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Cost-Volume-Profit Analysis · Acedra
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0:03
Bennet Tchaikovsky: Hello everybody, this is the accounting professor, Ben Tchaikovsky. We're here today to have more accounting fun. Can you imagine? Bennet Tchaikovsky: So today we're going to be talking about cost, volume, and profit specifically. How do we go through and determine cost functions, determining variable costs, fixed costs, and the margin of safety. Quick disclaimer, anything said in this video presentation is the opinion of myself.
0:29
Bennet Tchaikovsky: Does not represent the opinions of any of my employers or any other affiliated organizations, including, but not limited to, Irvine Valley College and the South Orange County Community College District.
0:41
Bennet Tchaikovsky: Yeah, if my cat decides to show up and zoom on us, it's gonna be a better day. Let's go ahead and take a look at our question today. So, today we're going to be looking at how do we go through and determine cost functions, variable cost per unit, fixed cost per unit. So.
0:58
Bennet Tchaikovsky: We have over here, ZZix has two types of freeway signs, Barstow and, Baker. Well, I drive up on the I-15, so I decided to basically do a little bit of anagram and reverse it. But we've got W and R that are sold in various states throughout the United States. Bennet Tchaikovsky: R sells for $800 each, while W sells for $900 each. Z believes that they can accurately allocate all overhead costs, of the two products.
1:26
Bennet Tchaikovsky: Meaning that they treat them as two separate companies. Okay, so… Bennet Tchaikovsky: I… we want to kind of go through first over here. I'm just gonna pause real quick, because I deleted something I should not have deleted.
1:41
Bennet Tchaikovsky: with the magic of the backward function up here on Google Sheets, we're back. So, when we look at this over here, we're kind of given data for a period of 2 months. Bennet Tchaikovsky: And if we're going through, and if the overhead is basically being allocated throughout, you know, basically evenly throughout, or they can accurately allocate overhead costs.
2:03
Bennet Tchaikovsky: There is a formula that we can go through and use to, essentially figure out what is my variable cost per unit of activity. Bennet Tchaikovsky: And the way we're gonna go ahead and do this is the formula that if you're taking my class, I will provide to you on the exam. Bennet Tchaikovsky: But what this is gonna be is that, the highest
2:29
Bennet Tchaikovsky: Costs, the highest production costs.
2:38
Bennet Tchaikovsky: Minus the lowest production costs. Bennet Tchaikovsky: And I'm going to be dividing this by my highest
2:48
Bennet Tchaikovsky: Production in units minus my lowest production. Bennet Tchaikovsky: in units. Okay, so… and what this is going to tell us is what is the variable
3:03
Bennet Tchaikovsky: Cost per unit. Bennet Tchaikovsky: Now, the thought is, is when we go through and do this, if we know what our total costs are, say, for product W of $1,090,
3:19
Bennet Tchaikovsky: I can take this value, and then take my number of units sold at that total cost.
3:28
Bennet Tchaikovsky: Times my variable cost per unit. Bennet Tchaikovsky: And then I can add, basically, my fixed costs. Bennet Tchaikovsky: Which should essentially come over here and get us what is our… what we're trying to go through over here and solve for.
3:45
Bennet Tchaikovsky: Now, the important thing is with this is we also want to kind of make sure, well, if it works like this, then to make sure that the fixed costs are going to be the same, we'll just call this fixed cost, we'll just call X.
3:59
Bennet Tchaikovsky: Right over here, then that means if the relationship holds, then we should have 290,000. Bennet Tchaikovsky: Equals 400 units, right, because this is the number of units sold that are, being cost, basically, at the number of units sold at this total cost. Bennet Tchaikovsky: Times, basically, my variable cost per unit.
4:22
Bennet Tchaikovsky: Which is gonna be the same, plus my fixed costs.
4:27
Bennet Tchaikovsky: And we should probably be saying this over here, as we'll call this units produced.
4:33
Bennet Tchaikovsky: But, and again, your units produced, units sold, we'll just go ahead and assume that they're exactly the same. Bennet Tchaikovsky: So, let's go ahead here and put in the values, right? So, at the highest production cost, we have $1,090.
4:50
Bennet Tchaikovsky: And… make this look a little bit nicer. Bennet Tchaikovsky: We're gonna subtract our lowest total cost over here at $290,000. Bennet Tchaikovsky: We're gonna have the units here of 2,000 units, and we're gonna go ahead and subtract these 400 units. Bennet Tchaikovsky: And what this is gonna go ahead and give us is we're going to get 800,000 divided by 1600, Bennet Tchaikovsky: or my variable cost per unit of product W. Bennet Tchaikovsky: And now…
5:24
Bennet Tchaikovsky: I need to make sure, whenever you do these computations and, you know, when you're doing these kind of questions, make sure it works. Like, plug it in, right? Make sure it's happening. Bennet Tchaikovsky: So here, we're gonna get $1,090.
