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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From the course by University of Pennsylvania

企业金融概论（中文版）

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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。

From the lesson

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

Finance

Welcome back to corporate finance. Last time, we applied our forecast drivers to our free cash flow formula to forecast free cash flows for a tablet project. Today, I want to take those free cash flows and apply our different decision criteria to come up with decisions regarding our project. Let's get started. Hi everyone, welcome back to corporate finance. Today we're going to talk about decision criteria. But before doing so, let's recap our previous lecture in which we forecasted free cash flows. Specifically, we took our forecast drivers, our assumptions about what would happen in the future and applied them to generate dollar forecasts of all of the components of the free cash flow formula. Which we then built up, aggregated into free cash flow forecast. Today we're going to turn to what to do with those forecasts by looking at different decision criteria. So let's get started.

So what do we do with our cash flows from last time? One thing we can do is we compute the NPV. And I'm going to assume a discount rate of 12%, that is R=12%. And if we do that, and apply it to our free cash flows that we computed in the last lecture, what we're going to see is that this project, this tablet project has an NPV of $708.42 million. Not bad, what that means is that firm value, debt plus equity, is going to increase by $708.42 million in expectation, if the project is undertaken.

That's what the NPV Rule tells us. It says accept all projects with a positive NPV, reject all projects with a negative NPV.

And while this has boiled it down to one number, I want to be careful, especially when we start doing our sensitivity analysis to recognize that we don't want to pin all our hopes to that one number.

Now another thing we can do is we can compute the internal rate of return. The internal rate of return of a project, recall is the one discount rate such that the net present value of the project's free cash flows equals zero. We've actually already seen this when we were talking about yields. Remember the yield is the one discount rate such that when you discount the cash flows by the yield, you get the price. But the NPV is nothing more than price minus the present value of all the future cash flows, okay? So IRR and yield are really one and the same.

So what's the IRR for this project? Well, we write our NVP formula, we set our NVP=0. And then we solve for the one discount rate.

Such that when we discount all of our free cash flows, we get an NVP of zero. If we do that, we find that the IRR on this project is 43.7%. Well, is that good, is it bad? Before getting there, I just want to mention, typically we're going to need to solve this numerically, unless you have figured out some amazing way to solve higher order polynomials. You can use the IRR function in Excel, I think you can use goal seek in Excel, you can try trial and error, though that's really inefficient. If you're using another software program or a financial calculator, you can do this as well. All right, so what do we do with this 43.7% IRR? Well, we're going to compare it to our cost of capital, our hurdle rate. And what we're going to do is undertake the project because the IRR is greater than the hurdle rate. Intuitively, it makes sense. And this is one of those cases where intuition actually works. It costs us 12% to raise money in the capital markets to fund our investments, to create value. If this project generates a return of 43.7%, that's substantially larger than what it costs us to raise the funds. That sounds good, that makes sense. And so what the IRR Rule says is accept all projects whose IRR greater than R and reject all projects whose IRR less than R, where R is our hurdle rate. Hurdle rate cost of capital, our discount rate.

Now, I do want to mention that the IRR Rule's informative. It's also somewhat intuitive and appeals a lot to investors who tend to think in terms of returns. But it's got a number of shortcomings that we're going to explore in greater detail in Topic 4, Return on Investment. Now one picture I'd like to show you is the following. I've plotted the cost of capital on the horizontal axis and the project NPV on the vertical axis. And what the blue line shows is it shows how the NPV of the project varies as I vary the cost of capital. Two points are worth noting. First is this point right here which is the 12% cost of capital of the project. You'll notice that generates an NPV as we saw earlier of a little bit over $700 million. The second point I want to point out, is this point, the point where the graph crosses the x axis, that's the point at which the NPV is zero which as we know from our definition earlier is just the IRR, that's 43.7%. Now, I think this graph is, let me clear this up a little bit, this graph is useful because from a sensitivity analysis, or a robustness perspective. Look, this R is an estimate, and to be honest with you, it's typically a noisy one.

What I see here is I see a really wide gap between my estimated cost of capital and the point at which this project just breaks even. So even if we disagree on the cost of capital and you're taking a more conservative view and you think it's up where our real cost of capital's 20%, that's okay. This project is still NPV positive. It's still value accretive and so what this gap here shows, is it shows that I've got a lot of room for error, at least on the discount rate dimension.

The third thing we can do with our cash flows or free cash flows is compute a payback period, which is the duration or the time until the cumulative free cash flows turn positive. So let's look at our project. Here are our free cash flows. I'm going to accumulate them year over year. So this 510, -510.4 is just 376.8 in year zero plus the -133.6 in year one. And on and on for years two through five. And then I'm going to look at the accumulative free cash flows and ask, when do they turn positive? Well, they turn positive right here in year three. So our payback period is year three. We turn cash flow positive in year three. Some people might say it takes three years to recover your investment. Is that good? Is it bad? How do we know if three is good, how does that help us in our decision on whether or not to take the project? Well what we do is we compare it to some threshold. And so the payback period rule says accept all projects with a payback period less than the threshold, reject all project with payback periods greater than that threshold.

But it should be immediately clear that the Payback Period Rule has several shortcomings, the first of which is it's ignoring the time value of money and risk of cash flows. The first sin that we learned way back at the start of the course. But fortunately that's actually quite easy to deal with. We can compute the discounted payback period by discounting the free cash flows, right? The discounted payback period of a project's just the duration until the cumulative discounted free cash flows turn positive. And so on this slide, I've computed those discounted free cash flows using our cost of capital of 12% and then I cumulate them and wait or count until they turn positive, which is right here in year four. So our discounted payback period is four which is greater then our payback period of three.

But even using the discounted payback period, this rule has a number of shortcomings. For example, it ignores cash flows after the cutoff and that's going to lead to myopic decision making. Let me go back a slide. What if, what if this cash flow in year five was $20 billion, well $20 billion 114 million.

It would be a shame to ignore that and the implication of that cash flow. So by ignoring those cash flows, you get myopic decision making. Number 2, it's not telling us the value implications of our decision.

It's not helping us quantify the effects of any decision that we make. It's also not helpful in choosing among projects with similar payback periods. So I've got three projects, they all have payback periods of four, which one do I choose if I can only choose one?

All right, so let's bring this all back together, let's bring it full circle. So there's several decisions criteria, NPV is unambiguously the best and should always be used.

But I want to emphasize that others, such as the internal rate of return and payback period, its discounted cousin, they're all informative. And the key is to understand the shortcomings of these alternative decision criteria to avoid any mistakes that feed into the ultimate decision. So what I want to turn to in our next class is sensitivity analysis which is an integral component of any DCF. Thanks again, and I look forward to seeing you.

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