0:13

All right, so let's recap the mini case challenge.

Â Now that we have all this information on the case,

Â as well as your colleagues analysis, let's address each of the three questions about

Â the Ithock history that we outlined at the end of the previous video.

Â First we are going to try and identify at least three significant errors

Â in your colleges cash flow analysis, followed by determining the relevent

Â net cash flows for the project in years one and two.

Â And to do this we need to identify whether each of these cash flow components,

Â that is, each row in the table is correct and whether it is an inflow or

Â it is an outflow.

Â Finally, we have to convince the Chief Financial Officer of the problems and

Â the limitations of using the payback period that he has specified and

Â is determined to use.

Â In fact, we want to show him how more sophisticated methods, like the NPV,

Â the net present value method, and the IRR, the internal rate of return method

Â could be used for a better evaluation of this case study.

Â 1:17

So the first question, this asked us to identify three significant

Â errors in the cash flow analysis.

Â Let's start by looking at each of the cash flow categories,

Â the first one is the investment, which is the letter A.

Â And, this looks just perfectly fine.

Â So, job well done here.

Â All of the items in B look all right too,

Â except there seems to be an oversight, or the exclusion of two items.

Â The first one being the opportunity cost and the second one, the clean up cost.

Â So the opportunity cost refers to the erosion of the regular ice scrapers

Â that is going to lose sales because we are investing in the ice thaw.

Â So, the case information gives us the number of $300 a year and

Â that must be Included in our analysis.

Â And there's also cleanup costs at the end of year two which is $500.

Â So we have to incorporate these two.

Â And why don't we do that by readjusting this analysis to one that I'm going to

Â draw right over here.

Â So, bear with me, we're going to recreate that table here.

Â So we're going to have, first of all let's give this a title.

Â I want to used a nice different color for this.

Â This is a new revised cash flow

Â analysis for the number of years that you're going to see.

Â And here we're going to have all of the items

Â that we will go over if they require any adjustments.

Â So when we draw, remember,

Â we're trying to visualize a spreadsheet, which is what we're doing here.

Â We have the items That are going to be displayed in these rows.

Â I've got plenty of rows to draw, so bare with me as I do that.

Â [BLANK AUDIO].

Â Hopefully these are going to be adequate number of rows.

Â 3:26

And of course we want to reflect the time period

Â in this particular case related to all of the items, so

Â we are going to have time period 0,

Â time period 1, and then time period 2.

Â So let's begin with the first item, the first item as we saw in

Â category A, which is just fine, is the investment.

Â [COUGH] And

Â the amount for the investment, I'm going to use a different color here.

Â 4:09

We've actually got two amounts for the investment.

Â We've got the initial time period 0.

Â We're going to pay $1,000 for those printers and

Â we have the installation cost of $200.

Â So that's just fine the way it was presented to us.

Â The next item however, has some items that are fine.

Â So let's identify those.

Â That's B, the first is the revenue line given to us and that looks perfectly fine.

Â So let's fill those numbers in.

Â The revenues for the two time periods,

Â 1 and 2, this is time period one and this is time period two.

Â We have revenue provided to us, 2,200.

Â Then we have 2,700.

Â Where as the next item,

Â which are expenses, these are the operating expenses.

Â So let's write those down.

Â Expenses, nothing wrong with those as well.

Â These are given to be $200 for each of the two years,

Â 200 and 200, but what was missed out were

Â the erosion amounts and the clean up costs, so let's drop that down.

Â We've got cleanup, At the end of the year, end of the project.

Â 500, let's drop that down, so we have to pay 500 here.

Â And then we've got these displacement costs through erosion.

Â 6:06

All right? Of course we make the adjustments,

Â we're going to get different numbers than what we have here.

Â If you subtract from your revenues, your expenses, these cleanup costs, and

Â erosion, what you get is the amount that will be taxed.

Â So this is the taxable income.

Â 6:30

Positive number, thankfully.

Â And, as you would have it, because this increase and we also have an increase

Â in cost actually doesn't change our taxable income, also 1,700.

Â Now we have to pay taxes, so let's adjust for the taxes and

Â simply jump from taxable to after tax income.

Â 6:59

be to take this number, subtract the 25, and therefore keep 75%.

Â So, we simply multiply this number by 1 minus the tax rate, which is 25%.

Â To do the math here were going to get 1,275 as a result.

Â Again, a positive number, 1,275.

Â All right.

Â So far so good.

Â So we've identified the first error.

Â Lets identify the second error and

Â that is the way in which depreciation was computed.

Â In fact, it was just a mistake in how it was calculated.

Â You'll recall the formula that we gave for

Â depreciation, that formula simply took the cost and

Â divided that by the useful life of the asset.

Â That's how you calculate straight line [COUGH] depreciation.

Â 7:58

And in this example, we know the cost, as we can see,

Â is 1,000 + 200, 1,200.

Â So our cost in the numerator is 1,200.

Â And the useful life is two years.

Â And so we have to charge $600 for depreciation.

Â 8:21

Now the mistake, of course, as you see here, is that the installation had been

Â forgotten, so we had underdepreciated the asset.

