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Often, CAPM is used to determine whether an investment is profitable or not. The idea is to first estimate how large the future profits will be. Thereafter one estimates how large the discount rate should be. Finally, one calculates the present value of the investment and determines if it is worth its cost or not.

We assume that we already have estimates of the future profits. We must then determine the riskiness of the project. That is often done by comparing it to other similar projects that already exist. If the new project cannot be considered either more or less risky than other projects in the firm, one can use the firm’s own internal rate of return as discount rate. However, suppose the firm is considering starting a new type of project. It is then possible to get an estimate of the riskiness by studying other firms with similar projects. The new project should have about the same (nondiversifiable) risk. Therefore, we use the other firms to get an estimate of $\beta$. Then we use that estimate in the CAPM formula and solve for what the discount rate, $R_j$, should be: $R_j=R_f+\beta\left(R_M-R_f\right)$

To give an example: Suppose we have a project that we expect will make a loss of 10 during the first year and then generate a profit of 200 during each of three consecutive years. Then we can sell the remains for 100 . The present value of the future cash flows is

$$P V=\frac{-10}{1+R}+\frac{200}{(1+R)^2}+\frac{200}{(1+R)^3}+\frac{200}{(1+R)^4}+\frac{100}{(1+R)^4}$$
Furthermore, suppose that the market risk premium, $\mathrm{R}{\mathrm{M}}-\mathrm{R}{\mathrm{f}}$, is $6 \%$, that the risk free rate of return, $\mathrm{R}_{\mathrm{f}}$, is $2 \%$ and that $\beta$ for a firm with a similar project is 1.5. We then estimate the discount rate to $2 \%+1.5 * 6 \%=11 \%$. If we use that value in the formula, the present value is 497 .

Should we invest or not? That depends on the price. If the cost of the project is less than 497, we invest; if it is more, we do not. Often, one includes the cost in the present value. This is then called the net present value (NPV). The investment criterion is then whether NPV $>0$ or not. Suppose the investment costs 450. Then NPV $=-450+497=47$, and we should go on with the investment since it is profitable.

## 经济代写|微观经济学代考Microeconomics代写|A “Robinson Crusoe” Economy

Consider an economy with only two agents on a desert island: Robinson and Friday. Those two are then the only consumers and the only producers. Let us assume that they also produce only two goods: Coconuts and fish. The question is then how much coconuts and fish to produce, and how to allocate them among themselves.
18.2 Efficiency
We have already mentioned efficiency several times in this book (for instance in Sections 11.4 and 12.1). Efficiency is about how much waste there is in an economy; less waste means more efficient. There are several related ways to define efficiency. An often-used measure of efficiency regarding allocations is Pareto efficiency. The definition of Pareto efficiency is:

• Pareto improvement. A change in allocation such that
• No one is worse off; and
• At least one, possibly several, is better off.
• Pareto efficient or Pareto optimal. An allocation such that
• No Pareto improvements are possible.
• The Edgeworth Box
• In Chapter 3, we discussed the basics of consumer theory. We described, for instance, indifference curves and the budget line. If we consider an exchange economy in which the quantities of the goods are fixed, we have a zero-sum game. This means that one individual can only get quantities that the other ones do not get; there is, for instance, no growth in the economy. The name “zero-sum game” comes from the fact that, the sum of what some people gain and what others lose is always zero.

# 微观经济学代写

$$P V=\frac{-10}{1+R}+\frac{200}{(1+R)^2}+\frac{200}{(1+R)^3}+\frac{200}{(1+R)^4}+\frac{100}{(1+R)^4}$$

## 经济代写|微观经济学代考Microeconomics代写|A “Robinson Crusoe” Economy

18.2 效率

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## 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。