学完本课程后，您将可以分析企业所做金融决策的主要类型。然后，您可以运用所学技能处理现实商务挑战，这也是沃顿商学院商务基础专项课程的组成部分。主要概念包括：净现值技术、资本预算原则、资产估值、金融市场运作和效率、公司财务决策以及衍生产品。

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学完本课程后，您将可以分析企业所做金融决策的主要类型。然后，您可以运用所学技能处理现实商务挑战，这也是沃顿商学院商务基础专项课程的组成部分。主要概念包括：净现值技术、资本预算原则、资产估值、金融市场运作和效率、公司财务决策以及衍生产品。

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Aus der Unterrichtseinheit

Week 4 第 4 周

本模块将结束现金流量折现法的讨论，开始投资回报率的讨论。本模块教学结束后，您将能够理解自由现金流的概念，而且能根据一系列预测变量，计算项目未来的自由现金流。本模块将介绍一些基础金融建模的知识，并将应用这些知识对平板电脑项目做出决策，分析我们估值背后的假设情况。

#### Michael R Roberts

William H. Lawrence Professor of Finance, the Wharton School, University of Pennsylvania

Welcome back to corporate finance.

Today we're going to turn to a new topic, return on investment.

But before doing so I want to briefly recap our last topic,

discounted cash flow analysis.

If you'll recall, you started off with a discussion of how firms, or people more

generally, should be making decisions through different decision criteria.

Then, we talked about free cash flow, at least from a conceptual standpoint.

We then discussed four cash drivers, or

the assumptions required to forecast free cash flows into the future.

If you remember, we did that in the context of a tablet.

We then applied our assumptions, our forecast drivers, to our our free cash

flow formula to get forecasts of free cash flows for a tablet project.

We then brought our decision criteria back in and

applied it to the forecasted free cash flows to come to a decision of whether or

not to proceed with our tablet project.

And we closed out the topic with a discussion of sensitivity analysis

to investigate just how robust our assumptions and decisions are.

Today I want to talk about return on investment.

And in particular what I want to discuss is the strengths and

weaknesses of the internal rate of return relative to the net present value rule.

So, let's get started.

>> Hey, everybody.

Welcome back to corporate finance.

Today we are turning to a new topic, Return on Investment, but

before diving in I actually want to spend a little bit of time recapping our

last topic, discounted cash flow analysis.

So what we did in our DCF topic is we began by introducing decision making.

We showed some evidence,

looked at some survey evidence of what people in practice were doing.

CFOs of non-financial companies, private equity managers and investment bankers.

And we showed that they used a number of different criteria, DCF or

NPV, IRR and payback period.

Then, we turned to looking at free cash flow,

one of the key components of any DCF.

And we talked about the components that make up free cash flow and

how to aggregate them.

Then we talked about Forecast drivers, or

the assumptions necessary to forecast each of the components of free cash flow,

and we did it in the context of a capital budgeting example of a tablet.

We then applied our Forecast drivers to forecast out each component of free cash

flow and aggregate up to get a free cash flow projection.

We then looked at different decision criteria.

That is, we figured out what to do with those cash flows and

ultimately what decision to make regarding the tablet.

Specifically we looked at NPV, IRR and payback period.

We talked about their strengths, some of their weaknesses.

And then we closed out the topic with a discussion of Sensitivity analysis.

An integral element of any DCF.

Now, I really want to continue on the theme set by DCF,

and talk about return on an investment, and really emphasis IRR versus NPV,

the two most commonly used decision metrics.

So, let's get started.

So recall, that the internal rate of return of an asset is

the one discount rate such that the NPV of the asset's free cash flows equals zero.

So, I have NPV, I have cash flow, we could have free cash flow don't let

the convention confuse you, IRR is much broader than just free cash flow.

As is cash flow but anyway IRR is just that one discount rate

such that the NPV is equal to zero.

The IRR decision rule, as you might recall,

says accept all projects for which the IRR is greater than R.

Reject all projects for which the IRR is

less than R, where R is our hurdle rate,

or opportunity cost of capital.

And the intuition was simple.

If it's costing us R percent to raise money to fund investment,

that investment should return something at least as big, if not greater, than R.

Preferably greater.

Now, I'm going to spend some time here talking about IRR,

a little bit of motivation here,

because rates of return are really popular measures used for making decisions.

Remember back to the survey evidence,

internal rate of return was the most popular decision criteria used by CFOs.

It just edged out NPV.