Â What really is important here is not just claiming the depreciation, but

Â trying to see its impact on cash flow.

Â The impact is going to be simply multiplied by the tax rate.

Â 9:08

Sometimes it's called the tax shield, it's the same thing.

Â Tax savings, so that's depreciation is shielding you from taxes.

Â So you pay less tax.

Â And how much is that?

Â Well, we just figured that out.

Â That's $150 for each of the next two years, okay?

Â That takes care of the second mistake.

Â See if we can find the third one.

Â Actually, we do find a third one.

Â It's a little bit trickier, because it has to do with the treatment of inventory.

Â Now, what is inventory?

Â These are products in stock, and they're part of your current assets.

Â Now current assets are a part of your net working capital.

Â The rule is that when current assets and

Â working capital are affected, we should be looking at three things.

Â Very important to think about three things when we look at working capital.

Â The first is, the changes in the amount of working capital.

Â 10:02

What is the change in working capital?

Â The second is the direction of that change on cash flow.

Â Is it going to increase cash flow or decrease cash flow?

Â And the third is whether the investment in working capital actually gets recovered

Â at the end of the project.

Â So those are the three things we're going to notice in our particular example.

Â And what had happened in our example is that we had, as you can see here,

Â inventory of 500 that we invested in the first year, and

Â then the inventory number reduces to 200.

Â So what does that really mean?

Â If your inventory goes from 500,

Â use a different color again.

Â So if we have an investment of inventory that is, we're putting in 500 in year one.

Â But in year two, you see the inventory has actually gone down to 200.

Â Well, what has really happened, if we look at the first point, is the changes.

Â Well, yes, it goes from 0 to 500.

Â So this amount is fine.

Â But now, when 500 goes to 200, the change is really 300.

Â So, we shouldn't be using 200, we should be using 300.

Â And notice now, when inventory decreases, that means you've sold inventory,

Â so cash flow increases.

Â And that was our second point, whether or not this is an increase or

Â decrease in cash flow.

Â So really, this is an inflow, and that's how it should be recorded.

Â So the numbers that we want to put here in our item, which is increases in inventory,

Â 12:02

a decrease in cash flow of 500 because you're investing 500 in inventory.

Â But then when your level goes down to 200,

Â remember that releases your cash, so you actually get back 300.

Â That's the tricky part, and that identifies our third mistake.

Â So that's all we were supposed to do, but in fact, we find two more mistakes.

Â The fourth mistake is, as you see,

Â in the cash flow presented to you, is the inclusion of interest and dividends.

Â And we know that is one of the rules we established.

Â We do not include interest and dividends in this cash flow

Â calculation simply because these are financing costs.

Â And the financing costs are going to be included in the discount rate, so

Â you don't want to double count.

Â That's simply why we do not include them, and

Â we will discuss this in the next video in more detail.

Â 12:58

The fifth mistake, of course, is that when you've done some additions and

Â subtractions here and we've made some adjustments,

Â our total cash flow will change.

Â So the fifth mistake is really the total cash flow.

Â Let's just arrive at the total with the information that we have,

Â we've dealt with most of the items, all we have to do is add them up now.

Â So we're just going to put our last

Â row here as the total net cash flow.

Â Sometimes it's simply call NCF or net cash flow, and if we add up the numbers,

Â we're going to get some very interesting results as you can see.

Â We're going to have, of course,

Â our investment here which is going to be negative, so

Â this is what is going to decrease our cash flow by $1,200.

Â And then if we just net these amounts we're going to get,

Â in fact, a positive number, 925.

Â And then if we do the second year, we end up with actually

Â a much greater value of $1,725, all right.

Â [COUGH] One of the nice things to do is immediately

Â calculate the payback as the CFO wanted us to do.

Â In order to calculate the payback, we need to cumulate these cash flows, right?

Â So if we cumulate the cash flows what happens?

Â Well, it means we need $1200, and we're going to get 925 in year one,

Â so if I subtract the two, I still need 275.

Â And you can see, I'm getting my money back, or

Â the payback occurs in the second year.

Â To get the proportion, you simply take the ratio of 275 divided by 1725,

Â and that is going to give you the proportion for

Â your payback, which is 0.19.

Â And so your payback is going to be 1.19 years.

Â That is your payback.

Â 15:13

Now, this payback that we've calculated is longer than

Â the one year the CFO wanted in terms of his cutoff period.

Â The way he came up with the cutoff period is anybody's guess, it was arbitrary.

Â So we just need to encourage him that that's probably not a good idea to reject

Â the a project just because it is above the payback that he was thinking about,

Â which was arbitrary.

Â So it's pretty close to one year anyways.

Â This is why we have a chance to argue that we need a more sophisticated

Â method than the payback to evaluate this project.

Â And so we can look at the two that we've learned,

Â the net present value method and the IRR method.

Â So again, to recap what the NPV and IRR are.

Â Why don't we just quickly remember what those two methods tell us.

Â The net present value method, in summary,

Â is simply the sum of the net cash flows,

Â which are these here that we've come up with, that we discount back

Â at a rate for the time period that is specified for the project.

Â And if the result is greater than zero, then we are going to accept the project.

