Re: Calculation premium warranty for industrial equipment

[Jonathan and Mary Frances Miller]

This is a complicated reply, because this is a really complicated subject.  You
have made a good start.

First, you should talk to the legal people and make sure that this is really a
service contract and not an insurance product, or to what extent it is which.  I
will not even start to think about the controlling law in your case.  In the US,
the product is a service contract, but insurance companies can insure the
offerer and then the product that is sold (usually to consumers) is a service
contract but the insurance (a contract between the seller of the service
contract and the insurance company) is insurance.  This could be really
important because US accounting rules require setting up a reserve to pay future
claims, but tax laws prohibit deducting this reserve, unless it's an insurance
reserve.  Which must be held by an insurance company.  So many manufacturing
companies set up a "captive" insurance company to do the insurance part of the
contract.

"k.j.a. postulart" wrote:

> L.S.,
>
> I am looking for some feedback on the issue of premium calculation for a
> warranty for industrial equipment. Assuming a number of periods that the
> warranty will be valid one must consider two main components:
>
> 1. periodical costs due to usage of the industrial equipment based on
> operational hours
> 2. stochastic costs due to unexpected failures of the industrial equipment
>
> I assume periodical costs can be calculated based on known manhours per
> activity as well as the material costs involved. These costs can be well
> established

Well, maybe.  See below.

> through time measurement and use of material, based on past experience.
>
> Total costs = labour costs + material costs
>
> Both costs must be calculated including the depreciation factor

Why?  it costs you what it costs.  These are cash outlays.

> , which may differ for both costs and even subelements of both costs. With the
> interest rate one can determine the present value of the costs.
>
> Stochastic costs are different. Due to past experience one can establish the
> MTBF ( exponentially distributed life ! ) or any set of parameters for a
> different probablistic distribution. The critical parts are:
>
> Part 1 : MTBF1    C1
> Part 2 : MTBF2    C2
> etc.

All valid and a reasonable approach.  However, what if a large number of
warranted machines all develop problems unexpectedly early?  And what if the
cost is different from the average?  This risk consists of essentially two
parts.  The first is statistical risk, that is, a sample may not accurately
reflect the population it is drawn from.  For example, if you poll one person
about who she will vote for in the upcoming election, you arrive at the
conclusion that one candidate will win 100% to 0%.  So you need to put something
in to cover the risk that you will not sell enough warranties to allow the law
of large numbers to work in your favor.  There are established techinques to
handle this.

The other problem is that, for some reason, the process may change.  That is,
perhaps the manufacturing process changed, and the metal parts manufactured
after some date succumb to fatigue earlier than your model (based on past data)
suggest.  Or maybe the manufacturing process is the same, but the customers and
their use of the equipment change.  Or maybe the service contract purchasers are
somehow different from the non-purchasers (this is called adverse selection).
Maybe they even skimp on maintenance because the warranty will cover damage!
There are no techniques for handling this risk (that I know of), but there are
rules of thumb in the insurance industry.  Whether they would be appropriate for
your circumstance I don't know.

> Simulating the life of the equipment through the Monte Carlo Method one can
> determine how many and when the different parts have to be exchanged or
> repaired during the pre-defined warranty life. Combining the costs of material
> and labour involved with the interest rate one can calculate the present value
> of the costs for each failure. After a number of runs one can determine the
> distribution of the stochastic costs.
>
> Finally one can add the resulting periodical costs and the stochastic costs

Which stotastic costs?  Mean?  Median?  75th percentile?  95th?  Whatever your
theoretical result, keep in mind that your competitors' prices for "the same
thing" (in quotes because it never is) will be much lower than yours, or for
"the same price" the customer is getting "so much more coverage".

> and determine the periodical payments the client must make in order to cover
> the costs involved plus the required profit for the supplier.
>
> For calculating the present value of the costs the timevalue formula is being
> used.

You need to make sure you are looking at the after-tax cash flows.  This is
important if you build up big early non-tax-deductible reserves.  Talk to the
finance guys about this.  You might want to even pay an insurance company to
insure you (so you don't have to take a nondeductible hit to your earnings) or
even set up your own.  Of course, this all depends on the legal environment
where you're doing business.

> Any remarks ( critical, constructive or suggestive ) are very welcome !

Interestingly, in the US, consumers are almost always warned not to buy the
service contract because it's such a bad deal (so much cost for so little
coverage), but investors are quite frequently warned to stay away from companies
that sell too much service contract, because it's such a big risk (so much
coverage for so little cost).  And salesmen are advised to not sell it because
the commission is so small!

Obviously, someone is not telling the whole story.  Where's the money going?
(Maybe to the accountants?)

You should expect that your first pricing is a first approximation to the true
price and that you will need to monitor results and change pricing accordingly.
That may mean that you want to phase in the contracts to avoid taking on too
much risk in one year.  It's a business decision about whether to have fixed
payments for the coverage or adjustable, and if adjustable by how much and under
what circumstances.  I have no idea what European law is, but US individual
health insurance contracts fall into three categories.  Noncancellable means
that the company can't cancel the contract (except for nonpayment of premium) or
change the rates.  Given recent (last 80 years) history, this means that it's
available for disability income but not medical expense insurance.  Guaranteed
Renewable means that the company can't cancel the contract (except for
nonpayment of premium), but they can change the rates _for the whole class of
insureds_, but _not for an individual_.  Cancellable means that they can cancel
the policy (with some protections for the insured) or change the rates (well,
maybe, it's real complicated).  But you need to determine what you are selling.
Is the cost of coverage $X per year forever, or $X per year this year but
adjustable based on experience (and adjustable how?), or what?

You may even want 2 or more contracts.  In the US medical insurance market, the
most common way for individuals to be covered is through their employer.  If the
employer is large enough, the premiums for the insurance will be fully rated
based on that employer's own experience.  For smaller employers, it's really
insurance.  So, for example, it may be that in your case all Russia pays one
rate based only on their experience, but a small company in Belgium pays based
on your average experience over all your service contracts.  Both are happy
because a big customer is really just buying service, and doesn't really care
whether it's pay-as-you-go or prepaid, but the small customer is really buying
insurance against the cost of repairs being too high.

Have fun.

Jon Miller



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