I'm Karl Ulrich, I'm a Professor at the Wharton School. This session is on breakeven analysis. There are really two distinct uses of the term breakeven in the context of entrepreneurship. The first, you might call breakeven time. It's also sometimes called payback time or payback period. Essentially, it's how much calendar time would be required for a lump sum investment to be recovered from positive cash flow and I'll give you an example here in a minute. The second use of the term is really breakeven quantity and this refers to how many units, transactions, quantity of product, orders, customers must we experience per unit time in order to cover our fixed costs? I'll go through both of these with some examples. The second idea of breakeven quantity is also sometimes referred to by the strange term, covering the nut. And that means, the nut is a term that refers to what are my monthly fixed expenses and how much do I have to sell to cover the nut? That is, to recover or pay for my monthly fixed expenses. First, breakeven time or payback time or payback period and let me just give you an example. Let's imagine that you're considering converting all of your delivery trucks from gasoline to compressed natural gas. Prices for compressed natural gas are quite low right now, much lower even, than gasoline and so, if you convert to this alternative fuel you can save monthly operating expenses. Let's imagine that buying a truck costs $40,000 U.S. dollars and let's imagine you save $1,000 a month in fuel costs by converting to CNG or compressed natural gas. Then put simply, the payback is 40 months. That's just 40,000 divided by 1,000 per month saving, so the breakeven time is 40 months, or the payback period is 40 months. Now let me just say, this is most commonly used in association with a lump sum, single investment that has some future savings associated with it, it's actually not very commonly used in other parts of entrepreneurship. You wouldn't normally see this in the context of financing or discussion with an investor, it would be more used in association with a lump sum investment. On the other hand, this notion of breakeven quantity is commonly used in entrepreneurship, and let me start by giving an example. I'm a founder and investor in a company called Belle-V Kitchen, and we make a quite lovely bottle opener shown here. Actually, I have one with me. Belle-V Kitchen makes a bottle opener shown here. I want to just consider the basic question of, how many of these would we have to sell a month in order to breakeven? I want to start with the definition we've used in this course for financial sustainability for a company that sells things. The basic condition that's required for financial sustainability is that the quantity sold times the difference between the price and the cost of each unit has to exceed the fixed costs of operating the business. Put simply, P minus C, or price minus cost is the gross margin, that's how much you make on each unit of product and the quantity sold is the quantity sold. The quantity sold times your profit per unit, that must exceed the fixed cost of operating the business. If you can achieve that, then you can achieve financial sustainability for the business. In setting breakeven quantity, we simply turn that around and ask the question, how many units would be required for us to cover our fixed cost, F? That can be expressed by the expression, quantity Q, breakeven quantity Q is equal to the fixed cost per unit period F divided by the profit margin per unit sold, or P minus C. Let me give you a numerical example to make that clear. Let's imagine that it costs us $300,000 per year to operate the business. These are the costs that don't vary with the quantity sold, this is things like rent, advertising, salaries we pay to the bookkeeper and to the marketing person. Let's say that's $300,000 per year and let's imagine that we sell these at a price of $25 and that they cost us $13.44 to make. That our breakeven quantity would be 300,000 divided by the difference between $25, our price, and 13.44, our cost. If you do that arithmetic, it comes out to 25,952 units per year or more typically, it's expressed monthly, so it'd be 2,163 units per month. The breakeven analysis simply says, we have to sell a little bit more than 2,000 units per month, about 2,200 units per month in order to cover the nut, in order to breakeven. Now if you don't sell a product and instead sell a service, then with recurring revenues and recurring customers, then you think about it just a little bit differently. I'm also an investor in a company called Gridium that sells software to companies that manage commercial office buildings and they sell it on a subscription basis. They have a couple of different subscription plans but some of them cost $79 a month, some of them cost $150 per month. It's essentially the same analysis but instead of asking how many transactions do we need to have per month, you ask how many customers do we have to have in our system, on our system, subscribing to our service to cover the fixed cost? So, a very similar kind of analysis, I don't think you'll have any trouble doing it. But I do want to point out that it's a little bit different for recurring services like you see in software service businesses or in other kinds of services. Now, there are some issues in breakeven analysis. It's fairly useful as a way to just test your intuition of how much business would we really have to do to sustain a company of the size we're imagining this business to be? It's good for calibrating your intuition around the feasibility of a new business but it does assume a fixed level of spending. It assumes that F, in fact, is fixed but those costs aren't really fixed. Those costs are the results of a managerial decision based on how big you think the company can be, how much resource you think you're going to need over the coming months in order to support that business. The breakeven calculations are probably best framed as, if we were this size of an organization, if we made this kind of commitment to rent and to payroll and to advertising, how many units would we have to sell to cover the nut? How many units would we have to sell to breakeven, to cover those fixed costs? It's sometimes useful to do this analysis for what you can imagine to be the minimum efficient scale for the business. What's the smallest we can imagine this business being at and still running itself, still being self-sufficient? Look at that set of fixed costs and answer the question, how many units would we have to sell, how many customers would we have to have to sustain a business of that size? And that can be a good test as to the basic feasibility of the business model that you're envisioning.