 Hello, and welcome to the session. This is Professor Farhad. In this session, we would look at an example for a cost allocation, and specifically deals with the reciprocal model. In the prior section, we looked at the direct, as well as the step method. And all these lectures are posted on farhadlectures.com. So you can go to my website and view those recordings. So the reciprocal model, what is the reciprocal model? The reciprocal model is a reflective of the fact that the service department, so the service department, they do provide, for example, S1 and S2. They do provide services to themselves, and we will take that into account. Why is this important? This is important because in the direct method, we ignore this relationship between the service department. In the step method, we only looked at it from a one-way perspective. We looked from the most, the longest service department going down. In the reciprocal method, it's going to be both ways. So let's take a look at the same example that we use for the direct method, and for the step method to illustrate the reciprocal method. So we have this company, the department cost allocation. We have Homeland Life Insurance, S2 service department, S1. So we're going to call it S1 and S2. S1 is actuarial, and S2 is the premium department. And they have two production department. So S1, this is S1 and S2. This is the premium. And they have two production department, P1 and P2. P1 is advertising, and P2 is sales. And this is the percentages how they support each other. Now what we have is we have to solve this equation. We have to use linear algebra. How do we use linear algebra? Simply put, department S1 already have direct allocation is $80,000. Service department 2 is $15,000. But before we proceed, before we proceed to allocate from the service department to the production department, once again, in the reciprocal method, the service department, they will need to allocate among themselves. Now how are we going to do so? Well, we're going to have to do some algebra, some manipulation. Let's look at S1, which is the actuarial department, S1, S1. What is S1? S1, how much does it have? S1 has $80,000 of direct allocation plus an S1 we are going to have 20% of the premium department. So it's going to be 80,000 plus 0.2. Where did I get that 20%? Well, the premium department allocate 20% to the S2, allocate 20% to S1, premium allocate 20% to the actuarial, plus 20% of multiplying by S2. S2, how do we figure out S2? S2, it has a direct cost of $15,000. Plus S2, it's going to get 80% 0.8 of S1. Now we have two linear equation that we need to solve for. So let's solve for S1. Let me just now switch color. Maybe this tool will work with the pen better. S1 equal to $80,000 plus 0.2, open the bracket, 0.2, multiply it by $15,000 plus 0.8 S1. How did I get 0.8 S1? 0.8 times S1 equal to 0.8 S1. Now let's solve S1. Sorry, my pen is acting up a little bit. S1 equal to $80,000 plus what is 0.2 times 0.2 times $15,000? 0.2 times $15,000 is $3,000 plus what is 0.2 times 0.8 S1? So 0.2 times 0.8 is 0.16 S1, 0.16 S1. Now basically, I'm just going to solve S1 equal to $83,000 plus 0.16 S1. Now basically, I'm just going to eliminate S1. So I'm just going to eliminate S1. So I'm going to add and subtract 0.16 from both sides. So this is S1 means 1 S1. This is 1 S1. So 1 S1, so I'm going to take 1 S1 minus 0.16. It's going to give me 0.84 S1 equal to $83,000. And basically, I'm going to just solve for S1. I'm going to divide both sides by 0.84. So if I divide both sides by 0.84 S1 equal to $83,000 divided by 0.84, S1 will equal to $98,810. This is what S1 is. Once I find S1, how much allocated to S1? It's easy to find S2. All I have to do is plug S1 into the formula of S2. And this is basically S2. So if I take $98,000, plug it here into S1. So let's see what it looks like now. So I'm going to go to clip this. So this is S1 S2. S2 equal to $15,000 plus 0.8 times S1. We know what S1 is, 98,810. S2 equal to $15,000 plus 0.8 times 98,810, $79,048. S2 equal to $94,048. So I have S1 and S2. Since my pen is not working well, I'm going to move to the Excel sheet and work this on the Excel sheet that's cleaner. Actually, in the real world, what happens is when you are dealing with multiple service departments, you don't do this manually. You figure this on an Excel sheet. So let's work this on an Excel sheet to see how it works. So just to know what S1 is, we need the number for S1 and S2. So let's go back. S1, we computed S1, we computed S2. S1 was 98,810 as computed earlier in S2. Happens to be $94,048. Now what we're going to do, we're going to set up the problem again as we did it earlier in the other method. S1, S2, service department one, service department two, P1 and P2. Okay, and basically what we're going to do, we're going to go back and now allocate. Yeah, well, before we allocate, let's make sure we 65,000. Let's just put the original direct allocation, 55,000. And this was 60,000. This was 40,000. Let me double check the figures just to make sure I have them right. It's 80, 15, that's the problem right there. 