第五章 Net Present Value and Other Investment Rules 净现值和投资评价法则
5.1 Net Present Value Rule 净现值法
1. The basic rules：
Accept a project if the NPV is greater than zero，reject a project if NPV is less than zero.净现值大于零的项目可以接受，净现值小于零的项目要拒绝。
And accepting positive NPV projects will benefit the stockholders.
另：
⑴ The value of the firm is merely the sum of the values of the different projects, divisions, or other entities within the firm. 公司是价值是其项目、部门以及其他实体价值总和
This property, called value additivity, is quite important. 价值可加性
⑵ We suppose the project is about as risky as the Stock market as a whole, where the expected return this year is perhaps 10 percent. Then 10 percent becomes the discount rate.假设项目的风险和整个市场风险一样，市场风险为10%，那么10%可当成是项目的折现率。
⑶ The discount rate on a risky project is the return that one can expect to earn on a financial asset of comparable risk. This discount rate is often referred to as an opportunity cost because corporate investment in the project takes away the stockholder's opportunity to invest the dividend in other assets. 某一项目的折现率是投资者投资于相同风险水平的金融资产所能获得的收益率（机会成本）
2. 特点
⑴ NPV uses cash flows. Cash flows from a project can be used for other corporate purposes. By contrast, earnings are an artificial construct. Although earnings are useful to accountants, they should not be used in capital budgeting because they do not represent cash. 项目的现金流是折现的对象而不是净利润。
⑵ NPV uses all the cash flows of the projects 包括了项目期内全部的现金流
⑶ NPV discounts the cash flows properly without ignoring the time value of money. 考虑了货币的时间价值
5.2 The Payback Period Rule 回收期法
The payback Period of the investment is the period within which the firm will recover its original investment. 项目回收期是指项目回收初始投资现金流所用的时间。
特点：
1. The payback period rule for making investment decisions is simple. 决策方法简单。
We can select a cutoff date, say two years. All investment projects that have payback periods of two years or less are accepted, and all of those that pay off in more than two years are rejected.
决策标准：未超过预定的回收期的项目可以接受，超过预定回收期的项目不能接受。
2. Problems with the Payback Method 问题
⑴ Timing of cash flows within the payback period. 现金流量序列问题
The payback period rule does not consider the timing of the cash flow within the payback period, especially the cash flow in each period is not identical. 多数情况下每期现金流的回收数额不等，这使得回收期不能完整反映项目价值。
⑵ Payments after the payback period 未考虑回收期之后的现金流
It ignores all cash flow occurring after the payback period. Because of the short-term orientation of the payback method, some valuable long-term projects are likely to be rejected. 未考虑回收期以后的现金流，可能会拒绝一些有价值的长期项目
⑶ Arbitrary standard for payback period 主观性强
The choosing of the payback period cutoff date is arbitrary. 回收期截止日的选择主观臆断，不够客观。
(4) 最大的问题：未考虑现金流的时间价值。
另：适用类型
⑴ The payback method is often used by large, sophisticated companies when making relatively Small decisions. 大公司的小项目适用回收期法。
⑵ Easy to control. 易于管理控制，能够快速的进行决策。
(3) It suggests that firms with good investment opportunities but on available cash may justifiably use payback method. For example, the payback method could be used by Small, privately held firms with good growth prospects but limited access to the capital market.
拥有好机会但缺乏现金的公司用回收期法合适，因为对于这类公司现金的快速回笼才是最关键的。
例如，前景好却难以进入资本市场的小公司。
5.3 The discounted Payback Period Method 折现回收期法
First discount the cash flows and ask how it will take for the discounted cash flows to equal the initial investment.
略
5.4 The Internal Rate Return 内部收益率法 IRR
The IRR is the rate that causes the NPV of the project to be zero 内部收益率是指使项目未来现金流的净现值为零的折现率。
The basic rules :
Accept the project if IRR is greater than the discount rate.
Reject the project if the IRR is less than the discount rate.
