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## AP®︎/College Macroeconomics

### Course: AP®︎/College Macroeconomics > Unit 5

Lesson 7: Public policy and economic growth# Return on capital

Introduction to return on capital and cost of capital. Using these concepts to decide where to invest. Created by Sal Khan.

## Want to join the conversation?

- What is the difference between ROC(return on capital) and ROA(return on assets), if any ?(5 votes)
- ROA = net income / total assets

ROC = NOPAT / (Book Value of Debt + Book Value of Equity - Cash)

NOPAT = Net operating profit after taxes. Which is essentially EBIT minus taxes, which is the same as net income if interest payments weren't subtracted.

Cash is subtracted from the denominator because you are trying to get an accurate representation of all of the invested capital (debt + equity) that has actually been used by the company.(11 votes)

- When you assume that the return of capital is 10 % and the amount of money returned is 100k dont you assume so after removing all the liabilities of the restaurant that is the 15% debt also ? (6:50)(3 votes)
- Not sure I quite understand what the question is, but it may be helpful to consider the difference between the owner of the business borrowing the money (as a personal loan, as Sal implied, with a personal obligation to repay it), and the company borrowing the money, in which case it would be part of the company's financial statements.

Put another way, Sal is saying it's a 10% ROC**prior**to raising the debt (but as I said, it wasn't the company raising the debt in the first place so Sal could keep things simple). I suppose Sal would say the ROC post-debt would be -5%, but he (again) didn't want to get into the (very common) tax deductibility of interest, and start explaining why it was really 10% - (1 - tax rate) * 15%. Sheesh, that would be a tough way to introduce the concept.

There are other problems that are permeating the Q&A on this page, which seem determined to shift from Sal's non-accounting "joe Investor" approach, which is all about cash (cash flow specifically). Some of the answers and themes are tying ROC to accounting positions and terms, e.g. NOPAT (I believe net operating profit after tax), which is a non-cash item. This is more advanced than Sal is trying to start with, so perhaps for new learners of this topic, presume that no knowledge of accounting or acronyms is required to be able to analyze problems as Sal has proposed.(2 votes)

- Is there a substantive difference between Return on Capital (ROC) and Return on Investment (ROI)? Or is it just a matter of labeling?(5 votes)
- Return on Capital (ROC). A measure of how effectively a company uses the money (borrowed or owned) invested in its operations.

Return on Investment (ROI) is measure of a corporation's profitability. ROI measures how effectively the firm uses its capital to generate profit; the higher the ROI, the better.

(3 votes)

- Towards the9:00minute mark, Sal glistens over the concept of Cost of Capital. Is there a video where this is explained in full? Thanks!(3 votes)
- I have two questions:

1. How do you figure risk into return on capital and

2. Is a 10% return normal for a project?(2 votes)- There is a whole branch of finance dedicated to answering your first question. It's much more complex than you might think. You have to make assumptions about the definition of risk, how you are going to estimate the risk of a given project, and what the required return should be for a given amount of risk. The most commonly taught and applied approach to this is the Capital Asset Pricing Model, which defines risk as volatility and asserts that the required return of a project should be equal to a risk-free rate plus a premium that is computed by multiplying the amount of risk by a measure of return per unit of risk. You can find more about it in most corporate finance textbooks, or online.

10% would not be an unusual expected or required return for a project.(0 votes)

- Is there a follow up video to this one?(1 vote)
- I quote " If you want to learn more about finance, watch precalculus videos (becuase some involve finance), micro and macro economics (good to study economy before finace so you you know when to buy, hold, or sell stocks), then watch the Venture Capital and Capital Market playlist (becuase it has more finance and then some). "(1 vote)

- At the end of the video, he mentions "in my next video I will go into more examples" but I cannot locate the next available video in this series. Can you point me to that location?(1 vote)
- but after 12 years or so wouldn't your return change from popularaty of the restraunt and price of your food and ingredants etc ps sorry bout spelling(1 vote)
- I'd like to ask why does the cost of capital consist only of interest money and not the money for paying off the principal too?(1 vote)
- Understanding why the 'capital' element (principal if deb/loan) of the investment is not considered in the cost of capital can be challenging when you're new at this. Both the principal and interest you pay on a home mortgage are cash flows, so that's a good start, but only the interest would be considered (directly) in the cost of capital.

How about a simple, you might say dumb, analogy. Suppose you borrow your neighbor's chain saw for a week, and then simply gave it back to him. What would you say is the "cost"? Most people would say, "Well, nothing". And that's how the finance markets like to think / present this metric.

What if you borrowed the chainsaw and never gave it back, i.e. never repaid the principal? You'd say that was a lot better deal than the transaction didn't "cost you anything" -- you'd probably say that was an awesome deal (and your neighbor would be pretty unhappy).

And if you think you can't lend money out at a rate below zero (what might prove to be a negative yield / return), just wait to see what happens to you when the borrower defaults and only hands you back half the principal : -).(2 votes)

- Do you pay taxes on a loan from the bank?(1 vote)

