CF 7-3A – Calculating OCF and NPV – Corporate Finance

Let's take a run through problem seven, three, a we're asked to calculate operating cashflow, as well as net present value of a project. Your company is considering a four year project that involves the purchase of a fixed asset for $2 million. The company will use straight line depreciation. We'll depreciate the asset to zero over the next four years. And the company does not expect to be able to sell the asset once the project is complete. Uh, okay. Well, a little bit of math here, right? We have a fixed asset, uh, $2 million. We're going to depreciate to zero over a four year project means it's $500,000 in depreciation per year. Okay. So, uh, that's just bubbling around in the back of my mind. The project will generate annual sales of 1.4 million and have annual costs of 750. The tax rate is 20%. First it says compute the OCF of the project. Well, to do it, I want to do one of those pro forma income statements just based on what I've got here. So my sales, and this is just a useful sort of thing to do. $1.4 million minus those cash costs. So cost of goods sold, selling admin expenses, maybe, uh, research and development costs. The total of those cash costs is 750. So 1.4 minus 750 is 650. That's my EBITDA, my earnings before interest tax, depreciation and amortization. We'll take out our depreciation to get EBIT. Our depreciation here, 500 grand. We just calculated that. So our EBIT is 150. Now, again, we do not consider interest in these calculations. We want to evaluate the, um, project on its own merit, taking interest into account. Just, you know, it's, that's not about the project. That's about how we funded the project. So, uh, we, we consider that separately, but in just looking at the project, analyzing the project, don't consider interest. So the only thing left to consider then is taxes, which are 20%. 20% of 150 is 30 lending us with net income from the project of $120,000. There we have a pro forma income statement, but we haven't answered any part of the question. That's a useful thing to do though. You should do this if you can, with the information given to you in your questions. It's good practice to have one of these. And then when you work from one of these, it's, it's easier. So it says, what's the OCF operating cashflow? Well, we recall OCF, the easiest way to do this is the standard way to do it. Take EBIT, you add depreciation, which is of course included within EBIT, but it doesn't involve cash and you deduct out, uh, taxes. So for us, EBIT is 150, depreciation, huge number, 500, taxes are 30. So 150 plus 500, 650 minus 30 is 620. Okay. So, uh, 620 is the OCF of the project. Uh, if the required rate of return of the project is 9%, what's the net present value? Okay. So let's think about, uh, the, the project on sort of a yearly cash flows basis. So at time zero, year zero, I got to buy a $2 million asset. So as year zero times zero, oops, not 200,000, $2 million in negative cashflow. Year one, year one, I'm just going to write Y one. I almost like Y wrote Y A R Y one. Uh, what's my cashflow in year one. It's plus 620 year two plus 620. Cause this is my annual cashflow from this thing. Year three plus 620 year four plus 620. Now, as we contemplate this, uh, other things that would be bubbling in my mind is like, okay, what if I can sell the asset at the end? Well, there'll be some positive cash flows from salvaging that. What if there's a working capital requirement? You know, I got to tie up some short-term inventories or something like that. Tie up money in short-term inventory. Uh, will there be a, a, a cashflow associated with that? And we'll deal with that in part C, but in part B, there's none of those complications. It's just like you spend $2 million to collect 620 per year for the next four years was the present value of that. So it says if the required rate of return is 9%, what's the net present value. All you're going to do is divide by 1.09 to the, you know, how many years are we discounting in this case? Zero years, 1.09 to the one 1.09 to the two 1.09 to the three and 1.09 to the four. Oops. Superscript that to four. So there we go. Uh, you would just run those numbers, add those up and you would get the net present value. Because I have a financial calculator, this'll be quicker in the financial calculator, but you should get the same answer if you do it by hand. And this is very doable by hand. I'm going to enter these cash flows into my financial calculator though. My cashflow at time zero is $2 million negative. Enter my cashflow at time one, six 20 positive enter. And I hit the down arrow and it says, what's the frequency? Well, actually I can use this for, I have four $620,000 payments and that's it. So then I go NPV. My discount rate is nine. I hit the down arrow NPV and it's asking me to compute. I hit the compute button. Eight, six, two, 6.3, eight, six, two, six. So the present value of all these payments is positive. Eight, six, two, six. Okay. So if you have a positive present value, you should do the project. So this is a project worth doing, right? It's on our list and we're, we're not going to delete it from our list. The NPV is eight, six, two, six. Let's do it. Now, again, I could solve it by hand. In fact, when we get to part C, I'll do it in the financial calculator first, but then I'll just show you how to do it by hand. It's, it's not complicated. Okay. Um, let me just copy this. Well, let's read part C and then I'll worry about copying it later. Part C says, assume the project requires an initial investment. Networking goes, right? Looked at myself all like my finger on my chin. I, I don't know. Sometimes you catch a glimpse of yourself and you feel like you look weird. I look weird all the time. I assume the project requires an initial investment in networking capital of $200,000. And the fixed asset can be sold for two 50 at the end of the project. Compute the cash flows for each year of the project and compute the net present