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毕业设计论文
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中北大学irr指标在项目评价中应用研究设计,毕业设计论文
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中北大学 2005 届本科毕业论文 第 1 页 共 9 页 英文原文 Internal Rate of Return The two most-used measures for evaluating an investment are the net present value and the internal rate of return. Two earlier tutorials discussed these concepts. It is often assumed that higher is better for both of the net present value and the internal rate of return. In particular, it is usually stated that investments with higher internal rates of return are more profitable than investments with lower internal rates of return. However, this is not necessarily so. In some situations, an investment with a lower internal rate of return may be better, even judged on narrow financial grounds, than an investment with a higher internal rate of return. This interactive lecture explores why and when this reversal takes place. To review, both the net present value and the internal rate of return require the idea of an income stream, so lets start there. An income stream is a series of amounts of money. Each amount of money comes in or goes out at some specific time, either now or in the future. The income stream represents the investment; the income stream is all you need to know for financial evaluation purposes. Here is an income stream example. Year 0 1 2 3 4 5 6 Income amounts -$1000 $200 $200 $200 $200 $200 $200 Here we see seven points in time ,At year 0 (now), the income amount is negative. Negative income is cost, or outgo. In this example, the negative income amount in year 0 represents the cost of buying and installing the machine. In the future, at years 1 through 6, there will be net income of $200 each year. All of the amounts in the income stream are net income, meaning that each is income minus outgo, or revenue minus cost. In year 0, the cost exceeds the revenue by $1000. In years 1 though 6, the revenue will exceed the cost by $200. nts中北大学 2005 届本科毕业论文 第 2 页 共 9 页 This investment evidently has no salvage value. That is, there is nothing that can be sold in year 6, the last year. If there were, the amount that could be realized from the sale would be added to the income amount for year 6. For simplicity, all my examples have the incomes and outgoes at one-year intervals. Real-life investments can have income and expenses at irregular times, but the principles of evaluation are the same. Now lets discuss our one measures in connection with this income stream-internal rate of return. DEFINITION: The Internal Rate of Return (IRR) is defined as the discount rate that makes the project have a zero Net Present Value (NPV). IRR is an alternative method to evaluate software investments and is somewhat similar to NPV calculations but without the need to estimate the discount rate. IRR takes into account the time value of money by considering the cash flows over the lifetime of a project. The IRR and NPV concepts are related although they are not equivalent. The IRR is calculated from the NPV equation as the startin point: The IRR is determined by “trial and error” by solving for the rate that would yield an NPV equal to zero. The “trial and error” calculation can by completed by using the solver function in a spreadsheet program or programmable calculator. Any project similar to the example above with a discount rate less than the IRR would yield a positive NPV. The higher the discount rate the more the cash flows will be discounted resulting in a lower NPV of the project. The company will approve any project or investment where the IRR is higher than the cost of capital as the NPV will be greater than zero. For example, the IRR for a particular project is 20%, but the cost of capital of the company is only 12%, then the company can effectively approve the project as the maximum value for the company to make money would be at the rate of 20%. If the company had a cost of capital for this particular project of 21%, then the company will have a negative NPV and the project will not be considered a profitable one. nts中北大学 