## Video transcript

Welcome to my presentation
on return on capital. Let me write that down. I'm using the wrong color. Let me use a nicer color. Let me go to white. I want to do this presentation
first, because I think this is really going to give you the big
picture on how you should think about what something
is worth. Whether you should invest
your money into it. And how you should weigh the
different options you have in terms of what you actually have
to do with your money, in terms of where you
want to put it. Do you want to put
it in the bank? Do you want to buy a house? Do you want to pay off
your credit cards? Et cetera, et cetera. So let's just define
return on capital. And just so you know, I'm not
necessarily going to be strict on the accounting conventions,
or the GAP conventions -- that's the accounting
conventions in this country. I'm going to do it more on a
hands-on, how Joe Investors should think about
their money. So in this scenario, I define
return on capital as just the cash you get per year divided by
the total cash you put in. And, well, I don't want
to just say, cash. There's other ways to
measure return. But actually, to keep it simple,
let's just say cash. So let's think about
how this works out. Let's say, I have an idea. I have a restaurant. And that restaurant, it'll
cost $1 million. It'll cost $1 million investment
in this restaurant. It's going to be a $1
million investment. And let's say that, per year,
after paying all the expenses, after paying the utility, after
paying the employees, after repairing, and
maintenance, and after paying taxes, everything, let's
say this restaurant makes $100,000 a year. And that's after taxes
and everything. That's what goes
into my pocket. So in this situation, my return
on capital, the way I've defined it, is $100,000
divided by $1 million, or we could just say a thousand
thousand dollars, equals 10%. Pretty straightforward. You're probably saying,
Sal, this is silly. Why are you wasting my time? Well, maybe it is. But I think you'll find that
this is going to lay a foundation that will eventually
blow your mind. So let's keep going. Let me do another. OK, so I said the restaurant
-- let's make it a pizza restaurant -- let's just say,
the restaurant return on capital is equal to 10%. Right? I can put in $1 million and I'll
get in $100,000 per year. That's where I got 10%. Let me write that down. I get $100,000 per year off
of $1 million investment. Now, that's one project. I'm not going to factor in
things like risk and probabilities just yet. Let's just say, for sure, I know
that if I put my money here, I'm going to get
10% on my money. And let's say the other
option with my money is a beauty parlor. And let's say that that
also costs $1 million. And this beauty parlor gets
me $50,000 a year. I think it's very obvious to you
already which investment you'd rather invest in. Because the return on capital on
this beauty parlor is only 50,000 divided by a
million, or 5%. So this is obvious. You'd rather do the restaurant
than a beauty parlor. And in general, after adjusting
for risk, you always want to go with the project
that has the higher return on capital. And, later on, there will be
nuances in terms of when you get that return. Maybe you would rather have a
slightly lower return if you get the money faster. Or a slightly higher return if
you're taking on risks, et cetera, et cetera. Or to compensate for risk. So we know we want to
do the restaurant. But do we definitely want
to do the restaurant? We'd rather do the restaurant
than the beauty parlor, right? But my question to you is, do
we definitely want to do the restaurant? And this is where the return
on capital becomes interesting. Because what matters, before
we put the money into the restaurant, is to think
about what the cost of that money is to us. And this is what I think will
be a little bit of a new concept to you. So I'm going to introduce you,
now, to the notion of a cost of capital. So let me erase this. OK. So the restaurant costs
$1 million. And it gives me $100,000
a year. And that's a 10% return
on capital. Now, let's say I have to
borrow all the money. And there's some bank that's
willing to give me all the money for this restaurant. And the interest rate on this
loan is, let's say, 15%. Is it still a good idea for me
to open up the restaurant? Well, if I have a loan and I
have to borrow the whole amount -- so I'm going to have
a loan for $1 million to buy that same restaurant. And I'm going to be charged 15%
in interest every year . And I'm not going to take taxes,
and the fact that you could deduct taxes, et cetera,
et cetera , into account just yet. Let's assume that my total
cost is 15% per year in interest. So I'm going to have
to spend $150,000 per year in interest. So my question to you is, does
it still make sense for me to open up this restaurant? Every year, I'm going to be
making $100,000 from the restaurant itself. But I'm going to be paying
$150,000 a year in interest. So you'll probably say, Sal,
once again, you have just restated the obvious. No, you would not want to
do this restaurant. Because every year,
$50,000 will be burning out of your pocket. Now, you might think that this
is obvious, but I'm going to show you many, many examples of
where people are actively doing this. People who you would otherwise
assume could do this type of math. And it's especially happening
in the housing market. But anyway. So in this situation, you
wouldn't want to invest in it. And a very simple way of
thinking about this is you'd only want to invest, you only
want to do a project, if your return on capital is greater
than your cost of capital. This is the only time that you
want to invest in a project. With that said, I'm not
going to go back to what we just did. I just showed you something that
we thought was obvious, but I'm going to re-ask
you a question. So we had the restaurant. And we have the beauty parlor. Let's call it BP for short. They both cost $1 million. Let me write ROC. The ROC of the restaurant,
we said, was 10%. And the ROC on the beauty
parlor, we said, was 5%. So right now, superficially, it
looks like the restaurant is just a better project. But then we said the cost of
capital, so the interest rate. How much does it cost for us
to get that $1 million? The interest rate to borrow
money for a restaurant is 15%. And we said that this is
not a good investment. Because our cost of capital
is higher than our return on capital. And you could do the math
and figure it out. But what if there was some kind
of government program? They just felt that there
weren't enough beauty parlors in the country. And they were willing to give
you a really cheap loan to buy a beauty parlor. And the government program, they
said, we're going to give you a low-interest loan of 2%. So my question to you is,
now, which project would you rather do? Superficially, it looks like
the restaurant was better. You get a 10% return,
as opposed to 5%. But your cost of capital, the
interest rate you would have to pay on a loan for the beauty
parlor, all of a sudden looks a little bit better. In fact, this is actually
a good investment. Because your cost of capital
is less than your return on capital. We can even do the math. Every year the beauty parlor
will generate $50,000. And you'll be paying $20,000
in interest. So you'll be netting $30,000 without having
to put any money for yourself. You'll be borrowing
all the money. So clearly this is a
good investment. So that's it, now, for the intro
on return on capital and cost of capital. And in my next presentations,
I'll go into a little bit more detail and do a few more
nuanced examples.