In this lesson we’re going to move through step one of our simplified P&C insurance company
operating model. Now I just called it a simplified operating model but actually if you look down,
it is not really that simple. It is simplified in the sense that it is less complex than
what you would actually see in a real insurance company’s financial statements. But on the
whole if you look around online or you look through other training programs or training
materials or other books on insurance, this model actually goes through a good number
of the key concepts, and it’s actually more complex than some of the other simplified
teaching-type models that I’ve seen before. So it is really an extension of some of the
previous lessons and the reason why I started with those lessons is to teach you basic concepts;
such as the gross written premiums, the ceded written and earned premiums, the net written
and earned premiums, the unearned premium reserve topics like that. So that this way
when we get to this lesson and our operating model here over this series of lessons we
don’t have to spend time re-explaining that and going over all of this again. So what
we’re going to do here is divide this into five steps. In step one we are going to go
through our basic assumptions up above, which I’ve already filled in to save us time.
Then we’ll move through the premiums calculations down here, look at how the reserves change
over time. And also look at the commissions and deferred acquisition costs. So that’s
step one. In step two, we will move to the loss side, and look at how the gross loss
and LAE reserve, and then the reinsurance recoverables and related items actually change
over time. Then in step three we’ll move into the insurance company’s income statement
and you’ll see where all these items are coming from. In step four we’ll look at
their balance sheet, which is mostly just plugging in items that we are already have
from above. And then also look at their cash flow statement, which again, is mostly just
linking to items from above. Then in step five, we will go through something called
statutory accounting, and then look at the key metrics and ratios for this insurance
company. Many of these we’ve been over before in the last few lessons, but there will be
a few new ones, and a few ones with differences, and just a few finer points to point out here,
when we’re dealing with an ongoing insurance company, as opposed to just what happens over
say a year or two in the simplified models from before. So those are the five steps and
the five lessons to our model here. We are going to get started with step one, which
is to look at the assumptions and then to calculate some of this premium information,
and then to look at the commissions and deferred acquisition costs here, which of course line
up perfectly with the premiums. So, on the assumption side we are dealing with a new
insurance company here, so it’s brand new. We start off by writing $10,000 in gross premiums.
Really this is actually $10 billion if you look at my footnote here, dollars in millions.
But I’m just going to keep referring to it as $10,000 throughout this, because that’s
how it appears in the Excel file. So that’s our initial gross written premiums. You can
see that all the other numbers here; the unearned premium reserve, ceded unearned premiums balance,
gross loss and LAE reserve, the reinsurance recoverables; those are all zero, because
it’s a brand new company. In terms of the other information we’re going to assume
that on average the company earns 50% of the written premiums in the current year, with
the remainder in the year directly following that. And we’re doing this mostly because,
on average if you think about the math here, if you assume a roughly normalized distribution
of when customers actually take out policies, the average is probably going to be 50% of
the way through the year. So as a result we’re going to say that 50% on average of the premiums
are earned in the current year, and then 50% are in the next year. Now for the initial
loss and loss adjustment expense ratio I’m setting it to 75% here. Now the interesting
thing if you look down here is that I have not filled in the loss in LAE ratio for Years
2-5 here. We’ll get into why that is and why we are leaving that out in the next lesson,
but for now just bear in mind that even though that’s the initial ratio it may not actually
stick to that over time. So it may actually shift and go up or down over time, depending
on some of our other assumptions here. Then the losses paid out in cash. In the other
lessons before this, the preceding lessons we went through the loss triangle, and how
let’s say you have losses that are paid out in cash in Year 1-2-3 how that actually
works. Here we are not going to bother with that, because we have multiple different years
in our model. For now we’re going to come up with a simplified assumption, and just
say that 70% are paid out in cash in Year 1, and then 30% the remainder, is paid in
cash in Year 2. The income tax rate of 40% is pretty standard, although sometimes insurance
companies have lower effective tax rates, especially if they have offshore operations.
A lot of insurance companies tend to be based in Bermuda, for example. So sometimes you
do see lower tax rates, but here we’re just going to go with 40% to make our calculations
easier. Now in terms of projecting the premiums here, which is where we’re going to start,
there are a few key pieces of information. First off we need to know how much our premium
volume is growing by, and then what the rates on those premiums are growing by each year.
Now for the growth in the gross written premium volume, we’re dealing with a brand new company
here, so it’s really hard to say anything concrete. But generally speaking, as you can
see from my note over here, generally the growth is going to be higher at the beginning,
as the company is getting started, and going and getting customers, as you’d expect.