5:42
Bennet Tchaikovsky: Equals 2,000 units times my variable cost per unit, or 500,
5:49
Bennet Tchaikovsky: Plus my fixed costs, which we don't know what those are yet, but we'll know it pretty soon. Bennet Tchaikovsky: So, over here, $1,090.
6:00
Bennet Tchaikovsky: I should say this is equal to…
6:07
Bennet Tchaikovsky: is going to be equal to a million dollars, which is my total variable cost plus X, Bennet Tchaikovsky: So my fixed costs… or X should be $90,000. Bennet Tchaikovsky: Okay. Bennet Tchaikovsky: So my fixed costs over here. Bennet Tchaikovsky: or product W should be $90,000. Now, how do we go through and check this? Bennet Tchaikovsky: Well, what we're gonna go ahead and do is we're gonna plug it into this over here. Bennet Tchaikovsky: So if we take 290,000 equals 400 units.
6:43
Bennet Tchaikovsky: Times 500 per unit. Bennet Tchaikovsky: which are my variable costs, which I computed up here by taking the high values minus the low values. Bennet Tchaikovsky: Plus $90,000. Is this true? Well, $290,000 equals $200,000, which is 400 times 500 plus 90,000. Therefore, we know that we computed the variable cost per unit. 500 is my variable cost.
7:17
Bennet Tchaikovsky: And then we know that our total fixed costs are $90,000. Bennet Tchaikovsky: So we know that this is correct. Okay. Bennet Tchaikovsky: Now, let's go through and then essentially solve this for R, right? We're gonna do the same thing. Bennet Tchaikovsky: We're gonna take the highest production units of highest production costs, Minus my lowest production cost. Bennet Tchaikovsky: My bar units produced.
7:50
Bennet Tchaikovsky: Minus my lowest units produced over here. Bennet Tchaikovsky: When I subtract this, I get 60,000 equals, minus, or divided by 100. Remember, the bottom is in units. Bennet Tchaikovsky: So my variable cost per unit is going to be $600. Bennet Tchaikovsky: What does this mean? Well, kind of similar to what we were doing over here, is that with the product R, that 263,000.
8:23
Bennet Tchaikovsky: Which is my total product cost, is going to be equal to 300 times my variable cost per unit. Bennet Tchaikovsky: Plus my fixed costs. Bennet Tchaikovsky: Okay. Bennet Tchaikovsky: Similarly, 203,000 is going to be equal to 200 times by variable cost per unit. Bennet Tchaikovsky: plus my fixed pause. Okay, so we have those two right over here.
8:47
Bennet Tchaikovsky: Now, if I plug this in, if I said that, well, my fixed costs for… basically, my variable cost per unit per product are… Bennet Tchaikovsky: was at 600. Bennet Tchaikovsky: So we got 263,000 equals 300. Bennet Tchaikovsky: times 600 plus my fixed cost, which I'll call this Y. Well, this means $263,000 equals 180,000 plus Y. Bennet Tchaikovsky: my fixed costs… Must then be 83,000.
9:22
Bennet Tchaikovsky: Okay. Bennet Tchaikovsky: So again, when we look at this total kind of cost, right, my total cost are going to be equal to my fixed costs, or my variable costs.
9:35
Bennet Tchaikovsky: plus my fixed cost. That's really what we're trying to go through in using this. We're trying to basically figure out, well, how much was the fixed cost, how much was the variable cost? Bennet Tchaikovsky: So if we know that this is, in fact, 83,000 per this equation here, then we should also be able to say, well. Bennet Tchaikovsky: 203,000. Bennet Tchaikovsky: is equal to, which is at the lower level of the production, is going to be equal to 600
10:02
Bennet Tchaikovsky: times 200 units. Bennet Tchaikovsky: plus $83,000, which are my fixed costs. So $203,000 is going to be equal to $120,000 plus $83,000. Bennet Tchaikovsky: So right over here, my variable costs per unit are going to be $600 per unit.
10:25
Bennet Tchaikovsky: And then over here, my fixed costs are going to be $83,000. Bennet Tchaikovsky: So, in terms of solving this part over here, given this limited data, I… you know, what are the variable costs per unit, and what are the fixed costs? Bennet Tchaikovsky: So, given this type of question, if you're taking my class, I will be providing you this formula over here, which is going to be the variable cost per unit of activity.
10:52
Bennet Tchaikovsky: High costs associated with the highest level of production, minus the cost.
11:00
Bennet Tchaikovsky: Minus the cost associated with the lowest level of production.
