CF 6-3A – Internal Rate of Return (IRR) and Net Present Value (NPV) – Corporate Finance

Let's take a look at problem six, three, a we're into one of the key concepts of our finance course. And that is the concept of net present value and IRR internal rate of return. We'll solve this one. We'll do part a by hand, and then I'll show you how to do everything in the financial calculator. You'll see it's, it's a lot quicker in a financial calculator. So global vision partners has a potential investment with an initial cost of $500,000 in the following projected cash flows. Uh, so you know, when we're thinking about cash flows, we actually have another cash flow at year zero, uh, that's not on this list in these years. Zero cash flow is $500,000 negative, right? Our initial investment, uh, you can see one 2160, 200, one 80. Hmm. Let's see. Total cash flow is six 60, just adding up that list. And so you might think, okay, well cost me 500, uh, and I'm bringing in six 60. This is a goal. And you know, if we were using payback period, maybe we would sort of say, oh, yeah, it pays back in three years or however long three and a bit years. Um, maybe that's sufficient for us, but a little bit more sophisticated is to bring in the time value of money and to bring in the time value of money. You need a discount rate. And so we're going to figure out the present value of these payments using a 6% discount rate. So how do I discount these cash flows? Well, very straightforward. You just divide by now I'll do this in the financial calculator, go quicker, but divide by one plus the discount rate. So in this case, 1.06 raised the power of the number of periods we're discounting. And for our initial thing, it's zero. Now you don't need to do this, but 1.06 to the zero. Is one, you can see there it's one. So 500,000 divided by one is 500,000 or negative 500,000 divided by one is negative 500,000. Now you just do the same thing for all these cash flows divided by 1.06 to the one. Divided by 1.06 to the two. Because of course the more years, the more the discount factor will be. Okay. So let's do 120 divided by 1.06 to the one. 120 divided by 1.06 is 113208. 160 divided by 1.06 squared, 1.06 squared, 1.1236. I go one over X times 160, 142399. 200 divided by 1.06 cubed, one over X times 200, 167924. And 180 divided by 1.06 to the power of four, 1.06 to the power of four. One over X times 180, 142577. Now you just add everything up. And the idea is if it's positive, this is a good project. If the total number here is negative, this is not a project worth doing. So 500,000 negative plus 113208 plus 142399 plus 167924 plus 142577 equals positive 6610866108. And so what we would say is the net present value here is 66,108. This is a go. We should do the project. If the net present value is positive at all, it means this is a project worth doing. Okay. So we've solved part A by hand. Now we'll do everything else in the financial calculator. You could do part B by hand, just the same thing. It's just 20%. So everything here, the 0.06 is what changed 2.2, 1.2 to the 0, 1, 2, 3, 4th power, but we don't need to run through that again when we have a financial calculator that make our life easier. So here's how we do this in a financial calculator. So I'll do part A just to show you. And then B and C are just going to be super duper quick once we get the numbers in. So if you want to do net present value, you have to say, what are my cash flows? So it's a CF button in our BA2 plus calculator. Every financial calculator will have something like this. Unfortunately, I can't support all financial calculators. This is a, I think widely thought of as the best or certainly the industry standard one I've seen. So CF, so this is CF at time zero. What is my cashflow at time zero? It's negative 500,000. So I just put in 500,000 negative. I hit enter. And then I hit the down, this is sort of telling you like what you can do here. So there's enter and then there's up and down. So I hit the down there. Cashflow at time one, 1, 1, 3, 2, 0, 8, 1, 1, 3, 2, 0, 8. I hit enter. I hit the down arrow. F01 is what's the frequency of, if you've got like an annuity with like 15 cash flows at this point, you could enter 15, but we only have. Oops. I did the wrong number. Oh my gosh. Let's go back up. A cashflow at time one is not 1, 1, 3, 2, 0, 8. It's 120. I discounted already. Sorry. I'm glad I caught that. 1, 2, 0, 0, 0, 0. Enter. So there's my cashflow at time. One frequency was one cashflow at time. 2, 1 60, 1 60. I hit enter. Uh, cashflow at time three. Again, the frequency there is one. So cashflow at time three, 200. Enter and the cashflow at time for one Haiti. And I'm just skipping past the frequencies because I only have one 120, one, 161, 200. If you had multiples of the same, you would, uh, uh, put frequency of two or three or whatever. Uh, so anyway, there we go. There's our cashflow at time four and now we're done. So I want to do the net present value. So I hit NPV. It says, well, what's your discount rate? 6%. So I hit six. Enter. I hit the down arrow. It says NPV equals. And it tells me compute is a button you might want to hit now. And so I hit compute 6, 6, 1 0 8. And you can see the numbers match, right? 6, 6, 1 0 8 is what we had calculated. That's what our financial calculator tells us. So now we can play around. We've got all the cash flows already inputted into our, uh, calculator. I consult part B in one second, right? All I do is I hit NPV again. It says, well, what's the discount rate? It was six. Let's make it 20. I hit enter. I hit the down arrow. I hit, now this is the old answer. I have to hit compute again. I hit compute and you can see it's negative 86, 3 43. So, okay. We've solved, right? We've computed the net present value at 6%. We've computed the net present value at 20% discount rates. Um, what is the internal rate of return? The internal rate of return is the discount rate where NPV is zero. You set NPV to zero and you solve for the rate. Now, not an easy thing to do here. Solving for the discount rate. Uh, if you do it by hand, it is trial and error. You're just, you know, punching in numbers and saying, well, that's a little too high, that's a little too low. So we know looking at this, it's going to be between six and 20%. You know, what's going to be like 12%, 11%. I don't know, but because I have a financial calculator, it's easy. I've got a button marked IRR. Let's hit it. IRR equals and it says, well, why don't you compute? So let's compute 11.24%. And there we have it. We've solved the problem. Now, if I entered this IRR as my discount rate, 11.2418, 11.2418. If I go into NPV and I say, no, my I is 11.2418, enter. And now I compute the, uh, the NPV. I hit the down arrow and it is NPV is negative 86, but I hit compute. NPV should be very close to zero. If I didn't round it all, it would be zero. Let's see what NPV is with that slightly rounded answer. You can see it's 0.4747 cents. It's zero essentially. So that's the, um, uh, internal rate of return to the project. And what does that mean? Well, it means if my required return is less than 11, this is going to have a positive NPV, my required return is more than 11, it's going to have a negative NPV and that's certainly bared out in parts A and B. All right, there we have it. Holy cow. Very important concept, right? Net present value fundamental to your life in a corporate finance class. Uh, so this is the first of many NPV calculations we'll be doing through the course. Thanks for watching. See you in the next one. Bye bye.