In this workout, we've been asked to calculate life insurance profits using the portfolio information below. And we're assuming that all cash flows occur at the year end, and that includes the premiums. Now we've been told that the insurance company expects to generate a return of 5% on its investments, and also the discount rate used for calculating reserves is 4.5%. Now we've been given premium information for years one to eight, as well as the insurance reserves calculations, and that includes the benefits paid each year. Now the first thing we'll need to do to calculate our investment returns is work out the cash available to invest. And as usual, our beginning cash balance will be equal to our prior year ending cash balance. And because all the cash flows occur at the year end, we can take that beginning cash balance and calculate the return on it. So that's the 5% rate of return there.

And then we'll add to that the premiums received each year and deduct the benefits paid. Now summing all that together, that gives us the ending cash balance for year one. Now we'll roll that forward only to year seven because that's when things stop moving around. Now you can see how the investment returns, they build in the early years of the policy as the premiums flow in. And then as the benefits start to be paid out, they start to level off and fall away. Now there's one more thing I'm going to do before I move on, which is to calculate the discount unwind in the change in insurance reserves, because that's gonna be useful to me later on. Now the way we do that is to take the beginning balance on our insurance reserves and multiply that by the discount rate of 4.5%.

So I'll roll that forward as well and we'll come back to this number a little bit later on. Now what we can do is calculate the profits from this portfolio for each year. And to start with, we need the premiums. And remember that for life insurance, the premiums are earned as they're received. So that's 120 in year one. And the investment income we've already calculated. We'll just take that from above. Now the benefits paid and change in reserves we have in the insurance reserve schedules above. And we can sum all that together to give the operating profits from this portfolio. So let's roll that forward again to year seven. Now you can see how the operating profits build in the early years and then start to fall away later on. Now that's partly because of what's happening with investment income, but also because of what's going on in premiums and also in reserves. So let's have a look at that in more detail. Now the way we can do that is to split our operating profits in a slightly different way, into the technical margin and the investment margin. Now, the technical margin is the premiums less the change in reserves and benefits paid but before the discount unwind. Whereas the investment margin is the investment income less that discount unwind. So let's calculate that now.

So the earned premiums less our benefits paid but adding back that discount unwind that's baked in to that benefits paid and change in reserves number. And then the investment margin is our investment income less the discount unwind. Now just to prove to ourselves that everything's still there, we can add that together and we still have the same operating profit. So that's a relief. Okay, so let's roll that forward and now see what's going on here. Now this is interesting because you can see the technical margin is stable in each of the years when the earned premium is stable. So effectively the profits are being released to earnings in line with the premiums. Now, the investment margin is just the spread. So that's the return that's being generated by the insurance company in excess of the interest cost on their insurance liabilities. Now, this way of cutting the profits into technical margin and investment margin is a common way for insurance companies to report their results, particularly in Europe.