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# 金融代写|公司金融学代写Corporate Finance代考|Problems Specific to Mutually Exclusive Projects

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## 金融代写|公司金融学代写Corporate Finance代考|Problems Specific to Mutually Exclusive Projects

As mentioned earlier, two or more projects are mutually exclusive if the firm can, at most, accept only one of them. We now present two problems dealing with the application of the IRR approach to mutually exclusive projects. These two problems are quite similar, though logically distinct.

The Scale Problem A professor we know motivates class discussions on this topic with the statement: “Students, I am prepared to let one of you choose between two mutually exclusive ‘business’ propositions. Opportunity 1-You give me $\$ 1$now and I’ll give you$\$1.50$ back at the end of the class period. Opportunity 2-You give me $\$ 10$and I’ll give you$\$11$ back at the end of the class period. You can only choose one of the two opportunities. And you cannot choose either opportunity more than once. I’ll pick the first volunteer.”
Which would you choose? The correct answer is opportunity $2 .^8$ To see this, look at the following chart:

Cash Flow at
\begin{tabular}{lcccc}
& $\begin{array}{c}\text { Cash Flow } \ \text { at Beginning } \ \text { of Class }\end{array}$ & $\begin{array}{c}\text { End of Class } \ (90 \text { minutes } \ \text { later })\end{array}$ & NPV $^9$ & IRR \
\hline Opportunity 1 & $-\$ 1$&$+\$1.50$ & $\$ 0.50$&$50 \%$\ Opportunity 2 & -10 & +11.00 & 1.00 & 10 \end{tabular} As we have stressed earlier in the text, one should choose the opportunity with the highest NPV. This is opportunity 2 in the example. Or, as one of the professor’s students explained it: ‘I’m bigger than the professor, so I know I’ll get my money back. And I have$\$10$ in my pocket right now so I can choose either opportunity. At the end of the class,I’ll be able to play two rounds of my favorite electronic game with opportunity 2 and still have my original investment, safe and sound. ${ }^{10}$ The profit on opportunity 1 buys only one round.”

We believe that this business proposition illustrates a defect with the internal rate of return criterion. The basic IRR rule says take opportunity 1 , because the IRR is 50 percent. The IRR is only 10 percent for opportunity 2.

Where does IRR go wrong? The problem with IRR is that it ignores issues of scale. While opportunity 1 has a greater IRR, the investment is much smaller. In other words, the high percentage return on opportunity 1 is more than offset by the ability to earn at least a decent return ${ }^{11}$ on a much bigger investment under opportunity 2 .

Since IRR seems to be misguided here, can we adjust or correct it? We illustrate how in the next example.

## 金融代写|公司金融学代写Corporate Finance代考|Redeeming Qualities of the IRR

The IRR probably survives because it fills a need that the NPV does not. People seem to want a rule that summarizes the information about a project in a single rate of return. This single rate provides people with a simple way of discussing projects. For example, one manager in a firm might say to another, “Remodeling the north wing has a 20-percent IRR.”
To their credit, however, companies that employ the IRR approach seem to understand its deficiencies. For example, companies frequently restrict managerial projections of cash flows to be negative at the beginning and strictly positive later. Perhaps, then, the ability of the IRR approach to capture a complex investment project in a single number and the ease of communicating that number explain the survival of the IRR.

A Test
To test your knowledge, consider the following two statements:

1. You must know the discount rate to compute the NPV of a project but you compute the IRR without referring to the discount rate.
2. Hence, the IRR rule is easier to apply than the NPV rule because you don’t use the discount rate when applying IRR.

The first statement is true. The discount rate is needed to compute NPV. The IRR is computed by solving for the rate where the NPV is zero. No mention is made of the discount rate in the mere computation. However, the second statement is false. In order to apply IRR, you must compare the internal rate of return with the discount rate. Thus, the discount rate is needed for making a decision under either the NPV or IRR approach.

## 金融代写|公司金融学代写Corporate Finance代考|Problems Specific to Mutually Exclusive Projects

$\backslash$ begin ${$ tabular $}{\mathrm{lcccc}} \& \$ \backslash$begin${$array$}{\mathrm{c}} \backslash$text${$现金流量$} \backslash \backslash$text${$在开头$} \backslash \backslash$text${$of Class$} \backslash$end${$array$} \$\& \$ \backslash$begin${$array$}{c}$正如我们在本文前面所强调的，应该选择 NPV 最高的机会。这是示例中的机会 2。或者，正如一位教授的学生所解释的那样: 我 比教授大，所以我知道我会拿回我的钱。我有$\$10$ 现在在我的口袋里，所以我可以选择任何一个机会。在课程结束时，我将能曶在 机会 2 上玩两轮我最喜欢的电子游戏，而且我的原始投资仍然安全无虞。 10 机会 1 的利润只能购买 轮。”

$I R R$ 哪里出错了? IRR 的问题在于它忽略了规模问题。蚎然机会 1 的 IRR 更高，但投洛要小得多。换句话说，机会 1 的高百分比回 报被至少获得可观回报的能力所抵消 ${ }^{11}$ 在机会 2 下进行更大的投资。

## 金融代写|公司金融学代写Corporate Finance代考|Redeeming Qualities of the IRR

IRR 可能会存在，因为它满足了 NPV 无法满足的需求。人们似乎想要一个规则，以单一的回报率来概括一个项目的信息。这种单一汇率为人们提供了一种讨论项目的简单方式。例如，公司的一位经理可能会对另一位经理说：“改造北翼的内部收益率为 20%。”

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。