Hey guys, it's MJ the Student Actree and this is CT5 Chapter 13 Profit Testing and Reserves. I like this chapter because it's actually very easy, it's very simple and it's almost like getting free marks. So without further ado, let's jump straight into what it is. Essentially, what we're going to do is we're going to be talking about this whole thing known as zeroization.
it's a strange word to say it's zeroization technique okay and basically what it is it's a method used for creating reserves hence why it's called profit testing and reserves so let's get to it okay to calculate the last non-zero reserve sorry okay so i mean there's all these formulas that i could talk you guys through um But what I did was I created my very own diagram. Okay, so instead of having to read through all of this like the textbook gives you, I decided to draw a very nice diagram. And here it is.
Okay, it can't all fit in the screen at once. So we'll start here. Basically, what you do with zeroizing is you'll have your profit vector.
Okay, let me see if I have an example of a profit vector. yeah here's an example of the profit sorry i'm jumping up all around but you'll you'll see why so we've got this profit vector here okay and what we want to do is we want to zeroize it zero i'm not even going to trust that um and how are we going to do that so that's what we have and this is what we want to result in okay so what you can see with this profit vector is that the only negative value that should be appearing the first one. All these others must either be zeros or positive values. So you can see over here we had a negative value here and a negative value here.
So what we do is so bearing that in mind, let's look at my diagram. And first step are there any negative cash flows after the first year? And the answer is yes.
That was number four. is negative. So yes, so start from the last negative entry and calculate the reserve one year before. And that's where this formula here comes in.
So it's the reserve one year before is going to be equal to the cash flow, make it negative, divided by the interest. So we set up this reserve. So for here negative 10.82, we set up this reserve at time 3. 3v is equal to that, that divided, you can see it's a little bit smaller because of the interest.
Okay, so now what do we do? We go back to our little diagram. Okay, it says this zeroizes the entry and decreases the one before it.
Okay, so what we do is we now use the purple formula. And what this is saying is the non-unit cash flow of the year before now needs to decrease by this reserve that we've set up times it by the probability that the person survives to that age. So if we come to our example this is now for year three okay we take its existing value and we subtract it by the reserves times the probability that the person is still alive. and we get 79.09 which if you see at the end is what we got over there 0.7909 so let's go back to our diagram okay is the entry before positive or negative so is the entry before it positive or negative okay and in our case it is negative so what we need to do okay is, oh no no sorry, this entry is positive.
It's positive because 89 becomes 79. So we say positive and we come back here. Any negative cash flow after the first year? And the answer again is yes because the second cash flow is negative.
So now what we do are the exact same steps. We're going to do the blue, we're going to do the purple and then we're going to check again with the white. So those are our formulas. In our example, year three is positive so you can see we went good but year two is negative so we set up another reserve at year one which is 5.02.
And we then zeroize and decrease the non-unit cash flow at time two. And at cash and at year one, we get negative 45.90. Which is fine because that's the very, so any negative cash flows after the first year, the answer is no. So we are finally done. And ja, so there we go.
That is actually how simple this whole thing is. I don't know if I complicated it. But I get this, it makes perfect sense to me.
What you're doing is you're making it zero, you're taking that value, you're putting it here, you're just decreasing it by interest and force of mortality, you're checking if that's positive, and then you just keep repeating the thing. I made a little cheat sheet, so let me just push it up here a bit. Here's my little cheat sheet. You can see I use a different app, that's why it's on the white background. This is basically if you didn't understand anything I said learn this off by heart and you should actually be fine in the exam I mean this is an easy question.
You should be getting these marks, but job that is chapter 13 It's the penultimate chapter of CT5. So I hope you enjoyed this video. Please hit like and subscribe and Leave me a comment in the comment section below.
Thanks guys. Cheers