And likewise,

for PE firms, private equity firms, internal rate of return is by far

the dominant decision criterion used for evaluating investments.

So it's really important to understand this criterion.

So let's compare it to NPV and let's do it by way of an example.

Shortly I should say.

So first the IRR is going to lead to the same decision accept or reject

as the NPV rule if all negative cash flows precede all positive cash flows.

So here are some examples of cash flow sequences, at least the sign

of the cash flows where the IRR and NVP rules will coincide, right?

So I pay a bunch of money today and then I get nothing but positive cash flows.

I pay money for

the first three years, right, I mean I don't like that, let's do this.

For year 1, 2, and 3, and then 4, 5 and on are all positive.

The key is that the negatives have to come before the positives,

then IRR and MPV lead to the same decision.

If that pattern of cash flow signs is violated, not only may IRR and

NPV rules not coincide, not lead to the same decisions, but

you can get some pretty wacky stuff from with IRR from multiple IRRs.

In which case, which one do you choose?

It's not obvious, to imaginary IRRs.

And, I mean, mathematically imaginary IRRs you'll get an IRR times some number

times the square root of negative one, which is really hard to convey to a CEO.

Trust me.

Let's think about whether or not we can compare projects using IRR.

Here is where I want to work in a context of a specific example.

Imagine Wharton wants to upgrade it's IT system and

overhaul it's network infrastructure.

So it puts out a request for proposals and RFP, and in comes a bid from Cisco.

And Cisco, the Cisco bid we evaluate to generate $60 million in cost

savings over three years for an up front cost, cost to Wharton, of $100 million.

Now, if our cost of capital,

Wharton's cost of capital is 12% what is our assessment of this bid?

First things first, write down the cash flows.

Here they are.

We're going to get, right, Bid #1, it's going to cost us 100 million dollars

today, then we're going to experience cost savings of 60 million dollars for

the next three years.

We can compute let's clear this up.

We can compute the IRR by solving this equation, right.

Just set the NPV for the project equal to zero and solve for IRR.

That gets us 36%.

Now, because the IRR is greater than the discount rate, our verbal rate,

remember that was 12%.

And the cash flow signs are proper.

That is, they follow right, negatives followed by positives.

This project looks good.

If we compute the NPV, if we just discount the cash flow,

the future cash flows by the warden"s cost of capital, 12 percent,

we're going to get an NPV of 44.11 million dollars Which is greater than 0.

Well that looks good too.

So both IRR and NPV point in the same direction.

This looks like a reasonable bid,

Wharton's is going to be better off by accepting it.

But then Cisco comes back.

And they say we're going to give you the same cost savings $60 million over

three years.

But now what we're going to do instead of charging you $100 million up front,

we're going to spread the costs over time.

$20 million today and then $35 million over three years.

So let's try evaluating this bit.

I mean, it sounds sound somewhat attractive if we can avoid that huge

upfront bill.

So for Bid #1a, here are the costs.

It's going to cost us $20 million up front, as opposed to $100 million.

But, we're going to have to pay $35 million over the next three years.

We still get the same cost savings, so the net cash flows for

this bid are -20, 25, 25, and 25.

Lets compute the IRR and MPV, IRR first.

Well the IRR we set the MPV of these cash flow's equal to zero solve for the IRR and

we get whoa, 112% that's impressive.

That is very impressive.

And we see that the IRR for Bid #1a, this bid,

is 112% is greater, much greater, I'm going to put much greater,

than the first bid from Cisco which had an IRR of 36%.

We can also compute the NPV by just discounting by the cost of capital, 12%,

Warton's cost of capital.

That gets us an NPV of $40.035 million.

So, Bid #1 had an NPV $44.11 million.

Bid #1 has an NPV of $44.05 million which according

to the NPV rule means Bid #1 is better than Bid #1a.

What's going on here?

Right?

NPV says Bid #1 is better right?

44.1 is bigger than the 40.05.

IRR says Bid 1A is better because 112% return is better than 36% return.

What do we do? Well, let's take a closer look,

that's the first thing we do.

Let's look.

Here's Bid #1.

Cisco's costs are $100,000,000 all up front.

For Bid #1a, sorry Cisco's cost.

Warton's costs are $100 million up front.

Bid #1a Warton's costs are only $20 million up front but

then $35 million every year thereafter.

And so what Bid 1a is doing is it's inserting a loan.

Cisco's lending us money.

Right, in particular they're lending us 80 million dollars today in exchange for

35 million dollars over the next three years.

Here's a question.

What's the interest rate on the loan?

