# Insurance Model: Net Written Premiums, Unearned Premiums, and Income Statement

In this lesson, we’ll project the gross and net premiums as well as the commissions and DAC asset for a brand-new insurance company – and you’ll learn how to make the key assumptions that drive the rest of the operating model.

## Insurance Model: Net Written Premiums, Unearned Premiums, and Income Statement

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.

[01:00]

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.

[02:00]

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.

[03:00]

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.

[04:00]

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.

[05:00]

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.

[06:00]

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.

[07:00]

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.

[08:00]

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.

[09:00]

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.

[10:00]

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.

[11:00]

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.

[12:00]

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.”

[13:00]

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.

[14:00]

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.

[15:00]

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.

[16:00]

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.

[17:00]

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.

[18:00]

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.

[19:00]

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.

[20:00]

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.

[21:00]

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.