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Calculating the real value of insurance

by Tony Novak, CPA, MBA, MT
, revised 11/17/11

Insurance is an important part of most financial planning. Yet some consumers and financial advisers over-estimate the value of insurance when considering their financial options. For example, when an insurance agent uses a phrase like “buy $100,000 coverage for $2,000 per year”, the implication is that the economic value of the insurance is $100,000 and the cost is $2,000. This oversimplified thinking would lead to poor financial decisions for the consumer.

The economic value of insurance could be expressed as the dollar amount of coverage (usually the lesser of the policy amount or the actual loss) multiplied by the probability of a loss multiplied by the probability that the loss will be covered by the insurance plan minus the cost of claim collection¹. This figure should then be adjusted to consider the time value of money when comparing the cost of a current insurance premium vs. the possibility of a claim in the future.

Note that the probability of loss and the probability that a loss will be covered are actually separate and distinct risks that are often ignored.

Estimating risk of loss

Risk of loss is usually the easiest factor to estimate based on published actuarial data. For our general financial planning purposes we could assume, for example, that 1 in 2 people will incur a long term care need, 1 in 3 people will incur a loss of income due to disability and 1 in 6 people will incur a catastrophic homeowners loss. These are obviously very rough estimates for general purposes; for other purposes it may make sense to research more accurate data. It usually does not make sense to “second guess” the statistically accurate averages based on personal hunches or emotions. Our personal biases are more likely to add error than accuracy to the estimate.

When making calculations about life expectancy remember that the older we are at the time of calculation, the longer our life expectancy.  For example, a healthy 65-year-old man has a longer life expectancy than a healthy 15-year-old male. This is simply because we face many risks to life between age 15 and 65.

Probability that a loss will be covered

Depending on the type of insurance and many other factors, the probability of a loss being covered will vary dramatically. Some insurance companies have a history of successfully denying a large portion of claims. Other types of insurance (like term life insurance) operate under the assumption that more than 99% of policyholders will intentionally or unintentionally lapse their insurance before the date of claim.

Claim collection costs

Cost of collection can be significant and is usually completely ignored until after the date of claim. In some types of insurance, the claim collection costs could be 40% or more of the total claim actually paid. This might be the costs of an attorney, public adjuster, appraiser, loss of time and other legal costs.  In far too many cases the cost of collecting the claim exceeds the actual amount recovered from the insurance company, leaving the policyholder in debt.  For financial planning purposes, it makes sense to assume some arbitrary claim collection cost. This arbitrary assumption might range from 10% for property insurance to 40% for disability income. This might be the largest “unknown” factor when planning using insurance, but clearly we are better off assuming an arbitrary risk – even if it turns out to be grossly inaccurate - rather than simply ignoring this risk altogether in our financial planning.

Example calculation

If we assume that the amount of a covered loss is $100,000, the probability of incurring a loss is 1 in 2, and the probability that the loss will be covered by insurance is also 1 in 2, with 10% cost of claim collection, then the actual value of insurance is:

$100,000 X .5  X .5 X .9 = $22,500

Of course, the cost of insurance is actually the total accumulated cost until the date of claim¹. Since we do not know the actual date of claim, we substitute “expected date of claim” for financial planning purposes.  If you are age 60, for example, your expected date of claim for long-term care insurance claim is about 12 years from now.  If the level annual premium is $2,000, for example, the total expected cost of insurance is $2,000 X 12 = $24,000.

So in the example above, the cost of insurance ($24,000) is approximately equal to the value of the insurance ($22,500) if we ignore the time value of money.  If we were to include the time value of money (what we would have earned if we had invested $2,000 per year for 12 years in the example above) then the real cost of insurance becomes more apparent¹.

The point of this article is something you already know: insurance has real economic value but is not a great bargain.  In many cases insurance is an important or even essential part of financial planning². It never makes sense to expect to achieve any financial windfall by loading up on insurance. In general, the faster we reduce our need for insurance by accumulating wealth and managing risk through other methods, the better.

***

Footnote:

¹ This article ignores the risk of premium cost increases, insurance company insolvency, changes in the legal environment or government entitlements, and the time value of money in order to simply the issues for discussion purposes.

² Some advisers point out that the value of insurance is linked to the psychological value it provides to policyholders. This article deals only with hard currency value and ignores the value of any psychological benefit.

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