2005 届本科毕业论文 第 3 页 共 9 页 The IRR is therefore the maximum allowable discount rate that would yield value considering the cost of capital and risk of the project. For this reason, the IRR is sometimes referred to as a “break even” rate of return. The IRR is then the rate at which the value of cash outflows equals the value of cash inflows. There are some special situations where the IRR concept can be misinterpreted. This is usually the case when the timing of periods of negative cash flow affects the value of IRR without accurately reflecting the underlying performance of the investment. Managers may misinterpret the IRR as the annual equivalent return on a given investment. This is not the case, as the IRR is the breakeven rate and does not provide an absolute view on the project return. EQUATIONS: The Internal Rate of Return (IRR) concept originated from a single equation and does not offer multiple interpretations as the Return on Investment (ROI) concept. The IRR equation is a unique case derived from the Net Present Value (NPV) equation. The IRR is found by solving the NPV equation for the rate that will yield an NPV equal to zero: IRR Equation Nonetheless, there are other variations of the IRR equation in an attempt to “fix” some of the shortcomings of the IRR concept. The most popular modification of the IRR concept is not surprisingly called the MIRR or Modified Internal Rate of Return. The goal of the concept is to correct for the intermediate “cash flows” that are reinvested at the IRR not the cost of capital of the company. IRR calculations are based on the assumption that returns earn the IRR for the entire duration of the investment. BENEFITS: The Internal Rate of Return (IRR) concept has been widely adopted by companies as they compare their cost of capital against the IRR for a particular project or investment. The main benefit of the IRR concept is that is simple, straightforward, and has an intuitive appeal. nts中北大学 2005 届本科毕业论文 第 4 页 共 9 页 Companies can easily compare the cost of capital of the company against the IRR of the project or investment. If the IRR is higher, then the project can be approved. In addition, the IRR method does not have the requirement of establishing the discount rate as you would need if completing a Net Present Value (NPV) calculation. Finding the appropriate discount rate can be a difficult task if including the unique risks of the project. The IRR concept therefore simplifies the process of estimating the value derived from a project. The IRR concept can also be complementary to NPV analyses. The IRR graph can be plotted out to understand the dynamics of the discount rates considering the cash flows. The graph can provide information on the discount rates that would yield a negative NPV. This information in itself will create a limit or bound on the maximum allowable discount rate or risk for the project. A company can then re-structure the project to minimize the project risk to a level that would yield a positive NPV. In the example weve been using, if you keep the income amounts at their original -1000, 200, 200, 200, 200, 200, and 200, and set the discount rate to 0.0547, the net present value becomes 0. This discount rate, 0.0547 or 5.47%, is the internal rate of return for this investment - it is the discount rate that makes the net present value equal 0. If you now raise any of the income amounts in years 1 through 6, you will need a higher discount rate to bring the net present value back to 0. That would seem to imply that projects with higher incomes have higher internal rates of return. Similarly, if you lower any of the income amounts in years 1 through 6, then a lower discount rate will be needed to bring the net present value back up to 0. That would seem to imply that projects with lower incomes have lower internal rates of return. These seeming implications are actually often true, if the projects being compared have about the same shape, but the time of the costs the benefits is not the same, then the implications might not be true. The internal rate of return does not require you to predict future