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Session 15: Investment Returns II - Getting to Time Weighted Cash Flows - YouTube
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[6]
- In this Session 15, of a 36-session
[9]
corporate finance class, I'd
like to talk about the process
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by which we go from
earnings to cash flows.
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From cash flows to incremental cash flows.
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And from incremental cash
flows to time-weighted
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incremental cash flow returns.
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We're now in the midst of
measuring investment returns
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on a project.
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So let's see where we are in this process.
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In the last session we
talked about why cash flow
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is better than accounting earnings.
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But we spent the bulk of
the session talking about
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an accounting measure return.
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Return on invested
capital, or its variant,
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return in equity.
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In this session, I want to talk
about moving from accounting
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earnings to cash flows.
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From cash flows, to
incremental cash flows.
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And then from incremental
cash flows to time-weighted
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incremental cash flows.
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To do this I'm going to return
to the accounting earnings
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that I estimated for this
particular theme park,
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and go through the three
step process for going from
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earnings to cash flows.
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So this is the accounting
earnings page for the project.
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Let's see if we can convert
these accounting earnings into
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cash flows.
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Remember again, add
depreciation amortization,
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subtract odd capital expenditures,
subtract our changing
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working capital.
Magic.
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I've got the cash flows in the project.
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Notice now that in your zero,
you get a big negative number,
[84]
that makes sense.
[84]
You're spending a lot of
money in your zero, but
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it was capital expenditures.
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Wasn't showing up in your
accounting earning statement,
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but it does show up now.
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So that's the first item you
see, is capital expenditures
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across the board.
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I've added back depreciation
and amortization, right?
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And if you remember, I
subtracted it out to get to
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accounting earnings.
[102]
That might make it seem like
depreciation and amortization
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is getting canceled out, but it isn't.
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Here's why.
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It leaves its imprint on
the cash flows because
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it saves you taxes.
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In fact, we know exactly how
much taxes we save because
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of depreciation and amortization.
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Take year one.
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A depreciation of 50 million, right?
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With a 36% tax rate, I'm going
to save myself 18 million
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dollars in taxes every year.
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The change in working capital
converts my cruel earnings
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into cash earnings.
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And each year I take the
total working capital,
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I compute the change in each year,
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and that affects my cash flows.
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So we've gone from earnings
to cash flows by adding
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the depreciation, subtracting
out capex, subtracting out
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change in working capital.
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Now you're ready?
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Let's talk about incremental cash flows.
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There are two big adjustments
I want to make here.
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First, in year 0, remember
there was half a billion dollars
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of that two and a half billion
that you'd already spent?
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You're not going to get that
money back if you reject
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this investment.
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In finance, we call that a sunk cost.
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And one of the first
principles in decision making
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is that you ignore sunk cost.
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I know it's easier said than
done, because as human beings
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we chase after sunk cost.
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It's very difficult
psychologically to ignore what's
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already happened, but you should.
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So I'm going to take the half
a billion dollars out of the
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initial investment saying, hey
I'm not going to get that money
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back if I reject this investment,
no point loading it into
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the decision making process.
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So that's the first
item I'm adjusting for.
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The second is notice that
I'm adding back a portion of
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the allocated GNA.
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That's 2/3 of the GNA that's
going to be there anyway.
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And because it's going to be there anyway,
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it's not incremental.
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Here's a very simple way
to test to see whether
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something is incremental.
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Ask yourself two questions:
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What'll happen if I take this investment?
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What'll happen if I don't
take this investment?
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If your answer is the
same to both questions,
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that item is not incremental.
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Think about the half a
billion you already spent.
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What'll happen if you
take this investment?
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You've spent a half a billion.
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What'll happen if you
don't take this investment?
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You've spent a half a billion.
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This particular investment
makes no effect on that cost
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that's why we treat it as a sunk cost.
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We take it out of the process.
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Same reasoning with the allocated GNA.
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What'll happen if I take this project?
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2/3 of the GNA will get
allocated to the project.
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What'll happen if I
don't take this project?
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That expense will just get
allocated somewhere else.
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The company will still bear the expense,
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so it's a non incremental expense.
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The one adjustment I have to make
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is because I got a tax benefit
from that allocated GNA.
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When I add it back, I'm going
to add back the after tax
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amount, which is the
allocated GNA, the 2/3 of it,
[258]
times one minus the tax rate.
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So with those adjustments
I've gone from cash flows
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to incremental cash flows.
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These are the cash flows
I should be focusing on
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when I look at this investment.
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There's one final step to take, right?
