 Hello and welcome to this session in which we would look at target profit analysis. What is target profit analysis? Simply put, we are looking for the sales volume. How much do we need to sell to achieve a specific target profit? And I'm going to be working this concept with tax and without tax. So first I'm going to show you how to compute the target profit ignoring tax rate. Then I will work another example explaining how to find the target profit including tax because in the real world, yes, you want to know how much do you need to sell to achieve a certain target profit. For example, a company have a profit, a goal of a million dollar. Well, how many units do you need to sell? Well, also the company will have to take into account the tax rate because the tax rate do change from year to year. So they have to take into account that tax rate factor and I'll also show you how to do that as well. This target profit analysis is derived from the cost volume profit analysis and the breakeven formula and you will see if you remember from the prior session, you don't have to remember, but it's very important if you remember how to do the breakeven is we're working with Adam electronics retailer Adam sells tablet. And for a particular month, we sold 400 tablets, the selling price is 500. Therefore, our total sales is 200,000. The variable expense is $300 per unit times 400 unit is 120,000 sales minus variable expense will give us contribution margin. This is the total contribution margin 500 minus 300 is the 200 contribution margin per unit. This is important. Then if we take the contribution margin per unit divided by sales will give us the contribution margin, margin percentage of 40%. And the total contribution margin is 80,000. And we're going to assume fixed expenses are 80,000. Therefore Adam will break even to calculate the breakeven in units, which we learned in the prior session. What we do is we take the fixed cost, which has happens to be 80,000 for our example, divided by the contribution margin per unit, which is 80,000 divided by $200. The contribution margin per unit will give us 400 units. Also, you could use the formula to break even in sales, which is also the fixed cost and the numerator divided by the contribution margin ratio, which will give you sales of 200,000. Now in the prior session, I spent much, much more time explaining those concepts. But it's very important that you know how they work, because it's going to make your life easier this session. And simply put, we don't want to forget the basically the profit formula, the profit equal to zero, when the unit contribution margin multiplied by the quantity minus the fixed cost will give us zero. In other words, unit contribution margin times quantity equal to the fixed cost. If those two are equal to each other, the profit equal to zero. That's another way to express the profit at break even, which is profit zero. All we are doing in this session is setting a profit rather than a zero setting a profit at a certain number. So it's the same exact concept, except your profit is a dollar amount. It's not zero. So that's why we can exactly use the same formula. Matter of fact, we could use those two formulas, the equation and the formula method to compute this. Now let's go ahead and show you how to do this. So the profit equal to contribution margin times the quantity minus the fixed cost. And we are working with this company right here. Let's assume Adam wants to earn $100,000 in profit. So what should be sales if we want to earn $100,000 in profit? Well, we're going to set the formula. Rather than setting the profit equal to zero, we're going to set the profit equal to 100,000. We're going to take 100,000. Contribution margin is 40%, multiply the contribution margin by sales, which we don't know sales minus 80,000. Well, let's solve for sales. Well, we're going to take 40,000 times sales, which is going to basically what we do. Hopefully, you know how to do this, we're going to add 100,000 for both sides or the 100,000. And we're going to switch the 40% and sales to the other side. Then we solve for sales, which basically end up 180,000 divided by 40%. And it appears that we need sales of 450,000. To summarize what we just did to summarize the formula, what we end up with is something like this. We took the target profit plus the fixed cost divided by the contribution margin ratio. And if you remember, in the prior session, if we took fixed cost divided by the contribution margin ratio, this is equal to the break even, all what you are doing is adding to your numerator the target profit that you want. So now you need the contribution margin ratio to cover your fixed cost and give you that additional target profit. Therefore, you put the target profit in the numerator. So this is basically the shortcut or the formula, which is target profit plus fixed cost, which is let's see if it works. Well, this is the profit. And this is the fixed cost, add them together, divide them by 0.40 will give you 450,000. Now let's see if indeed, we can prove that $450,000 in sales will equal to that. Now what is $450,000 in sales in terms of unit? Well, guess what? Since we can use the formula for the sales, we could also use the formula for the unit. So remember to find the unit, unit target, what we do is we'll take the profit plus the fixed cost divided by the contribution margin per unit. And let's do this to show you this. So 180,000 divided by the contribution margin per unit for this example is $200. If we do so, we find out that we need to sell 900 units. So the target profit per unit is 900 units using the same using the same figures or 900 unit is the same as 450,000 because we're selling each unit for $500. So 450 divided by 500 equal to 900 unit. Let's prove this in a contribution margin income statement. If we sell 900 unit, our total sales is 450. If we sell 900 unit, our total variable cost is 270,900 times 300. Our contribution margin is 180 less fixed cost of 80,000, which will give us a net operating income of 100,000. You remember I told you, we're going to have to show that if we sell a certain amount, we need the profit of 100,000 and that certain amount is 450. That's fine. But what about if we have to take into account taxes? So if we want our target profit to be 100,000 after taxes, how do we do so? Well, before we work with this, if solving