11:12
Bennet Tchaikovsky: Good job, Tchaikovsky, you're doing this on the fly, always fun in units. Bennet Tchaikovsky: and lowest activity in units. Okay, so this is what's giving this part over here to us. Okay. Bennet Tchaikovsky: Let's now go ahead and take a look at our next question over here. Bennet Tchaikovsky: how many units of W&R need to be sold in order to reach break-even? Okay, now, there's a lot of different ways we could go through and compute this.
11:40
Bennet Tchaikovsky: Okay, one way I would probably go through, and I have my students, when we're going through and doing this, is always to basically write out the formula. Bennet Tchaikovsky: So we've got our sales, less our variable costs. Bennet Tchaikovsky: It's gonna give me my contribution margin.
12:00
Bennet Tchaikovsky: Right, meaning, like, how much am I basically contributing to the coverage of my fixed costs? Bennet Tchaikovsky: Which is gonna basically give me my net income. Bennet Tchaikovsky: By definition, and over here we've got units, Per unit, and my total. Bennet Tchaikovsky: Over here, by definition, break-even. If I'm being asked for W, how many units do I need to go through and sell to reach break-even? Well, I have to cover my fixed costs, which I determined to be $90,000.
12:31
Bennet Tchaikovsky: Cam. Bennet Tchaikovsky: Similarly, if I'm doing this for the other product.
12:44
Bennet Tchaikovsky: Basically, my fixed costs over here are going to be $83,000. I need to reach break-even, so that means my contribution margin Bennet Tchaikovsky: Must have been $90,000 for product W, 83,000 for product R. Bennet Tchaikovsky: So, how do we go through and do this from here? Well, we know that our variable cost per unit Bennet Tchaikovsky: It's gonna be 500. Bennet Tchaikovsky: Right? Right over here for product, for product W.
13:14
Bennet Tchaikovsky: But how do we figure out the contribution margin? Well, if we look up here, I'm told that Bennet Tchaikovsky: W, product W, sells for $900.
13:25
Bennet Tchaikovsky: And I'm also told that product R sells for $800.
13:33
Bennet Tchaikovsky: So right up here, I'm given this data, R sells for $800, while W sells for $900 each.
13:41
Bennet Tchaikovsky: So, coming over here, my variable costs over here for product under now. Bennet Tchaikovsky: If I come over to this part here. Bennet Tchaikovsky: my contribution margin for product W. Bennet Tchaikovsky: Right? Must have been her unit, must have been $400 per unit. Bennet Tchaikovsky: That means, and remember, there's a relationship between all of these. That means I must have had a contribution margin for 2225 units.
14:10
Bennet Tchaikovsky: That means to reach break-even, I have to go through and sell 225 units of product W. Bennet Tchaikovsky: Now, what's another way, and let's go ahead and do this also for product R. Bennet Tchaikovsky: If I had, over here… Bennet Tchaikovsky: If I had a… my sales for product R were $800, I determined that my variable costs were going to be at 600, that means my contribution margin must have been $200 per unit.
14:39
Bennet Tchaikovsky: That means, because of the relationship of their units times the per unit, Right, buying units over here. Bennet Tchaikovsky: must then be at 415 units. So if I have a contribution margin of 415 units, I must have gone through over here and basically sold over here in terms of sales.
15:06
Bennet Tchaikovsky: And I have variable costs over here. So these… so the number of units to break even. Bennet Tchaikovsky: For product W are going to be at 225. The number of units to achieve break-even for product R are going to be at 415. Bennet Tchaikovsky: Now, are there some other ways I could have gone through and solved this? Sure, right? Let's go ahead and take a look. Let's pull up some of these nice, ratios over here.
15:34
Bennet Tchaikovsky: Okay, so I'm gonna come back over here, go here to Problem 7 Solution, and let's check these out. Bennet Tchaikovsky: So, the first thing I need to do is that I could basically say over here, well, my break-even point in units Bennet Tchaikovsky: is I could say, well, for product W, my fixed costs were over here, were at $90,000. My contribution margin per unit, remember the contribution margin per unit is my sales price per unit.
16:10
Bennet Tchaikovsky: Minus my variable cost per unit. Bennet Tchaikovsky: Okay, that's basically my contribution margin per unit. Bennet Tchaikovsky: My contribution margin per unit is at 400. Bennet Tchaikovsky: Therefore, my break-even point in units is going to be at 225. Bennet Tchaikovsky: Now, what about my break-even point in sales dollars? Okay, well…
16:33
Bennet Tchaikovsky: Again, it's going to be my fixed cost divided by my contribution margin ratio. Well, what's my contribution margin ratio? Bennet Tchaikovsky: It's gonna be my contribution margin per unit divided by my sales price per unit. Bennet Tchaikovsky: over here, and if I take this beautifully numbered down over here. Bennet Tchaikovsky: I'm gonna get $202,500. And let's just kind of make sure that this is… yeah, this looks good.