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I want to time weight these cash flows.
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That's just a fancy way of
saying, I want to discount
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these cash flows, because that's exactly
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what discounting is.
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When I talk about discounting
a cash flow in the future,
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I'm going to discount it more.
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The further in the
future that cash flow is,
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and the riskier that cash flow is.
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So the discounting is effectively
time weighting cash flows.
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So if I can figure out a way
to discount these cash flows,
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I've time weighted them.
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So I'm going to spend a page
listing out some very simple
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present value equations.
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Don't read too much into this
page because much of this
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is built into your
financial calculators now,
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I just prefer to see the
equations behind those
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present value buttons.
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So fundamentally there are
only five types of cash flows
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you're ever going to face in finance.
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First is a simple cash flow
of 100 dollars 5 years out.
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10 million dollars 10 years out.
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Discounting it is simple,
just take the cash flow,
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divide it by 1 plus the
discount rate raised to whenever
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you get that cash flow.
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The second type of cash
flow you might run into is
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an annuity.
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An annuity is a constant
cash flow that occurs
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at regular intervals.
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10 million dollars every
year for the next 20 years
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is an annuity.
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The equation that you see
there is the present value
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of an annuity.
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Incidentally this is exactly
what happens in the background
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when you hit the payment,
the N the R and the PV button
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on the financial calculator.
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It goes through this equation and comes up
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with the present value.
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Try it out if you don't believe me.
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The third is a growing annuity.
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Let me explain what a growing annuity is.
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A hundred dollars growing at 5% a year
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over the next 25 years
is a growing annuity.
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You can compute the present
value of a growing annuity
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in two ways: the long way is
to get the cash flow each year,
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discount each cash flow
back to the present,
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add up the present value,
that'll always work.
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The other is use equation
that you see listed here,
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that'll give you the present
value of growing annuity.
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A very useful equation
to use when you have an
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annuity stretching out over 25 or 30 years
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and is a fixed growth
rate over that period.
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The fourth cash flow is a perpetuity.
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That's a constant cash
flow every year forever.
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The present value of
perpetuity, assisted cash flow
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divided by the discount rate.
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And the final and the
most dangerous cash flow,
[401]
is a growing perpetuity.
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That's a cash flow growing
at a constant rate forever.
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The present value of a
growing perpetuity, is the
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expected cash flow one year
out, it's always one year out,
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divided by the difference
between the discount rate
[414]
and the growth rate.
[415]
Now you can see why it's so
dangerous because if you look
[417]
at the denominator, if
you let the growth rate
[420]
get out of control, this number
can move towards infinity.
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Those are the five types of
cash flows you will face.
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And the present value
equations are listed there.
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Now let me get back to the project,
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because I'd like to bring
this into the process
[432]
to compute a time weighted
incremental cash flow return.
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There are two basic time
weighted incremental cash flow
[438]
measures of return.
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The first is called a net present value.
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And here's what to do in
the net present value.
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You take the present value of
each cash flow in a project,
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you add up those present values,
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and you come up with the sum.
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The sum of the present values
of all of your cash flows
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is the net present value.
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How do you use it?
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Very simple.
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If that net present value
is greater than zero,
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even if it's one dollar,
it's a good project.
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That sounds weird right?
[464]
Five billion dollar project,
you're saying that present
[466]
value of a dollar is still good?
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Remember the net present
value is over and above
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your cost of capital.
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So you're earning what you need to make
[474]
plus an extra dollar.
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Would you rather make a billion?
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Sure.
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But if you have a choice
between taking a project
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with a net present value of
one dollar and doing nothing,
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I'd suggest you take the
project with the net present
[484]
value of a dollar.
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The second measure of
incremental cash flow returns
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is called the internal rate of return.
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It's that discount rate
that makes the present value
[493]
of your cash flows and
the net present value of
[495]
your cash flows equal to zero.
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It's a time weighted
incremental cash flow analog
[499]
to the accounting return and capital.
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How do you use it?
[502]
You compute the internal
rate of return on a project.
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You compare it to the cost of capital.
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If the internal rate of
return is greater than
[510]
your required return, you
have a good investment.
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So you either do an NPV
which is a dollar value
[514]
or an absolute value compared to zero,
[517]
or your compute the IRR, or
the internal rate of return,
[520]
and you compare it to your hurdle rate.
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Either way you computed
an incremental cash flow
[525]
measure of return.
[526]
Let's try this for our project.
[528]
Before we do that though,
there's one loose end
[530]
I want to tie up.
