Hello everyone. In today's example, I wanted to focus our attention on the obligations side for the pension accounting. The projected benefit obligation, or actually the accumulated benefit application. I want to take an example to see how those elements are different. How do we calculate each one of them? So we're going to focus instead of all collective for all employees were going to take an example on one employee so that we can scope down and see how does this accounting those actuary work for predicting and estimating the obligation for the pension liability. So let's take a look with an example. Here you go. Universal company has a defined benefit pension plan that specifies any wool year end retirement benefits equal to, and here is the formula for calculating the pension. It's 1 and half percent times the number of service years that the employee has worked times the final years salary. This is a typical formula that is being used when we calculate the pensions. And now we're going to focus on one employee. Jason King was hired by universal at the beginning of 2001. King is expected to retire at the end of 2045 after 45 years of service. His retirement is expected to spend 15 years. So after he retires, the pension will be paid out for him is expected to be for 15 years. At the end of 2020, which means 20 years after being hired, his salary is 100,000. The companies actually projects Jason salary to be 250,000, at retirement 2045. The actuary discount rate is 7%. Okay, what are the requirements here? We need to focus on number one ,what is universals projected benefit obligation at the end of 2020 with respect to Jason King? Number two, what is universal accumulated benefit obligation at the end of 2020 with respect to Jason King? So now the difference between one and two and one focus on the projected benefit obligation while number two focus on accumulated benefit obligation. What is the difference? Obviously, simply the difference is that the projected benefit obligation will take the projected salary at retirement, while they accumulated benefit obligation will take the current salary. Obviously there is a discrepancy here. Because in 2020 his salary was 100,000, which is expected to be in 2045, is expected to be 250000,. Obviously, using 250,000 versus 100,000, will make a big difference to the obligation. And that simply difference between one and two. In three and four were taking it to a different level. In three, the requirement three if we assume no estimates change in the mean time, what is the companies projected benefit obligation at the end of 2021 with respect to Jason King? So now I'm moving one step further. One year later, I want to take a look at how much would be the projected benefit obligation one year from now. Current today I'm in 2020, now I'm looking at it one year later. How would the projected benefit obligation be? Number 4, decomposed the 2021 increase in PBO. So now I have a number 3 projected benefit application for 2021. Number one, I have the projected benefit obligation on 2020. Then I want to see the increase and I wanted to compose that into the two components of the service cost versus the interest cost. Very interesting question and that will give us an idea imagine how much work is being done. Because this is basically only for one employee. Imagine that the company has to do all that for all its employees. And the amount of actuary assumptions that are going to be actuary assumptions that are going to be used. Okay, let's get started. The projected benefit obligation at the end of 2020, that's obviously the formula. So now Jason King will be paid after retirement 75000, each year, but that starting at the end of 2046. I am currently now in 2020. So I'm going to take and calculate that annuity and I have an annuity for 15 years because it is expected that the pension will be paid out for, the horizon will be for 15 years. So I'm going to take that 75,000, and calculate the present value of it using an ordinary annuity. And that is the present value factor for n equal 15 i equal 7%. Then obviously now I'm calculating the present value of all the pension payments that will be paid to Jason King from 2046 up till his expected spend whatever. So actually this will give me the present value till or at 2045. But I don't want it, the present value For 2045, I want it for 2020. Then I obviously will take that lump sum, which is the $683,093. I am going to take that and calculate the present value of it as a single sum today in 2020. And that's why I'm going to discount it with using n = 25 as a single sum, and that is the projected benefit obligation at the end of 2020. We're going to do the same thing, exactly the same thing now, with the accumulated benefit obligation, exactly the three steps. But actually, all what I'm going to change is the 250,000. Now I'm going to use the 100,000. So the ABO, the accumulated benefit obligation. Now, first of all, here is the formula. So I'm calculating the new formula. Now, because I'm using the 100,000, the 30,000 instead of 75,000 will be paid out as retirement for pensions. To discount to the 2045, year 2045, I'm taking it as an annual annuity and using the same factor. But that is the present value of the annuity of the pension at the end of 2045. I want to discount it back to the end of 2020, and that's simply the next step, which is to discounted it to 2020 as a present value of a single sum. So that is showing number one and two, the difference between PBO and ABO. Now let's go to PBO in 2021, one year later, what is going to happen, here you go. First of all, the 75,000 has changed because now the number of years of service, instead of 20 that I used in requirement one, now it's 21 years because Jason has worked one additional year. So now with 21, the pension is going to be the annual pension payment after retirement will increase to 78,750. Do the same thing to discount it to 2045 with the present value factor of an ordinary annuity, then discount it again now into 2021. And that's why n has changed to 24 instead of 25, because now I'm discounting it to year 2021. And obviously, the present value of this pension retirement plan for Jason King, or the benefits that will be paid today in 2021 is 141,405. Now let's take a look at this versus the PBO in 2020, and see what is the difference between the two. And that's where I want to analyze the increase, the change in PBO. Here you go, in 2021 I calculate 141,405, in PBO under requirement one I had 125,860. Then the change in PBO equals 15,545, out of this amount is the interest cost, which is calculated based on the beginning. For 2021, the beginning balance of that PBO was 125,860, multiply it by the 7%, which is the discount rate. And that is the element, the component that belonged to the interest cost. Now the service costs is the deficit. Very good, so now that is the decomposition between the two elements or the two components. Actually, there's another way that we can calculate it, and here is how to confirm another way of calculating that split or that decomposition. But here I'm actually going to start with the service cost instead of getting the service cost as a plug-in number. In the first one, I calculated the interest costs and I got the service cost as a plug-in number. The other one I'm going to actually calculate how much service cost that I incur because of Jason King working for me additional year. One year that's the additional year that he worked for 2021, and I multiplied it again by the present value factor 4, the annuity. Because that is the amount of the increase, what is this 1.5 times 1 times 250? This is the additional portion of the retirement that he is going to get because of this single year that he is working for me. So I took that excess, that increase, and I actually discounted as an annuity, discounted as a single amount, so I got the 6,734. Notice that there is a 1$ difference between those two, just for approximation rounding error. So after getting the 6,734, then obviously I can now infer the interest cost as a plug-in number, take the amount of the difference between the PBO. The dot that element that belongs to the service costs, and then I get the interest cost as a plug-in number. Hopefully that this example have illustrated and showed you the difference between the different ways of calculating the obligation. Obviously we are going to maintain our analysis with the PBO, the projected benefit obligation. I just wanted to show you the difference when we calculate the ABO versus the PBO. But the one that accounts is that we take into consideration is the projected benefit obligation based on the projected salary at retirement. Thank you.