17:01
Bennet Tchaikovsky: You know, so again, I, for myself personally. Bennet Tchaikovsky: Right? These ratios can be great, but I always like to go through and plug it through the formulas, right? And it's just… it makes it so much more definitive.
17:15
Bennet Tchaikovsky: And especially if you're taking my class, what I like to do during exams is I'll say, well, what if the sales price went up by 20%, and then what happens if fixed costs go down by 20 grand? What goes on next, right? So, if you go through, though, and you put in the hard values into this.
17:34
Bennet Tchaikovsky: then you can just kind of go through and skip these formulas. Well, let's go ahead and do this for the other part over here. Well, my contribution margin ratio, over here is going to be at, 200. Bennet Tchaikovsky: Divided by the sales price, or at 25%. Bennet Tchaikovsky: my break-even sales dollars, if I take $83,000 divided by .25, I should get $332,000.
18:05
Bennet Tchaikovsky: If I were to do this in units, I can take 83,000. My contribution margin per unit, so I've got over here my break-even point in units is going to be 415. Bennet Tchaikovsky: Okay, so that takes care of this part right over here. Now, let's go ahead and take a look at Bennet Tchaikovsky: This next part over here. Bennet Tchaikovsky: Which is gonna essentially be the margin of safety, okay? So, and it's asking us for…
18:35
Bennet Tchaikovsky: What is the margin of safety in both dollars of sales, and also in terms of units? Bennet Tchaikovsky: Now, if we kind of go through and look at this, we also have to have some other data. Bennet Tchaikovsky: is that how many units were actually sold, right? So, and it tells us here that I sold 300 units of W and 505 units of R. Bennet Tchaikovsky: Well, what exactly does this mean? Margin of safety is really comparing our break-even
19:08
Bennet Tchaikovsky: Right, to the level of production where we currently are. Bennet Tchaikovsky: So, what I'm gonna do over here is I'm gonna say, well, If our sales… Bennet Tchaikovsky: we're at, for product W, We're at 300. Bennet Tchaikovsky: And my per unit is at 900. Bennet Tchaikovsky: bed over here, My total sales at 300 units would be $270,000. Bennet Tchaikovsky: So my margin of safety, really, between what I'm currently selling and reaching break-even.
19:43
Bennet Tchaikovsky: is going to be in sales dollars is $67,500. Bennet Tchaikovsky: Or the difference also between how many units I sold versus the units sold at break-even. Bennet Tchaikovsky: So my margin of safety in dollars is gonna be $67,500, Bennet Tchaikovsky: My margin of safety in units is going to be at 75. Bennet Tchaikovsky: And if you're taking my class, I will be kind enough, because I do not allow any sorts of extra sheets of paper.
20:15
Bennet Tchaikovsky: And, right over here, again, the margin of safety formula measures the difference between actual or budgeted sales and the break-even point, indicating how much sales can drop before a business becomes unprofitable. Bennet Tchaikovsky: Higher percentage signifies a lower amount of risk. Bennet Tchaikovsky: So I'm coming over here, and then I'm gonna go back to this part, right over here. I'll just copy these in.
20:40
Bennet Tchaikovsky: So… Do the same over here for, product R. Bennet Tchaikovsky: So over here, for product R, I'm told that I sold 505 units. Bennet Tchaikovsky: This was selling for $800 per unit. Bennet Tchaikovsky: So my margin of safety and sales dollars is going to be my sales at my current level of production, minus the sales at break-even. Bennet Tchaikovsky: Or over here, it's $72,000.
21:09
Bennet Tchaikovsky: Over here, this is going to be my units sold minus my units at break-even, or this is going to go ahead and be at 90. Bennet Tchaikovsky: So right over here, you're gonna go ahead and have this at 90. Bennet Tchaikovsky: And then my break-even point in terms of dollar, you know, basically my margin of safety and sales dollars is at 72. Bennet Tchaikovsky: So, this right over here is an example of determining, going through and determining the margin of safety.
21:39
Bennet Tchaikovsky: And obviously over here, if given certain costs, as well as we know that there's a relationship between these, there you go. So anyways, thank you for being with me here today. By the way, if you ever got a question, where you're coming up with Bennet Tchaikovsky: Saying, like, well, my break-even point is, like, say if it wasn't over here, say if it was, like, 225.13, just round it up to the nearest whole unit.
22:08
Bennet Tchaikovsky: It's going to be slightly off, but we can't really solve fractions of units, and that just kind of sometimes happens with us accounting professionals. Bennet Tchaikovsky: not… our accounting professors not, going through and doing our Excel in advance. So, in anyways, thank you so much for being here today. I look forward to seeing you on the next video, and if you have any topics you want me to go through and cover, please feel free to leave a comment below.
22:34
Bennet Tchaikovsky: I'll see you on the next video. Have a great day.
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