[531]
In the last session I talked
about cutting this project
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off after 10 years and
why it was so unfair
[536]
given that it was a theme park
with potentially a lifetime
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of 50, 60, or even 100 years.
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Not much you can do about it
with an accounting return,
[544]
but with cash flows, there's
something you can try to do.
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Here's what I'm going to try to do.
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I'm going to assume that the
cash flows beyond year 10
[551]
will continue to grow
at the inflation rate.
[554]
But differently, I'm assuming
that Disney will be able
[557]
to raise ticket prices for the
theme park at the inflation
[560]
rate after year 10, but
then the number of tourists
[563]
will level off in year 10.
[565]
Do you see why I'm making this assumption?
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If I let the number of
tourists continue to grow after
[569]
year 10, my theme park is
going to get really crowded,
[572]
and I'll have to make fresh
investments to expand it.
[575]
This way, the theme park stays
fixed, but the cash flows
[578]
continue to grow at 2% a year, forever.
[581]
I know the forever scares you,
and I'll come back to that
[584]
in a minute, but if you make
that assumption of cash flows
[586]
growing at 2% a year forever,
you have a growing perpetuity,
[590]
right?
[591]
The present value's expected
cash flow 1 year out, which in
[594]
this case is the cash flow in year 11.
[596]
And that's basically what you
see in the numerator here.
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Is the 715 million is your cash flow.
[602]
In year 10, grown out
one extra year at 2%,
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that's a US dollar inflation rate
[607]
because I'm doing
everything in US dollars,
[609]
divided by the cost of
capital we came up for the
[612]
theme park of 8.46%
minus the 2% growth rate
[616]
in perpetuity.
[617]
11,275 million is what I'm
estimating the value of your
[622]
theme park to be at the end of year 10.
[624]
This is called a terminal
value, as opposed to a
[627]
salvage value.
[628]
There are some projects where
at the end of the project
[631]
life you shut the project
down, you sell off the assets
[633]
for whatever you can get for them,
[634]
and you collect that money.
[636]
That's called the salvage value.
[638]
This is a going concern
value or a terminal value.
[641]
And that terminal value
is my rough estimate,
[642]
of what I think I can sell
this theme park for at the end
[646]
of year 10, lock, stock,
barrel, and Mickey included.
[650]
Everything's got to be
included in the theme park
[652]
if somebody's going to be willing
to pay you 11,275 million.
[656]
But what I've done by
doing this computation
[659]
is brought in what happens
after year 10 into my cash flows
[662]
without explicitly having to
estimate year 11, year 12,
[666]
year 13, etc.
[668]
I'm now ready to compute the
net present value of this
[671]
theme park.
[672]
What you see on this table,
are my incremental cash flows
[675]
every year over the next 10 years.
[676]
That came from the previous table.
[678]
11,275 million, which is my
estimate of this theme park
[681]
is a going concern after year
10, and the present value,
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at the cost of capital of 8.46%.
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The net present value that
I get for this theme park
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is roughly 3.3 billion dollars.
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Now before I go further,
let me go back and clarify
[697]
this forever assumption.
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I know you're saying,
nothing lasts forever.
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Ever, even the very best theme park.
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You're absolutely right.
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But here's why I went with a forever.
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If I'd used 50 year life after year 10,
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the net present value that I'd
have gotten would have been
[712]
very close to 3.3 billion.
[715]
In fact, my value for this
theme park, if I use a
[717]
50 year life instead of
forever, is about 11 billion.
[719]
So by using a perpetuity, I
got a much simpler equation,
[722]
it didn't change the value very much.
[724]
What I'm arguing for is
for very long term projects
[728]
there is nothing wrong with
using a perpetuity assumption
[731]
even though you know that the
project will not last forever.
[735]
And based on the net present value,
[737]
here's what I see as my conclusion.
[740]
This is a good project.
[741]
By taking this project,
Disney will increase its value
[744]
as a company by 3.3 billion.
[746]
That is one of the most useful properties
[748]
of a net present value.
[750]
When you take a project with
a positive net present value,
[752]
your value as a business
increases by that amount.
[756]
Conversely, if you take
a project with a negative
[758]
net present value, your
value as a business will
[760]
decrease by that amount.
[762]
You might wonder why you
would ever take a project
[764]
with a negative net present value.
[766]
But that's exactly what you're
doing when you're overpaying
[767]
for another company in an
acquisition, for instance.
[770]
That's why many bidding
companies, when you see them
[772]
win an acquisition battle,
we'll often see the stock
[775]
prices go down after they win the battle.
[778]
So the net present value
says that this project
[781]
is a good project.
