0:13

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

Now that we have all this information on the case,

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

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

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

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

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

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

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

it is an outflow.

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

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

is determined to use.

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

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

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

1:17

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

errors in the cash flow analysis.

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

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

And, this looks just perfectly fine.

So, job well done here.

All of the items in B look all right too,

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

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

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

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

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

that must be Included in our analysis.

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

So we have to incorporate these two.

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

draw right over here.

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

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

I want to used a nice different color for this.

This is a new revised cash flow

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

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

that we will go over if they require any adjustments.

So when we draw, remember,

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

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

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

[BLANK AUDIO].

Hopefully these are going to be adequate number of rows.

3:26

And of course we want to reflect the time period

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

we are going to have time period 0,

time period 1, and then time period 2.

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

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

[COUGH] And

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

4:09

We've actually got two amounts for the investment.

We've got the initial time period 0.

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

we have the installation cost of $200.

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

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

So let's identify those.

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

So let's fill those numbers in.

The revenues for the two time periods,

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

We have revenue provided to us, 2,200.

Then we have 2,700.

Where as the next item,

which are expenses, these are the operating expenses.

So let's write those down.

Expenses, nothing wrong with those as well.

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

200 and 200, but what was missed out were

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

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

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

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

6:06

All right? Of course we make the adjustments,

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

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

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

So this is the taxable income.

6:30

Positive number, thankfully.

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

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

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

simply jump from taxable to after tax income.

6:59

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

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

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

Again, a positive number, 1,275.

All right.

So far so good.

So we've identified the first error.

Lets identify the second error and

that is the way in which depreciation was computed.

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

You'll recall the formula that we gave for

depreciation, that formula simply took the cost and

divided that by the useful life of the asset.

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

7:58

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

is 1,000 + 200, 1,200.

So our cost in the numerator is 1,200.

And the useful life is two years.

And so we have to charge $600 for depreciation.

8:21

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

forgotten, so we had underdepreciated the asset.

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

trying to see its impact on cash flow.

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

9:08

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

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

So you pay less tax.

And how much is that?

Well, we just figured that out.

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

That takes care of the second mistake.

See if we can find the third one.

Actually, we do find a third one.

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

Now, what is inventory?

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

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

The rule is that when current assets and

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

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

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

10:02

What is the change in working capital?

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

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

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

at the end of the project.

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

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

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

then the inventory number reduces to 200.

So what does that really mean?

If your inventory goes from 500,

use a different color again.

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

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

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

Well, yes, it goes from 0 to 500.

So this amount is fine.

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

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

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

so cash flow increases.

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

decrease in cash flow.

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

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

12:02

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

But then when your level goes down to 200,

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

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

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

The fourth mistake is, as you see,

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

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

We do not include interest and dividends in this cash flow

calculation simply because these are financing costs.

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

you don't want to double count.

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

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

12:58

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

subtractions here and we've made some adjustments,

our total cash flow will change.

So the fifth mistake is really the total cash flow.

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

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

So we're just going to put our last

row here as the total net cash flow.

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

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

We're going to have, of course,

our investment here which is going to be negative, so

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

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

in fact, a positive number, 925.

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

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

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

calculate the payback as the CFO wanted us to do.

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

So if we cumulate the cash flows what happens?

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

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

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

the payback occurs in the second year.

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

and that is going to give you the proportion for

your payback, which is 0.19.

And so your payback is going to be 1.19 years.

That is your payback.

15:13

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

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

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

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

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

which was arbitrary.

So it's pretty close to one year anyways.

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

method than the payback to evaluate this project.

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

the net present value method and the IRR method.

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

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

The net present value method, in summary,

is simply the sum of the net cash flows,

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

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

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

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

And that's the NPV method.

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

we simply need to discount these net cash flows,

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

We need to bring these back.

So, why don't we do that?

16:57

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

So this is simply going to be 1200 negative.

This one we have to bring back for a year.

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

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

The r here was given to be 10%.

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

17:31

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

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

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

two years, so raise to the power two.

Do the math here, crank it out and

you get the number 1426, 1426 a positive number.

18:01

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

We want to net them out, and

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

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

It is plus, is it positive?

So, this project is a goal.

Something that we would like to do.

18:26

One way to interpret the NPV,

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

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

So the profitability index simply says take your NPV plus or

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

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

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

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

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

What does that mean?

This means, well it's an excellent result.

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

of value for every dollar invested, okay?

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

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

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

19:44

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

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

And what is that method?

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

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

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

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

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

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

year one discounted at the IRR for your one,

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

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

If I plug the numbers in for our particular case,

you can see that our initial investment is 1200.

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

We want to bring it back at the IRR for

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

we bring it back at the IRR for year two.

21:07

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

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

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

Now, remember we also drew an NPV profile.

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

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

have the NPV's on my vertical axis and

discount rates on my horizontal axis.

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

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

So let's say this is 1067, and

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

We also saw that when the NPV is zero.

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

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

22:43

So let's come up with some conclusions.

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

all the information provided,

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

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

this many cases shown that specifying the correct cash flows at

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

23:28

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

And as it turns out, in this particular case,

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

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

But what if the numbers weren't good?

What would we do then?

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

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

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

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

perhaps, because this is a strategic project.

You want to get a foothold in this new market.

This is an innovative company, but

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

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

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

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