Â If it is less than zero, we are going to reject the project.

Â And that's the NPV method.

Â So if we want to plug the numbers in that we have,

Â we simply need to discount these net cash flows,

Â the ones that we see here in this total net cash flow row.

Â We need to bring these back.

Â So, why don't we do that?

Â 16:57

We don't have to bring back the 1200 because it is already in present value.

Â So this is simply going to be 1200 negative.

Â This one we have to bring back for a year.

Â And in order to do that, we need to take this number, 925, and

Â divide it by 1 plus the rate, and the problem did give us a discount rate.

Â The r here was given to be 10%.

Â So we're going to divide it by 1 plus the rate for one year.

Â 17:31

And if you do workout this value, this workouts to 841.

Â And then we do the same thing for the second year's cash flow, which is 17.25.

Â We bring it back, this time we bring it back for

Â two years, so raise to the power two.

Â Do the math here, crank it out and

Â you get the number 1426, 1426 a positive number.

Â 18:01

So, you can see we've got a negative and two positive numbers.

Â We want to net them out, and

Â the net present value is going to be the sum of this number,

Â this number and this one, which in fact works out to be $1.067.

Â It is plus, is it positive?

Â So, this project is a goal.

Â Something that we would like to do.

Â 18:26

One way to interpret the NPV,

Â other than to say that going to create value of over $1000 is to calculate

Â something known as the benefit cost ratio, also known as the profitability index.

Â So the profitability index simply says take your NPV plus or

Â minus, whatever it is, add the investment, and then divided by the investment.

Â So, if we apply that formula to the numbers that we have here,

Â we take our NPV, which we can see is 1067.

Â We add the investment, 1200, and we divide it by the investment,

Â 1200, to get our profitability index, which in this case works out to 1.89.

Â What does that mean?

Â This means, well it's an excellent result.

Â Because for every dollar that we put in, we create $0.89

Â of value for every dollar invested, okay?

Â And remember, we've incorporated all the side effects.

Â We've taken care of the clean-up, we've taken care of the erosion.

Â We've dealt with the depreciation, tax saving, working capital,

Â 19:44

The last technique that we could try and persuade the CFO to use,

Â besides the naive payback period, is the internal rate of return method.

Â And what is that method?

Â The internal rate of return method says that will, basically,

Â you equate the NPV here to 0, and you look for the discount rate.

Â So, if we create an equation for that, that's going to be

Â the NPV, as you see up here, is going to equal to 0.

Â And that, forcing the MVP to equal zero, allows us to find the IRR which,

Â in this example, is going to be our initial investment plus our cash flow for

Â year one discounted at the IRR for your one,

Â plus the cash flow for year two discounted at the IRR for year two.

Â So we have an equation, and we try to solve for the IRR.

Â If I plug the numbers in for our particular case,

Â you can see that our initial investment is 1200.

Â We add the first year's cash flow, which is 925.

Â We want to bring it back at the IRR for

Â a year, and then of course we have the second year's cash flow, which is 1725,

Â we bring it back at the IRR for year two.

Â 21:07

And financial calculators are terrific for doing that, you plug the numbers in and

Â you're going to get an IRR equals 64.48%,

Â a fantastic result, very consistent with the result that we found with the NPV.

Â Now, remember we also drew an NPV profile.

Â I can very quickly draw a profile to summarize all of our results over here.

Â That profile, if I can just draw it here, would

Â have the NPV's on my vertical axis and

Â discount rates on my horizontal axis.

Â And what we have seen so far by computing the NPV at 10%,

Â so for this count rate is 10%, the NPV worked out to a very healthy 1067.

Â So let's say this is 1067, and

Â there's our first point on the graph that coincides with 10%.

Â We also saw that when the NPV is zero.

Â The IRR is a whopping, so let's sort of break up this graph and

Â pretend this is going to be the 60, 4% that we came up with.

Â 22:43

So let's come up with some conclusions.

Â Let's first begin by congratulating your colleague, with all the details and

Â all the information provided,

Â your colleague did a fantastic job and so, congratulations to her.

Â As we start applying all of the concepts we've learned in the previous video,

Â this many cases shown that specifying the correct cash flows at

Â every single stage is absolutely critical, otherwise you get a distorted result.

Â 23:28

the payback, the NPV and the IRR are the basis for the evaluation.

Â And as it turns out, in this particular case,

Â all the numbers were good because we had a positive NPV,

Â we had a pretty close one-year payback, and we had a very fantastic IRR.

Â But what if the numbers weren't good?

Â What would we do then?

Â Well in that case, if you asked me, this particular project,

Â even if it had a negative NPV, even if the IRR was less than 10%,

Â because you evaluate the IRR compared to the rate that you must earn,

Â even if this number was lower than 10%, I may still accept this project,

Â perhaps, because this is a strategic project.

Â You want to get a foothold in this new market.

Â This is an innovative company, but

Â that is a much broader context that goes beyond the numbers.

Â So, let's make sure we understand all of these calculations are nothing

Â more than a starting point to really start making those tough decisions of whether or

Â not we're going to go ahead with this project or not.

Â