And then over time just as with companies in any other industry it’s going to slow
down, and eventually converge on the overall industry growth rate, the overall GDP growth
rate, or something else like that, some kind of macroeconomic variable. Now with P&C insurance
it’s also important to note that the industry is highly cyclical. So in general, when you
see periods of accelerated growth with premium volume you’re also going to see margins
that go lower and lower, because as the industry is growing they’re spending more, and so
their margins go down. And then likewise, when the growth slows down and let’s say
that you are in the down part of the cycle that’s when the profitability is going to
go up as companies consolidate. They focus more on profitability. They cut their expenses,
because they’re not growing as quickly anymore. So there’s an element of cyclicality to
this. We’re not going to deal with that fully in this model, because it’s not particularly
relevant, but we’ll see an example of that and we’ll see some equity research coming
up later on that spells it out and gives a few more examples of this in more detail.
Now the growth in the average premium rate, if you think about it, what we’re really
doing here is actually very similar to how you’d project your revenue for a normal
company. We’re looking at effectively the unit sales. So the number of units sold, in
this case the number of premiums sold in percentage terms, and then average selling price. In
this case the rates for those premiums. So we can put those two variables together to
get to our overall number for the gross written premiums, and the growth rate for the dollar
value there. And as I say over here, for the average premium rate, this is also going to
converge on the GDP growth rate, the inflation rate or something else like that over time.
And again, insurance is very cyclical so you see that cyclicality with the growth or decline
in premium rates as well. So that gets us to our gross written premiums. Here, notice
that I am not splitting this into direct and assumed written and earned premiums. I’m
combining them, because I don’t want to bother with splitting it out in that much
detail for now. Instead for our calculation and our derivation we’re just saying gross
minus ceded equals net down here, and we’re sort of combining direct and assumed already
with our gross calculations at the top. Now in terms of the ceded side, we’re assuming
that the company has a 30% quota share reinsurance policy in place, reinsurance treaty in place
really. We’re not specifying which companies they have this with or which business lines.
Instead we’re saying that overall all things considered, their insurance is 30% reinsured
by other companies. This might be one company. This might be 10 companies, it might be 100
companies. We don’t know. We are just looking at the aggregate picture here, and using that
to establish the reinsurance percentage. Now in reality they are probably going to have
excess of loss (XOL) treaties. They’re going to have all sorts of other terms for their
treaties. But even when you’re modeling real companies, it’s not really practical
to look at all that, you don’t have all that information. So often you come up with
some kind of simplifying assumption like this and say, “Okay, maybe we’ll look at the
QS side and then the XOL side,” but normally you don’t go beyond that, unless you actually
have enough information to do so. So those are some of the key pieces of information
that we’ll need to project our premiums. With all that in place, now let’s get down
to the business of actually doing this. We’re going to start with the premiums here, and
with our gross premium reserve, and also with the ceded unearned premiums balance. Once
we have those then we’ll look at the commissions and deferred acquisition costs. So let’s
start with the gross written premiums. For the initial number remember we have defined
this above as one of our assumptions, so I’m going to link to this $10,000. And then for
Years 2-5, so if you think about the growth rate here, basically we have two things going
on. The volume is going up and then the rates, the prices are going up. So how do we determine
the Year 2 number? Well, we take our Year 1 number and multiply it by one plus the premium
volume, and then one plus the average premium rate. And we can copy that across. And if
you take a look at the growth rates here, you can see that essentially we’re going
to be adding up these two to get to the overall growth. So let’s just take these, copy it
across, you see 12%, 10%, 8%, 7%, and if you look at the numbers it’s really just adding
the volume growth, and then the average premium rate growth. Now for the gross earned premiums
this one is a bit of a non-standard item, you will not really see too much if you look
in insurance companies filings. But, I’m listing it here as I say in my note over on
the side, to make our calculations a little bit easier. So to do this we’re going to
take the previous year’s gross written premiums, which are zero for Year 1, and multiply it
by one minus the percentage that’s actually recognized in that year. So we’re recognizing
the remaining amount in Year 2 here. And then we’ll take the current year’s numbers
and then multiply it by the percentage recognized in this current year. And we can copy this
across. And again, this is a little bit of a stretch, but I’m listing it here for ease
of calculation. The real way to handle this would be to look at direct and assumed premiums
separately, but we’re not doing that here, so as a result we’re doing this instead.
