In this workout, we've been told that an insurance company has written some insurance policies on the first day of year one and has paid upfront broker commissions of 10.

Now, we've been asked to calculate both the DAC asset and underwriting profits in years one and two. Now, we've been told that the premiums written were 100, and also that the coverage period for the policies was two years, and that's going to be important to us both when calculating the DAC asset and when calculating the underwriting profits.

Next, we also know that the expected loss ratio is 60%, and finally, those are the broker commissions of 10.

So let's start by calculating our DAC asset, and we're going to make our beginning balance equal to our ending balance from the prior year.

And because these are new policies at the start of year one, that's nil.

Next, we're going to add the deferrable expenses, and that's the broker commissions, which we're going to capitalize as part of the DAC asset.

Next, we need to subtract the amortization of those capitalized expenses. So we're going to take those capitalized amounts of 10 and divide them by the coverage period of two years.

So that gives us an amortization of five in year one.

Now, we can sum all of those together to give the ending balance of the DAC asset for year one, and we can roll that calculation forward for year two. And you can see that by the end of year two, that DAC asset is showing as nil because all of those capitalized costs have been amortized throughout years one and two.

Now, we can calculate our underwriting profits, and we start with our earned premiums. So we know the premiums written were 100, and we're going to spread that over the two-year coverage period.

So that should give us premiums of 50, which it does.

Now, we can calculate the claims expense by taking our expected loss ratio of 60% and multiplying that by our earned premiums, which gives us a claims expense of 30 in year one.

Now, the acquisition expenses are just our amortization charges relating to our DAC, so we can take that from above.

Now, we can sum all of those items above, and that gives us total underwriting profits of 15 in year one. And let's roll forward that calculation so we can see what happens in year two. And you can see that the underwriting profits in year two are also 15, and that's because what we've done is essentially take the premiums written, the claims, and the broker commissions, and spread all of those consistently across year one and two, which is the coverage period for those policies.