We can figure that out!

Right, I can figure out what the interest rate on this loan is.

How?

Just compute the IRR.

Just compute the IRR.

And if we do that, we see that the interest rate is 15%.

Again, this is just the IRR, I want to emphasize that.

Let me clean that up.

It doesn't look, right, if I move this over here this will be zero.

And this will, oops let me, having trouble, equals minus 80, right?

Okay so that is just the IRR, it's 15%.

It's also the Yield-to-Maturity.

Okay? Which we've discussed in the past.

Well is the 15% high or low?

Is it good or bad?

Well it's terrible.

Cisco's charging us a higher interest rate than our cost of capital.

In other words, we can go to the capital markets and raise the money for

a loan at 12% as opposed to implicitly borrow from Cisco at 15.

See what happened is, the IRR increased because initial investment fell

more than the future cash flows.

Right, small payoffs on a really small investment can generate very

large returns.

We're dividing by small numbers here but the NPV rightfully fell.

Because Cisco's leading us money at an interest rate that's greater than our cost

of capital.

So the IRR spiked because we have this smaller upfront investment.

That's very misleading.

The NPV fell,

it accurately captured the bad loan Cisco was inserting into the deal.

So the lesson here is that IRR projects can mislead when we're deciding

among projects.

Where as NPV will not mislead in comparisons.

The larger the NPV, the greater the value.

Now, let's briefly talk about a couple of additional bids,

just to hammer home the point.

We also heard from Juniper and Huawei, who had costs and

cost savings for us, as laid out in this table.

And how would we rank these bids according to the IRR and NPV?

Well, we know how to compute the IRR and NPV.

We just replicate or repeat what we did for Cisco, or what we've done in past

lectures, and you can get this set of IRRs, and this set of NPVs.

And what you'll quickly see is that the IRR ranking is that the Huawei #3

bid is better than the #2 bid from Juniper which is better than the #1 from Cisco,

the exact opposite ranking relative to what NVP tells us.

And here's a picture of what's going on.

I've got the discount rate.

We've seen a picture like this before.

I've got the discount rate on the horizontal axis, and

I've got NPV on the vertical axis.

And each line graphs the relation between NPV as a function of the discount rate.

So, at our cost of capital, here, if we go up to each line,

we can see the NPVs of each of the bids.

And, quite clearly, the Cisco bid on the green line is better than the Juniper

bid on the red line, which is better than the Huawei bid which is on the blue line.

When we go over here, where the lines cross the x axis,

these are the IRRs right.

By definition, the IRR is the discount rate where the NPV equals zero.

Here are the IRRs.

In this case, we see that the IRR for Huawei is much bigger than the IRR for

Juniper, which is bigger than the IRR for Cisco okay.

The exact opposite ranking according to the IRR rule or relative to the NPV rule.

What's going on?

Well if you look more closely at the cash flow streams you can see that

Huawei has small upfront cost, that increases the IRR relatively speaking.

And Juniper has front-loaded cash flows

which is going to increase the IRR relative to the Cisco bid.

So one lesson is the IRR does not address differences in scale and

there's no better way to emphasize this point then to ask would you rather

earn 100% on a $1 investment or 10% on $1 million of investment.

Well quite clearly the latter, you're going to wind up with a lot more money.

Some more intuition,

Juniper's bid is actually like Cisco's with an embedded loan, right?

Then you can see that here,

where Cisco charges 100 million, then you get the cost savings.

What Huawei's doing is it's giving you an $80 million loan and

then charging you 40 every period.

As opposed to the 35 million that Cisco's 1A bid was was charging you

and if we ask what the loan is on this interest rate.

What the interest rate is on this loan, we see it's 23%.

The IRR to this loan is just 23%.

Which is much bigger than the 12% cost of capital that Wharton faces.

Okay, let's summarize this.

What are the lessons here?

Look, internal rate of return is useful.

It's a way to convey the attractiveness of a project or

an investment in a manner that investors get.

Returns.

The problem with the IRR Decision Rule is that it only works, or

overlaps with NPV in certain situations when we're not comparing projects and

when the cash flows lines are all negative cash flows proceeding positive cash flows.

So, I think key end message here is that, use IRR in your project evaluation and

your investment analysis, your capital budgeting.

But, be cognizant of the limitation.

Know when to use, know when now to use it, that's what's critical.

So thank you so much for listening, and I look forward to seeing you in the next

lecture in which we're going to talk about, what are we going to talk about?

Oh, the cost of capital.

Bye bye.

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