Now on the ceded side, very simple, there’s really not much to this. All we do is take
our gross written premiums; I’m putting a negative sign in front; and then I’m going
to multiply by the quota share reinsurance percentage up here of 30%. And what I can
do to make this even easier is to anchor the row part there of 26, so that way we can make
copying and pasting this easier. And so we have that. So we are essentially giving up
30% of our gross written premiums, and 30% of our gross earned premiums, as well. You
can see another implication of the way we set this up. Which is that if you think about
what’s going on here, essentially we’re saying that not only are we assuming premiums
from other companies, but once we assume them we are also perhaps, ceding some of those
to other companies. And so effectively they’re getting reinsured twice, and who knows those
other companies that are taking them on, they might be ceding them, and having other companies
reinsure them as well. So it goes back to that point that I made in one of the overview
lessons that with insurance you can have many, many layers of this going on. You can have
insurance that gets insured by another insurance company; that gets insured by someone else;
that gets insured by someone else in turn. So there’s really no limit to this. You
can go many, many layers and levels deep here, but I’m just bringing this up to show you
one consequence of the way we set up our model here. Now for net written premiums normally
here, you take direct plus assumed, minus ceded, here gross already is assumed plus
direct, so all we do is take gross and then subtract out – really add, because it has
a negative sign – the ceded written and earned premiums. So we have that. And that’s
really all there is to it. Not too complicated, because you’ve already learned all the concepts
before, really just putting everything together in this part of the lessons, and in this model.
So now the next two items on here, so the gross unearned premium reserve and then the
ceded unearned premiums. So remember why we need these, because with insurance companies
– let’s go down to their balance sheet quickly – with insurance companies they
present their balance sheet on a grossed up basis. So in other words this unearned premium
reserve and the loss and LAE reserve, these are both gross numbers. And then what happens
on the asset side of the balance sheet, the reinsurance recoverables, this is a net against
the loss and LAE reserve. This means what part of the loss and LAE reserve the reinsurers
are responsible for, what portion has been passed on to them. And then the ceded unearned
premiums – this corresponds to the net portion of the gross unearned premium reserve. So
this is saying, “Okay if you take the gross unearned premium reserve, you subtract the
ceded unearned premiums that tells you your net reserve. What you are actually responsible
for.” The reason why we’re listing these here anyway, even though they are technically
covered by their companies, once again, is for more transparency to see exactly what’s
going on in this case. So that is why we need these numbers in addition to just the unearned
premium reserve and the loss and LAE reserve that you are used to. And this is how you
are pretty much always going to see it in insurance company’s filings, so that’s
why it’s important to go through this here, and to go over this concept of grossing up
a balance sheet. So for the change in the gross unearned premium reserve for this remember
our formula from the overview lessons, all we do is take our written premiums minus our
earned premiums in this year. This give us the change. And then for the gross unearned
premium reserve itself in Year 0 the initial part of our model here, we’re going to start
off with our initial assumed balance of $0 for this initial unearned premium reserve
right here. And then what’s going to happen is that over time we take this number, and
then we add in the change, and then you can see that it keeps going up over time. In some
of the previous lessons this actually went down over time, because we stopped writing
premiums, but assuming that your written premiums keep going up each year, then the gross unearned
premium reserve is also going to keep going up each year. Now for the part that goes to
the reinsurers instead, so for this one it’s also pretty straightforward, we’re going
to take our ceded written premiums – I’m going to put a negative sign in front, because
we want to effectively subtract our ceded earned premiums from our ceded written premiums
and look at that. We want that to be a positive difference as well. So we have that, $1,500.
And then going across it goes down to much smaller numbers. Now if you think about the
math here this makes perfect sense, because let’s take our change in ceded unearned
premiums and divide by the change in the gross unearned premium reserve. And sure enough
30% each year, why is it 30%? Because our quota share reinsurance percentage here is
also 30%. So pretty straightforward but it is important to track both of these separately.
As I say here over on the side, our net unearned premium reserve, if we want to do that instead,
would just be the gross reserve, minus the ceded unearned premiums balance on the asset
side on the balance sheet. So then for the balance here, once again we’re going to
take our assumption from above, this initial balance for the reinsurer’s unearned premium
reserve, and then we’ll take the previous number, plus the change, and copy that across.
So we now have all of our information on the premium side, which comprises a good portion
of the revenue for this particular company. We know what our reserves are going to look
like. We can even start filling in the balance sheet if we wanted to. But before we do that
I actually want to finish the rest of this section, go through the losses paid in these
loss reserves. And then also before we get to that, go through the commissions and deferred
acquisition costs. So as I mentioned before the losses are going to be coming up in part
two of this series of lessons. For now though, for the rest of this lesson, now that we have
our premiums numbers, and now that we’ve been through some of our assumptions above
what I want to do is turn our attention to the commissions and deferred acquisition costs
down here. And you remember the basic idea for how this works from our overview lessons,
but essentially we pay out this entire commission expense that we owe to brokers or salespeople
in cash up front. So if sell a policy for $10,000 and we sell it on June 30th we will
only earn $5,000 of that, only collect $5,000 most likely from the customer in cash over
the next six months. But the broker doesn’t want to get paid the commission on just that
$5,000. He wants to get paid the commission on the entire policy. So we have to payout
whatever the policy is worth, times the commission rate in cash up front. But on the income statement
because of the matching principle of accounting, we cannot actually recognize that entirely
on the income statement. So instead we have to defer part of that and create this deferred
acquisition cost asset, very similar to the intangible assets and how those get amortized,
if you’re familiar with that. But same basic idea here, you’re paying out everything
in cash up front. Also very similar to capitalized financing fees, you’re paying out those
in cash up front, and then you are expensing them and recognizing them on the income statement
over time. So for the cash commission expense we are going to take our net written premiums
right here, and then we’ll multiply it by the net commission rate on the net written
premiums of 15%; 10-20% as I say over here, is pretty standard for the net commission
rate for P&C insurance companies. And we’ll copy this across. Now why did I take the net
written premiums here, rather than the gross written premiums? Why am I not looking at
this on a gross versus ceded basis, and then using that to get to a net deferred acquisition
cost asset? The answer is that it’s not really worth the time and effort in this case.
