CF 8-2A – Break-Even Points – Corporate Finance

Let's jump into problem eight to a, we're doing break even points again, and we've just done this. If you've done a one, you've seen the accounting break, even point fixed costs, including depreciation divided by the price minus the variable cost, I should say per unit. And this is called the contribution margin in accounting jargon. So let's jump through the problem. We're going to calculate the accounting break, even point. We've already done that. We're going to calculate the cash break, even point again. We did that in eight one a, but the new material here is part C and D and pay particular attention to part C. That's the new ground. We're breaking part D. We're going to explore more in problem eight, three operating leverage, but we'll get to that when we get to it, let's jump into the accounting break, even point. So here we have a company that's considering a project with the following information, selling prices. The product they're going to make is 80 bucks. The variable cost is going to be 50 fixed costs of 60 grand. And they got to make an additional initial investment of $20,000. It's going to run for five years. So I, you know, assuming they're buying some asset or assets to, to produce this return, it's 50,000. No, not 50, 20 divided by five is 40, $40,000 per year in depreciation, which I will put as depreciation. Assume the company wishes you straight line depreciation. Well, we just did that and assume taxes are ignored. Okay. I'm ignoring them now. The required rate of return is 10%. I love ignoring that. I wish I could ignore taxes in my real life. The required rate of return is 10%. Okay. So discount rate. Now the discount rate doesn't come into play in these first two calculations. It rarely comes into play in accounting. The discount rate is for finance where we're doing these longer term projections. Accountants can use a discount rate, but it's, it's a less frequently used in accounting exercises. So in any event, the first two parts of this problem, we don't need to worry about that required rate of return. Let's calculate the accounting breakeven point fixed costs plus depreciation, 60,000 plus 40,000 divided by price minus variable cost per unit, 80 minus 50. And let's crunch that number a hundred divided by 30, right? 60 plus 40 is a hundred thousand divided by 80 minus 50, which is 30, 3, 3, 3, 3, 3. So 3,334 units. That's our breakeven point, uh, according to the accountant and remember what breakeven point means. The accounting breakeven point is the point where net income is zero. And I always bring this up, like you don't run a business to break even. So why do you care about the breakeven point? You want to make money. And the answer is you, you don't run the business breakeven, but it's still useful to know, Oh, once I've sold my 3,334, the unit, everything after that is gravy. I'm making profits after that. So if you're running a business and you're like, I'm not going to reach 3,000 units, you know, you're going to be losing money and you can project based on that information. So it's a useful information to have in your back pocket. Also useful information is the cash breakeven, which is, are we going to run out of cash? That's useful to know. And it's easier to hit the cash breakeven than the accounting breakeven. Why is that? Well, look at the formula for breakeven. The accounting one, fixed cost plus depreciation divided by price minus variable cost per unit. The cash breakeven just says, take out that one because there's no cash flow, right? And we're in finance, we're worried about cashflow. So take out the piece that has no cashflow. We'll go fixed costs, you know, ignore the 40, 60 divided by 80 minus 50. So let's do that 60, oh, divided by 80 minus 50 is 30, it's 2000 units. So it's easier to breakeven on a cash basis than an accounting basis. What we'll find next, and this is the new concept, is the financial breakeven is harder to reach where I'm expecting a bigger number here. Usually I think always, but I'm going to say usually, I think it's always, the math makes sense that it's always, but let's, let's figure out what this is. So the financial breakeven, so accounting breakeven is when profits are zero. So obviously you want to do better than that. Cash breakeven is where cashflow ends up being zero. Financial breakeven is where net present value of the future cash flows equals zero. And again, you generally want to have positive net present value, but this is a useful number to know. So how many units do I have to sell to have my net present value be zero? And so, because of that, because we're looking at net present value, this discount rate matters and the project's life matters. And the reason it's harder to get net present value of zero than to get accounting breakeven is because of that time value of money. Presumably your projects are making you money, but they're making you cash flows in three, four, five years from now. We have to discount those positive cash flows. So that makes them less valuable. And so finance takes that into consideration where our accounting breakeven does not. Okay. So how do I do it? Well, I'm going to do it with my financial calculator. It is just an annuity, right? This project is essentially an annuity. And so we can do it by hand with the present value of an annuity formula. We will do it by hand at the end of the video, but I'll do it with a financial calculator. If you're fortunate enough to get to use one of those, then, you know, this is a slightly easier process, but it's not that hard to do by hand. Okay. So here's what I'm going to enter into my financial calculator. N of this project is five. I'm just using the, uh, same, uh, annotations that's on the calculator. IY is the discount rate, uh, 10% PV, uh, the cost 200,000 negative. So we're outlaying 200,000 negative our PMT. That's what we don't know. Oh, by the way, sorry, what are we solving for right now? I didn't say that we're going to calculate. So, uh, we're going to calculate the operating cash flows required to have NPV equals zero. So we calculate, and again, this is building on material from last chapter. If you're shaky on operating cash flow, you know, that's, that's an important concept here. Operating cash flow, uh, required to make NPV equal zero. So that's what the PMT is. That's what we're solving for. That's our OCF. And again, we can use OCF in other calculations shortly. Uh, our future value here is zero. And so we got one variable let's solve for it. Um, so N is five, five goes in as N, 10 is my discount rate. 200,000 negative is my PV. My FV is zero and I compute PMT. I get 52, seven, five, nine