discount rates. That would seem to make the internal rate of return the more useful measure. Sometimes, though, the internal rate of return can fool you. nts中北大学 2005 届本科毕业论文 第 5 页 共 9 页 LIMITATIONS: The Internal Rate of Return (IRR) concept has several limitations and although the concept is somewhat simple, it can be easily misinterpreted and confused with the actual project rate of return. These limitations are explored in further detail below: Timing of costs and benefits. Projects that require investments at a later stage may yield IRR that are not representative of the value of the project. These later expenditures may turn the net benefits of a project in a particular year negative. From the equation stand point, these negative net benefits or cash flows are treated the same as borrowing money resulting in misleading IRR. In this scenario, the IRR concept can generate among others multiple IRR values for the same project, making it difficult to compare which IRR value is the true IRR for the project. To avoid these scenarios, the IRR concept is best suited for projects or investments having positive cash flows throughout their lifetime. Relative and absolute values. The IRR concept does not provide an indication of the magnitude of the value of the project. This constraint presents a problem when comparing the IRR values from different projects. For example, a project with a high IRR may appear more appealing than a project with a lower IRR, even if the project with the lower IRR has a greater NPV value. In summary, the IRR model is a good first approximation or filter as to the value of a project. In fact, the IRR model is somewhat better than a Return on Investment (ROI) model to perform this first approximation of value of a project. The IRR inherently considers the projects risk and time value of money which are not incorporated in a ROI analysis. Nonetheless given the limitations presented above, the IRR model should be combined with a more robust financial evaluation tools such as Net Present Value (NPV) or Real Options. 资料来源： Jack Smith .The Internal Rate of Return. USA,McGraw-Hill book Company.1998. nts中北大学 2005 届本科毕业论文 第 6 页 共 9 页 英文译文 内部收益率 最常见两种投资评价方法是净现值法和内部收益率法，早期学者就已讨论过这些概念。 通常的假设是净现值和内部收益率越高的会越好。实际中，一般认为具有较高内部收益率的投资项目比具有较低内部收益率的投资项目更具有收益性。 但是，并不绝对是这样。在有些情况下，具有较低内部收益率的投资项目也许会更好，甚至在财务评价上，也会比具有较高内 部收益率的项目好，这种说法揭示了为什么和会在什么时候发生这种相反的情况。 回过头来说，无论是净现值还是内部收益率都与净现金流量有关，那么我们就从这里开始。净现金流量是一系列数量的现金，每一定数量的现金流入或现金流出都发生在一个特定的时期，现在或将来。净现金流量代表了投资项目；净现金流量是你进行经济评价必须知道的。 这里有一个净现金流量表。 年 0 1 2 3 4 5 6 净现金流量 -1000 200 200 200 200 200 200 在这我们看到有 7 个时间点，在第 0 年（即现在时刻），净现金流量是负的，负的净现金流代表是花费或支出。在这个例子中，在第 0 年中的净现金流代表成购买或安装设备所花费的费用。 在将来，从第 1 年到第 6 年，每年有 200 元的净现金流入。 这里面的所有现金流量都是净现金流量，意味着每个都是收入减去支出，或者收益减去成本所得。在第 0 年，成本超过了收益 1000 元，在第 1 年到第 6 年，收益将超过成本 200 元。 这个投资项目显然没有利用价值，那是由于，在第 6 年 最后一年没有任何东西可以出售。如果，销售收入能够体现出来，那么在第 6 年中的净现金流量会有所增加。简单nts中北大学 2005 届本科毕业论文 第 7 页 共 9 页 地说，我的所有的例子在每一年的间隔中都有流入和流出。实际的投资项目中收入和支出都发生在无规律的时间中，但它们的评价原则还是一样的。 现在让我们来讨论与净现金流量有关的其中一种方法 -内部收益率。 定义： 内部收益率（ IRR）被定义为使项目的净现值等于零时的折现率。它是用来评价投资项目的一种可选择性方法，有点类似于 NPV 的计算，但不需要估计折现率。 IRR 重点考虑现金流超过项目寿命时的时间价值。尽管 IRR 与 NPV 不是等价的，但是它们的概念有相关之处。 从净现值的等式中可以估算到 IRR。 nnI R RCI R RCI R RCCN P V)1()1()1(0 22110 通过使 NPV 等于零时的“反复试算”可以计算出 IRR。“反复试算”的计算可以通过运用电子制表软件程序里的函数或可编程的计算实现。 任何一个类似于上面例子的项目其折现率低于 IRR 时将产生一个正的 NPV，折现率越高，使项目产生一个更低的 NPV 的现金流的折现就越大。公司会赞成任何当 NPV远大于零， IRR 高于资本价值的计划或投资。例如，一个项目 IRR 使 20%，而公司的资本价值只有 12%，这时公 司就能有效地证明在利率为 20%时，项目具有最大的价值为公司赚钱。如果公司在这个项目上的资金成本是 21%，那么公司将会有一个负的 NPV，这时项目就不合适。 因为 IRR 是指考虑了资本成本和项目的风险下，最大的可允许的折现率。基于这一点， IRR 有时指利润率的得失相当，即现金流入值等于现金流出值时的利率。 在一些特殊情况下， IRR 的概念易被曲解。负的现金流的延迟期影响 IRR 的值没有正确的反映投资的潜在表现就是一种通常的情况。管理者可能误解为 IRR 是使投资项目在每年都得到相等的回收利润的利率，并不是 IRR 是指无亏损率 并且不会对项目的利润提出绝对的观点这种情况。 等式： IRR 的概念来自于单个的方程式，不像投资利润率的概念那样有多种解释。 IRR 的等式是来自于 NPV 等式的一个独特的形式。 IRR 在解使净现值等于零时这个等式的利率时可以求出。 nts中北大学 2005 届本科毕业论文 第 8 页 共 9 页 nnI R RCI R RCI R RCCN P V)1()1()1(0 22110 然而， IRR 方程还有其他变换形式来力图修正 IRR 概念的不足，对 IRR 概念最盛行的修正方法是 MIRR 即修正内部收益率。 概念的目标是对中间的再投资于 IRR 而不是公司的资本成本的现金流量作出矫正。IRR 的计算基于在整个投资期内获得的收入以 IRR 再投资于内部的假设。 优势： 内部收益率（ IRR）的概念被广泛地采用在公司对项目或投资进行评价时将资本成本与 IRR 进行比较。 IRR 的
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