for after tax, I would like to remind you whether you are a student or a CPA candidate, and most likely you are one of those and you're looking for some help. This is why you're watching. Go to farhatlectures.com. I don't replace your CPA review course. I don't replace your college course. I'm a supplemental tool. You could use me. You could use my lectures, my exercises, my multiple choice to help you understand the material better, to do better in your course as well on your CPA exam. Don't sure change yourself. It's a nominal investment. Connect with me on LinkedIn, like this recording, connect with me on Instagram, Facebook, Twitter, Reddit, and I do have a CPA exam group on group me. Please join as well. So how about finding your profit after tax? What you need to do is you need to gross your profit. So you need to gross your profit. What do I mean by gross your profit? Let's assume you want to work at a company and you want to earn $10,000 per month net. Let's assume that's your net. That's what do you want to earn? Net. Net means after they take your taxes. So how much you will need to earn per month? Because remember, the company you'll have to pay taxes. How much do you pay per month if you want to net $10,000? To basically to gross this amount, what you do is you will take the $10,000, divide in it by one minus your tax rate. And hopefully you know this as an accounting student, one minus the tax rate. And let me show you. Let's assume your tax rate for the sake of illustration is 25%. So one minus 0.25 equal to 0.75. So let's take now $10,000 and divide the $10,000 by 0.25 times divided by 0.75, not 0.25, 0.75. You will need to earn, you will need to earn gross $13,333. Why? Because after you earn this much, you're going to keep 75%. So if we take this amount, multiplied by 0.75, what you keep, then you will keep $10,000. In other words, they're going to take 25% taxes. So simply put the formula. Now what's going to happen is to find the formula. First, you're going to take your target profit, whatever your target profit is in grossed. Grossed means you want to find out what's your gross profit before tax, because you have to pay taxes on that profit. You divide it by one minus the tax rate. Assume the tax rate is 20% for the sake of our example. Now we'll take $100,000 divided by 0.8, one minus 0.2 is 0.8, which is what's going to be left, which is 0.8. And your target profit should be $125,000. Now rather than setting the profit at $100,000, you set the profit at $125,000. And you say, well equal to 40%, what should be my sales minus $80,000. Now you sold four sales, exact same concept. And you will find out your sales should be $512,500. Now the best way to do this is to also show you from a contribution margin income statement how it works. But before we do so, you could also find it finding this using the shortcut. And what's the shortcut? Once you find 125, you will take 125 plus 80, which is the target plus 80 divided by 0.4, which is this part here, to find $512,500, which is $512,500. If you divided by $500, you will find out it's 1,025 units. Or you can take 125,000 plus 80,000 divided by rather than 40%, if you divided by 200, which is the contribution margin per unit, you would also get 1,025 unit. Let's see if 1,025 unit will give you 100,000 after taxes. Well, selling 1,025 units at $500 will give you sales of 512,500. Your variable expense will be 1,025 multiplied by 300. Your contribution margin is 205. 205 minus the fixed cost will give you a net operating income of 125. And when you take 20% of 125 when you multiply 125 by 0.8, what's left after you take the taxes, you will end up with how much exactly 100,000. So to make a profit after tax of 100,000, obviously you will need to sell more 512,500 and you'd need to sell more unit rather than 900. Now you would need to sell an additional 125 units. And those 125 units basically goes to Uncle Sam, the US government or the government wants a share of the profit. Let's work this example to illustrate the concept. How many units must be sold in order to achieve a target profit of 35,016, which is we're going to keep the tax function out, but you know how to do this if they told you a target profit of this much after tax, they're going to have to give you the tax rate and you will convert into the tax rate. But I'm going to keep it simple for the purpose of this example. In this example, by the way, is from my website farhatlectures.com. This is what I have on my website where you can work additional exercises. ABTAC company has provided the following contribution margin format income statement, sales is 5,000 unit and the sales for that is the total sales is 235,000, variable expenses 165,000 for again 5,000 unit. The contribution margin is 70,000, which is sales minus variable expense. Then they will take the fixed expense out and they will end up with net operating income of 9,000, 9,900. And the question is, let's assume this company wants to earn net operating income, they want to make more than this, they want to make exactly 35,000 and 16 dollars. How much they will need to sell in terms of unit? Well, what we need to do, we need to find out either their contribution margin ratio or the contribution margin per unit, which have either or is acceptable. Okay, I'm going to show you both. So this way, you know how it works. I'm going to first show you the contribution margin per unit. How do we find the contribution margin per unit? If we selling 235,000 unit, 35,000 dollar and we're selling 5,000 unit, our selling price is 47 dollars. 165,000 divided by 5,000, our variable cost is 33. 47 minus 33 will give us 14 dollars, the contribution margin per unit. Now, all we have to do is take our target profit, which is 35 dollars and 16, 35,000 and 16 dollars plus the fixed cost 60,100 divide those by the contribution margin per unit. And let's say if we take 35,000, 16 dollars plus 60,100 equal to 95,116 divide this by the contribution margin per unit and I need to sell 6,794 units. 6,794 unit. My answer is C. What should you do now? Please go to farhatlectures.com to work additional multiple choice questions that's going to help you do better on your exam. Invest in yourself. Don't shortchange yourself. Your education is important. It's an investment. It's going to pay you dividend for years to come. Good luck, study hard and of course stay safe.