value. Okay. So, uh, we've done this cash flows for the four years of the project. I'm just going to copy it and move it over here in case I need it again. I don't think I'm going to need it again, but I just want to like, not lose those numbers because I want to adjust this. So let's look at this project again. And here were the cash flows. I'm going to erase this stuff. Here were the cash flows from the initial version of the question. Now it's just saying, we're going to add a couple of wrinkles. I'll do this in a slightly different color of ink. So it says, assume the project requires an initial, initial, uh, investment in networking capital of $200,000. Okay. So we're going to have to pony up $200,000 more money and probably tying it up in inventories or something like this, right? We need $200,000 more, not just to buy the asset, but to invest in something else. Now, if it is that at the end of the project, we actually get back the $200,000 because I'm not going to have those inventories any longer. My money's not going to be tied up. The project's over. So we get a $200,000 positive cash flow at the end. What else happens here? The fixed asset gets sold for $250,000. Well, remember we experienced a gain on this sale because we depreciate it down to zero. We think the asset's worth zero, but if we sell it for $250,000, we have a $250,000 taxable gain. Gets taxed at 20%, meaning there's $50,000 in taxes. So I get $250,000 from selling the thing, but I lose $50,000 in taxes. That nets out to another plus $200,000, right? So $200,000 flows in, $250,000 flows in, but then I got to pay $50,000 in taxes. So I got to consider those as future cash flows as well. That's it though. That's all I need to do. So if I sum this up, I go, okay, I'm $2.2 million down at time zero. So divide by 1.09 to the zeroth power. I'm 620 up at the end of year one. I'm 620 up at the end of year two. So I'm just going through the discounting method. So that's 1.09 to the one, 1.09 to the two, 620 up at the end of year three, 1.09 to the third power. And I am going to have to use a calculator here. 620, clear, clear, clear, clear. 620 plus 200 plus 200. Actually, I could do that in my head, but we're here now. So plus 200 plus 200 is 1020 plus 1020 divided by 1.09 to the fourth power. Okay. So there we have it. Uh, now we just need to run those numbers. I'll do it in the financial calculator first. That'll be the end of the question. And then I'll show you how to do it by hand for those that want to stick around, but let's do it in our financial calculator. So I go CF. I've got some old cash flows in there. I go second function, clear work. And then I just try it again. CF 2.2 million negative enter down arrow cashflow at time one. I'm going to do these ones individually. I think I could do a frequency three here. Cause there's one, two, three of them. Uh, I just, I'm antsy about screwing this up. I'm 10 minutes into a video. So if I screw it up, I wouldn't be happy with myself. Cashflow at time two is six 20 cashflow at time three is six 20. And cashflow at time four is 10 20. Enter. I just want to go up through them, make sure I didn't miss click anything. Cashflow at one. Yeah. So cashflow at zero. Okay. There we go. Uh, let's go ahead and calculate the net present value of those cash flows. So I go MPV. Our discount rate is still nine. Hit the down arrow, hit compute. And I get 91, nine, nine, six, 91, nine, nine. Actually, let me do it down here because we're going to be calculating these in a second. 91, nine, nine, six. That is the net present value of part C. We've solved the problem. So if you got to this point and you're using financial calculator, like me, horrific, that's it. Go ahead and hit the thumbs up button and get on out of here. Uh, if you're sticking around, why don't you hit the thumbs up button? Anyway, it feels good to do. You're doing me a favor and I genuinely appreciate it. So let's go ahead and solve the rest of this by hand. We're just going to prove that this does equal 91, nine, nine, six. And if I wasn't gifted or didn't have gifted is the wrong word. Given the ability to use a financial calculator, right? If your professor says no financial calculators, um, you can do it by hand and it's not hard. So all we do is calculate it out. 2.2 million negative divided by 1.09 to the zero is just divided by one. So divide by one oops. And it's 2.2 million negative six 20 divided by 1.09 to the power of one. So divide by 1.09, five, six, eight, eight Oh seven, because I'm rounding here. You can see there's pennies. We might end up off by a dollar or two at the bottom of this. This is the correct answer, but might end up off a buck or two, but who cares? Uh, 1.09 squared to the power of two. I just go one over X times six 20. I get five, two, one, eight, four, two, five, two, one, eight, four, two, 1.09 to the third power X three, the one over X times six 20, four, seven, eight, seven, five, four, and one Oh two divided by 1.09 to the fourth, one point to the power of four, one over X times one Oh, two Oh, seven, two, two, five, nine, four, seven, two, two, five, nine, four. Now we just add up. There's a list of numbers, negative 2.2 million plus these four numbers. And we hope that we get the right answer. 2.2 million negative plus five, six, eight, eight Oh seven plus five, two, one, eight, four, two plus four, seven, eight, seven, five, four. And last but not least, we add seven, two, two, five, nine, four. And we get done, done, done drum roll, please. Nine, one nine, nine, seven. So we were off by a dollar as predicted. This number is more accurate, but at the end of the day, we're predicting cash flows four years out. So being off by a dollar is not the craziest thing in the world. Okay. You've made it to the end of seven, three, eight. Now, if you really did make it to the end, smash one of those unless you hit it before then don't hit it twice, but thank you so much for watching, have a great day and I'll see you in our next video. Bye-bye.