How Expected Value Exposes the Break-Even Failure Rate of an Extended Warranty

“Peace of mind” is real, but it is not the same thing as a positive financial expectation. I built this calculator to separate those questions: what is the expected covered loss, what does the warranty cost, and how likely would failure need to be before the math breaks even? The intended reader is comparing a real plan with a repair estimate and wants to see which assumptions drive the conclusion, not receive a fake certainty about whether every warranty is bad.

Calculate the claimable loss before applying probability

The form accepts warranty price, coverage months, estimated failure probability, repair cost, deductible, product price, and an optional claim limit. The component subtracts the deductible, clamps the result at zero, then applies the claim cap:

const grossLossAfterDeductible = computed(() =>
  Math.max(0, repairCost.value - deductible.value)
);
const claimableLoss = computed(() =>
  claimLimit.value > 0
    ? Math.min(grossLossAfterDeductible.value,
      claimLimit.value)
    : grossLossAfterDeductible.value
);

That ordering matters. For an 18,000 repair with a 1,000 deductible and a 15,000 claim limit, the loss after deductible is 17,000, so claimable loss is 15,000. The warranty does not magically reimburse the deductible. If the deductible is larger than the repair cost, the clamped loss is zero. If claim limit is zero, the source treats it as “no stated cap” rather than capping at nothing.

All monetary inputs pass through safeNumber, which clamps invalid and negative values to zero. Failure probability is clamped to 100% and converted to a fraction. The product price is collected for context and display, but it does not enter the expected-value equation. That is a useful reminder that an expensive product does not automatically make a repair claimable.

The two key equations are intentionally visible

Expected claim value is estimated failure probability multiplied by claimable loss. Net expected value subtracts the warranty price:

const probability = computed(() =>
  Math.min(100, safeNumber(form.value.failureRate)) / 100
);
const expectedClaimValue = computed(() =>
  probability.value * claimableLoss.value
);
const netEv = computed(() =>
  expectedClaimValue.value - warrantyCost.value
);
const breakEvenRate = computed(() =>
  claimableLoss.value <= 0
    ? null
    : (warrantyCost.value / claimableLoss.value) * 100
);

With a 3,990 warranty, 12% estimated failure probability, and 15,000 claimable loss, expected claim value is 1,800 and net EV is -2,190. The break-even failure probability is 26.6%, because 3990 / 15000 * 100 is the rate at which expected reimbursement equals price. This is not the probability that the device will fail; it is the threshold your estimate would need to cross under this simplified claim model.

The result card labels positive, negative, and near-break-even outcomes. “Near” uses a tolerance of the greater of 10 and 5% of warranty cost, so a small difference is not presented as a dramatic win. A second visual compares the user's estimate with the break-even rate. If claimable loss is zero, the marker is omitted and the result says there is no covered loss rather than dividing by zero.

Why the ordering and scope matter

Expected value is an average over repeated similar decisions. It does not predict the timing of one failure. A device can fail tomorrow, after the coverage period, or never fail. The model also treats the estimated failure probability as one event and does not add a second probability for approval, parts availability, or replacement depreciation.

Coverage months are input and shown as part of the decision context, but the arithmetic does not annualize the rate. Therefore a 12% estimate must already describe the selected coverage period. Mixing a one-year failure rate with a three-year warranty would produce a confident-looking but mismatched comparison. This is a limitation worth preserving rather than silently “fixing” with an invented hazard curve.

The break-even display is useful for sensitivity testing. Hold the warranty price at 3,990 and raise the claim limit from 5,000 to 15,000: the same price requires a much lower failure probability once more loss is actually claimable. Then increase the deductible and watch claimable loss fall. These experiments show why quoting a warranty price alone is not enough; the contract's deductible and cap are doing as much mathematical work as the probability.

One subtle input boundary is that the calculator does not infer a probability from the product price or coverage length. Coverage months appears in the form, but the expected-value calculation treats the supplied failure rate as already belonging to that coverage period. That keeps the formula inspectable, though it puts the responsibility on the reader to compare like with like. A warranty salesperson's annual failure statistic cannot be pasted into a multi-year scenario without first deciding how the periods relate.

The limitation is the point of the tool

The page does not contain a brand, store, or model failure-rate database. The reader supplies the probability and repair cost, while real policies may contain exclusions, service fees, depreciation, claim friction, waiting periods, and replacement rules. Product price is not a proxy for any of those details.

A negative EV result is not a command to reject coverage. Cash-flow risk, inconvenience, inability to self-insure, or strong risk aversion may justify paying for protection, but those are separate reasons from the arithmetic. I turned this decision model into a small free tool: Extended Warranty Calculator.