and a half, but I won't take the decimals with me. Um, okay. So there we have it. 52, seven, five, nine. That's the annual operating cash flows I need, but I still don't have my breakeven point. Here's how you figure out the breakeven point. And it's, it's actually using a very similar formula to this. And we're just using the cash components of it. So fixed costs, excluding depreciation, our cash depreciation is cash, but we, we want to, we have to cover more than our fixed costs because I need to generate $52,759 above my fixed costs. So I'm going to add the OCF and I just divide by the same denominator. I'm still selling the same product. It's got the same price. It's still got the same variable cost per unit. So it's just subbing in OCF for depreciation, but it makes logical sense, right? You got to cover your fixed costs and you got to generate this much operating cashflow on top if you want to have net present value of zero, as we just sort of calculated. So fixed costs here are 60. Our required OCF to get a net present value of zero is 52, seven, five, nine. P minus VC is still the same, 80 minus 50. All right, so 60. So I'm just going to add 60. And now we divide by 30 and we get three, seven, five, nine. Now we're in the ballpark, right? Of our other units. So that's always a good sign. If it wasn't like 2 million or something, I'd be like, Oh, I screwed something up. So sometimes you get absurdly high or absurdly low answers and just means you screwed something up, but we're in the ballpark here and slightly higher than accounting break even point, which we figured to be. Uh, our break even point for finance is three, seven, five, nine. Units. Beautiful. So that was the key for this one. Eight, uh, not eight, three, we're going to move on to part D now. So, so again, just to reiterate what we're doing, the key to that, this problem is this financial break-even point. It's how many units I sell, need to sell to have a net present value of zero. Uh, and I'll show you how to calculate this OCF by hand at the very end of the video. But let's jump ahead to part D. Uh, D says at that financial break-even point, calculate the degree of operating leverage. This is a new concept. We explore it in some more detail in problem eight three. For now, I'm just going to give you the formula. We're going to solve, I'll explain what it is that we're calculating, what we're doing here. Um, but we'll go into more depth when we do problem eight three. So here is, uh, the formula I'm doing this from memory. I always screwed up. It's one plus fixed costs. Divided by operating cash flow. That's the formula to get a degree of operating leverage, which is just a ratio. It's just a number. And it's like a number that, well, we'll, we'll explain, let's solve it. And then I'll kind of explain what the number means. Uh, so again, this is degree of operating leverage. This is part D that we're solving for here. So one plus fixed costs divided by operating cash flow. Well, there's our fixed cost. There's our operating cash flow. So one plus, uh, 60. Oh, oh, oh. Divided by five, two, seven, five, nine, 60. Oh, oh, oh. Divided by five, two, seven, five, nine equals 1.14. So one plus 1.14, one plus 1.14 is 2.14. And what you're going to get is a number. And that number is going to be somewhere above one. Obviously it's not going to be negative number. Um, so it's going to be, I don't think it can be a negative number. It was thinking out loud here. Yeah, it can't be a negative number. Um, it would be a weird situation. Uh, so it's going to be a number over one. Typically it's not a huge number, like unusual to be like over six, but you know, between say one and five, one and six is fairly typical. Here's what the number means. For every blank percent increase or decrease, I would say change in units sold, OCF will change by 2.14 times blank percent. So let me explain. So let's say units sold goes up by 10%. Okay. My units, those go up by 10%. I would expect my operating cashflow to go up by 2.14 times 10, 21.4%. So it's a measure of how sensitive our operating cashflow is to changes in sales volume. And it's, it's typically a measure of fixed costs. Like what, uh, proportion of our capital structure is fixed versus variable for very, very fixed. This tends to be a big number. If our costs are mostly variable, this tends to be a small number, but it's how sensitive operating cashflows are. And cashflows are really important to us to changes or fluctuations in sales. So if sales are going up and we have big OCF, this is great news, right? If you're an investor and owner of the company, you're like swimming in cash. If sales go down and this is a big number, it's a catastrophe for you. You're in big trouble. So it's a measure of leverage, right? How much things will move. So that's the discussion point. We explore this more in problem eight three. So let's stop the video there for those that are, um, not going to follow along when I do the calculation by hand, just hit the thumbs up on your way out of here. No hard feelings. You can leave now you're free to go. Uh, but for those that are sticking around, you hit the thumbs up too. And, uh, let's, let's dig into this. I always think I'm being silly when I do that, but there's a reason people do it. It works. It's really important. It helps me so much that people do. Some people hit the thumbs up, but if you're here and you haven't hit the thumbs up button, you should try it. Just try it. It's like fun. It's super fun to do. Um, okay. So we're just going to recalculate this number that I had done in my financial calculator. Our present value here. $200,000. That's what we're solving for equals C, which is our payment amount times one minus one over one plus our, our discount rate was 10%. So 1.1 to the T, which is five, um, all over our, which is 0.1. Okay. So again, put some brackets around everything. We just have to solve for C C is that payment amount. Um, okay. So 1.1 to the power of five, 1.61. I go one over X 0.62, one minus that. So I go minus one plus minus 0.37, 0.37 divided by 0.1 is 3.79. So what's in brackets is 3.79. So I just divide 200,000 by 3.79 and I'm out of here. One over X times 200,000. That's one way to do this. And I get 52759.49. Well, look at that 52759.49. It's the same answer because we're doing the same thing. So that did not take me long. If your professor is making you do stuff by hand, you know, it's not the end of the world. We've solved the problem. I hope this video helped you. And for goodness sakes, if you watched all the way to the end, smash that button. Don't just hit it, smash it. Thanks so much for watching. See you in the next video. Bye bye.