[782]
Now let's try the IRR.
[783]
Now the way in which most
people compute internal
[786]
rate of return or IRR
is they use the function
[788]
on Excel or on the calculator.
[791]
I actually prefer to draw
what's called a net present
[794]
value profile.
[795]
Sounds fancy, right?
[796]
But it's really not that complicated.
[797]
What I do is I compute the
net present value at different
[800]
discount rates and then plot it out.
[803]
You see the graph there.
[803]
You see what does it tell me.
[805]
First, see the point at which
it crosses the axis, that's
[807]
where the net present value is zero,
[809]
that's my internal rate of return
[811]
for this particular project.
[812]
In this case, this theme
park's IRR is 12.6%.
[816]
That's higher that my cost of capital.
[818]
Here's the other thing I learn when I do a
[821]
net present value profile.
[822]
It tells me how sensitive my project is
[824]
to changes in my discount rate.
[826]
If you're familiar with the
concept of bond duration,
[830]
bond duration measures how
sensitive a bond price is
[833]
to changes in interest rates.
[835]
This is the analogous measure for project.
[837]
This is a measure of project duration.
[840]
It measures how sensitive
the net present value of my
[842]
project is to changes in my discount rate.
[845]
Now the 12.6% IRR, is that a good project?
[848]
That's simple.
[850]
Compare it to your cost of capital,
[851]
and we compare to the
cost of capital is 8.46%,
[854]
it confirms a conclusion
[855]
that we got from the net present value.
[857]
This is a good project.
[859]
Now before we go any further
there's one final byline
[863]
I want to talk about.
[864]
A lot of corporate finance
classes, a lot of times
[866]
spent talking about NPV vs. IRR.
[869]
And we often talk about why
and when they're different.
[873]
And in three cases when
you can get differences.
[875]
The first is, when there
are differences in scale.
[878]
When you're comparing
two projects with very
[880]
different scales.
[881]
What I mean by that is you
compare a million dollar project
[884]
to a billion dollar project,
NPV is going to tilt you
[887]
towards a larger project
because it's a mesure
[889]
of absolute value.
[890]
IRR's going to tilt you
towards smaller projects.
[893]
We know that.
[895]
The second issue where
there might be a difference,
[897]
is you can get only one NPV for a project,
[900]
but you can get multiple IRRs.
[902]
In fact, anytime there's a
change in sign in your cash
[906]
flows, when you look at a
project, there's another
[908]
internal rate of return
waiting to be found out.
[910]
That again is an issue
sometimes when your project has
[914]
changing cash flows.
[916]
One, you might have a
negative to positive,
[919]
you might see another switch
in your seven and again
[921]
in your fifteen.
[922]
And the third and final
issue, and this is an issue
[924]
that's worth thinking about,
is these rules make slightly
[928]
different assumptions about
what you do with cash flows
[931]
you get in year 1, 2, and 3.
[933]
So if you have a 10 year
project, what do you do
[935]
with those earlier cash flows?
[936]
The NPV assumes you can
reinvest those cash flows at the
[939]
hurdle rate.
[940]
The cost of capital, if you're
doing a cash flow analysis
[943]
to the entire business,
or the cost of equity,
[945]
if you're doing an equity analysis.
[947]
The IRR assumes you can make the IRR.
[950]
So in the context of this theme park,
[952]
when I use the NPV I'm
assuming that the cash flows
[955]
that I get at the theme
park will get reinvested
[957]
at the cost of capital.
[959]
But if I use the IRR of
12.6% I'm assuming Disney
[962]
is going to be able to invest
those cash flows that it gets
[964]
in the earlier years, at a
12.6% return, which might be
[968]
a little dangerous,
because this might be a
[970]
once-in-a-lifetime investment.
[971]
So the IRR is a little more
dangerous that the assumption
[974]
it makes about reinvestment.
[976]
But here's the bottom line.
[977]
If you're looking at an
individual project as we are,
[980]
95 times out of 100, when
the NPV is positive, the IRR
[984]
is going to be greater
than the cost of capital.
[986]
We're fighting about the small change.
[988]
So if your choice is IRR or
return on capital, I'd rather
[992]
you use the internal rate of return
[994]
than the return on capital.
[995]
If it's between the NPV and IRR,
I'm not going to make as much
[998]
of an issue about which one
to use because they're both
[1001]
time weighted, incremental
cash flow returns.
[1004]
That's about it for
this particular session.
[1008]
Next session, we'll tie up the loose ends
[1010]
on measuring investment returns.
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