The commission expense is not really the key driver in the model. It is good to look at,
it will definitely affect things. It is going to be a fairly large expense, but in general,
you don’t care about separating the deferred acquisition cost into a gross asset versus
a net asset. You may see it, I’m not going to say that you will never see it, so you
may see it sometimes on the balance sheet, but in general it’s not one of the more
important items to list on a gross and net basis. So that’s why we’re not doing it
here. That’s why I’m looking at the net numbers instead, and why our deferred acquisition
cost asset here is essentially a net number. Now for the increase or decrease in deferred
acquisition costs, so for this one we have a problem because if we’re looking at this
on a net basis, then remember for the deferred acquisition cost it’s going to go up or
down by however much the unearned premium reserve changes by each year, times that commission
rate. So whatever we’re deferring into future years, times the commission rate, that is
how much we’re going to defer in terms of expense recognition, and how much our deferred
acquisition cost asset is going to go up by over time. But we have a problem, because
we don’t yet know what the net change in the unearned premium reserve is. Fortunately,
there’s an easy way to solve this problem, which is we take our change in the gross unearned
premium reserve, and we subtract the change in the ceded unearned premium balance. So
we have that. And with that in place now we can take our net change in the unearned premium
reserve, and multiply it by the net commission rate of 15% up here, and we can see it’s
going up, which makes sense because once again, if our written premiums are going up, if we’re
earning more and more each year, then we are also deferring more of these acquisition costs.
Yes, we are paying out some of them in cash, and we’re recognizing more and more of them
over time, but in general, if our written and earned premiums keep going up, then this
asset is going to keep going up over time. Now for the asset itself let’s link to our
initial assumption above for the initial deferred acquisition cost asset. And then for how it
changes we’ll link to the old balance, we’ll add in the increase or decrease and copy that
across. So now we have our deferred acquisition cost asset for the balance sheet. We have
our change, which of course is going to show up on the cash flow statement. And then the
last thing we need to do here is figure out what is going on, on the income statement.
So for this part let’s just take our cash commission expense, copy that across. And
then we’ll flip the sign on the deferred acquisition cost asset here, on the change
in the deferred acquisition cost asset I mean. Because again, this is the amount that gets
deferred into future years, so if we’re deferring $525, even though we’re paying
that out in cash, on the income statement we have to subtract that deferral amount and
that is actually what we are actually going to be recognizing. So let’s sum up these
numbers now, and that gets us to how much we’re actually going to be recognizing on
the income statement each year. So with all that in place, we’ve now completed part
one of our simplified P&C operating model here. To recap what we did: In the beginning
we started out with our baseline assumptions for the premium recognition; the premium growth
based on the volume and the average rates, and also the quota share reinsurance percentage;
and then our baseline gross written premiums and deferred acquisition costs. We’re assuming
these reserves are all zero. Then we went down and projected the written and earned
premiums based on those assumptions, also the ceded written and earned premiums, got
to our net written and earned premiums, and then figured out what our unearned premium
reserve and our ceded unearned premium balance on the other side on the balance sheet are
going to look like over time. Then based on those numbers we calculated the commissions
in cash and then also the amount of commissions that we’re actually recognizing on the income
statement each year. So not too complicated, it’s really just a build-up and the culmination
of all the previous lessons in this course. But it is important that you understand all
of these concepts to get started projecting this type of company. So coming up in the
next lesson we are going to move over to the expense and loss side, and we’ll learn how
to estimate the losses in LAE incurred and paid, and all these different reserves and
how they change over time. We’ll also learn about a different way to project the loss
in LAE ratio. In the simplified lessons, the overview lessons from before we just assumed
a constant percentage here. In reality, this percentage and this ratio are probably going
to be changing over time. So you’ll learn how that works in a different alternative
method for estimating this as well.