a house fire, a big medical bill. Turning a loss that would ruin you into a small sure cost is worth paying extra for. Small losses you could cover, like a phone or a fridge repair, are the ones to cover yourself: keep the money in savings instead.
Check what already covers you
Before buying cover at the counter, check what you already have. Many credit cards include rental car damage cover. New products come with a maker’s warranty, usually for the first year, and some cards extend it. Home and renters policies can cover theft. Paying twice for the same cover is the worst deal of all.
For learning, not financial advice.
For learning, not financial, medical or betting advice.