80 and 15, keep. Okay, 80,000 and 15,000. Just give me one moment, please. Okay, now what's going to happen is I am going to go ahead and start to unlock 15,000, 15,000. Now I'm going to go ahead and start to allocate S1. I'm going to start to allocate S1 to S2, P1 and P2 and S2 to S1, P1 and P2. So what's going to happen, let me just show you in a moment. So I'm going to take S1, allocate S1 to S2 to P1 to P2. Then I'm going to take P2, allocate it to S1, allocate it to P1, allocate it to P2. So this is what the reciprocal method is. So let's see how are we going to do this? Well, how are we going to do this is based on the allocation that's given to us in the prior session and the prior session. What were the allocation? Well, basically what we were given is this. We were giving that S1 department or S1 department allocate 80%, let me go back to the figures, from 80, 10 and 10. So 80, 10 and 10 is right there in the problem. So let me just show you one more time. So S1 is 80, 10 and 10. And for S2 is 20, 20 and 60. This is how we're going to allocate this based on what we are giving in the first original data. This is going to be 80 divided by 100. Let's do it as a decimal. 80 divided by 100, 10 divided by 100, 10 divided by 100 and 10 divided by 100. So this is how S1 is going to allocate to S2 and P1 and P2. So now S1 has, remember S1, we're dealing with this is S1, just going to have noticed. This is S1, I've just highlighted in yellow. S1 is going to allocate to S2. It's going to allocate to S2. S1 is going to allocate, let me highlight this in yellow so we all know where this is coming from. Okay, there we go. Okay, so we're going to allocate to S2, 80%, 80%, 0.8 times this figure. So basically what happened is of S2, we allocated already $79,084. Then we're going to allocate of this amount, then 10%, we're going to allocate, let me just make sure I take it out first. So 98,000 times 10%, we're going to allocate out of this amount to P1. It's going to be this number positive. So I'm just going to have to do this positive, negative, and it's going to be positive. And I'm going to allocate out of this, out of S1, again, 10%, I'm going to make it negative, to indicate I'm allocating it out of this amount and taking it to P2. So what I did, I took the 98,100 and allocated them to S2, P1, and P2. Let me highlight those in red, so this way. So what I have in yellow, what I have in yellow here in S1 in this box, or in this cell, okay, gets allocated some of it to S2, some of it to S, P1, and some of it to P2. Now I'm going to have to do the same thing for S2. S2 has, let me highlight S2 in yellow, S2 has 94,000, S2 has $94,048. Okay, now I'm going to do the same thing. However, the allocation is going to be not the same percentages, because it has a different percentages, it's going to be 2020 and 60. And again, how do I get those percentages? There we go, right here, 20, 60, and 20. So it's allocating 20 to the S1, 20, and 60. How did I know this? I just computed 20 plus 20 plus 60 equal to 100, happens to be easy number, 20% to 20% and 60%. So they could be any other number, but in this example, they made it very easy for us. So it's going to be 20% for S1, 20% for P1, and 60% for P2. So here we go, let's do this now. Now I'm going to take out of this department, out of S2, I'm going to take, make this a little smaller, so we can capture the total S2 in figure. So I'm going to take out of S2, I'm going to make it minus, out of S2 I'm going to take 20% out of it, I'm going to take 20% out of it and give it to S1, because it's going, again, the reciprocal is basically, we're going to give to the other department, we're going to take, make it minus once again, 20% of S2, okay, minus and give it to P1. So it's this number plus allocated to indicate it's allocated, it's being allocated. Then we're going to take 60%, make it minus, 60% of S2 and allocate this amount to P2. And allocate this amount to P2. Make this plus, okay. So what did I do? It didn't work, now it worked. So what I did, I took the 98,000 and allocated the 98,000, I'm going to use a different color here. You can use blue maybe, see it's good, okay. So I took the 94,084 dollars of S2 and I allocated them to S1, P1 and P2, okay. Now what you can do if you want to just confirm, sometime it may or may not be exactly zero, because you need to make sure everything, all the service zeroed out. And hopefully it's like rounding point, point four and point zero. So just basically because of rounding. So notice S1 and S2, I allocated everything out of them. Now I have the total for P1, just so P1 total is 88,690. And P2 total, let me copy and paste the formula is 106309, the total for that, okay. So once again, this gets a little ugly if you have too many service department in the real world, you'd use Excel, there's something called Solver in Excel and you can solve this. Maybe I will do an Excel sheet later on that deals with Excel and solve this. Or there's a special software accounting software that you could use or some sort of an automated package that's gonna help you allocate those costs. But this is basically the reciprocal method. Again, the reciprocal method is considered superior, considered, why? Because it's allocating the service costs in both direction and in the real world we want to be as imperative as possible in pricing our product. So if you have any questions, any comments and at the end of the day, always add those two numbers up, this plus this, okay, equal to 195,000 which is equal to just kind of, this is a double check, equal to all of this which is, but they have 100,000 plus 15 plus 80 which is 195 to make sure you accounted for all the cost as a reconciliation. So basically if you have any questions, any comments by all means email me or if you're taking my class, see me in class. If you're studying for your CPA or for your CMA exam, by all means study hard, it's worth it.