接受内部收益率大于折现率的投资项目，拒绝内部收益率小于净现值的投资项目。
It should be clear that the NPV is positive for discount rate below the IRR and negative for discount rate above the IRR. If we accept projects like this one when the discount rate is less than the IRR, we will be accepting positive NPV projects. 接受折现率小于内部收益率的项目等于接受了一个净现值为正值的项目。
Problems with the IRR Approach 内部收益率法存在的问题
1. Independent and Mutually Exclusive Projects 独立项目和互斥项目
An independent project is the one whose acceptance or rejection is independent of the acceptance or rejection of other projects. 独立项目是对其接受或者放弃的决策不受其他项目决策影响的投资项目
Mutually Exclusive Investment 互斥项目
You can accept A and B，or you can reject both of them, but you cannot accept both of them.
2. Independent Projects' Problems 独立项目中的问题
⑴ Investing type project and Financing type project 投资项目和融资项目
Compared with investing type project, financing type project initially receives money and then the cash outflows each period.融资项目的特点是：项目初始现金流为正数，以后各期现金流为负数。
And the basic IRR rule is exactly the opposite of previous result ：
Accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate.
融资项目决策的标准与投资项目相反：接受内部收益率小于折现率的融资项目，放弃内部收益率大于折现率的融资项目。
⑵ Multiple Rates of Return 多重内部收益率
Some projects have several negative cash flows and positive cash flows. We can calculate that the IRR may have not one results. 有些项目既有现金流入也有流出，频繁变换，这导致计算出多个内部收益率，使得无法做出判断。
In theory, a cash flow stream with k changes in sign can have up to k sensible IRR.
理论上，现金流的流入流出方向的改变k次，最多会计算出k个内部收益率。
3. Mutually Exclusive Projects' Problems 互斥项目中的问题
⑴ The scale problem 投资规模问题 ( for investing type project 投资项目)
①The problem with IRR is that it ignores issues of scale. 内部收益率法忽略了投资的项目的规模。
Assume there are two mutual exclusive projects. Project 1 has greater IRR than 2, but the investment scale is Smaller than 2. 计划1的内部收益率高但规模小
The high percentage return on project 1 is more than offset by the ability to earn at least decent return on a much bigger investment under project 2.
有时，高内部收益率的投资项目掩盖了其绝对收益额低的事实。这使得内部收益率法忽略了项目的绝对收益额。
② 解决方法
首先计算增量现金流，使用大项目各期的现金流减去小项目各期的现金流。
1. Calculate the incremental NPV 比增量净现值
If incremental NPV is positive, we should pick the large-budget one. 增量净现值大于零，则选大项目。
2. Compare the incremental IRR to the discount rate 比较增量内部收益率和折现率
If the incremental IRR is larger than the discount rate, we should take the large-budget one.对于投资项目，增量内部收益率大于折现率则选大项目
另：Calculate incremental NPV and incremental IRR 计算增量净现值和内部收益率
Example：
cash flow at date 0 cash flow at date 1 NPV25% IRR
Small budget -10 40 22 300%
Large budget -25 65 27 160%
Incremental cash flows(大减小)-25-(-10)=-15 65-40=25 5 66.7%
The incremental NPV is positive and incremental IRR（66.7%）is greater than discount rate（25%），which means that it is beneficial to invest additional 15，so we should choose the large budget. 增量现金流的净现值大于零且其内部收益率大于折现率，说明额外投资的部分会带来更多的收益。
⑵ The Timing Problem 时间序列问题
Example：
date 0 date1 date2 date3 IRR NPV10% NPV15%
A -10000 10000 1000 1000 16.04% 699 109
B -10000 1000 1000 12000 12.94% 751 -484
B - A 0 -9000 0 11000 10.55% 83 -593
Both project A and B have large scale cash flow after the project begin，but occur in different time. 在两个互斥A、B项目中，大额现金流产生在不同时间点。对于不同的折现率，有时A项目的净现值较大，有时B项目净现值大。通过计算内部收益率会可能做出错误的选择。
调整方法：
首先计算增量现金流，使用后产生大额现金流的项目各期的现金流减去先产生大额现金流的项目各期的现金流
1. 比较增量现金流的内部收益率与项目折现率。如果增量内部收益率大于折现率，则选择后产生大额现金流的投资项目；如果增量内部收益率小于折现率，选择较先产生大额现金流的投资项目。
2. 计算增量现金流的净现值。如果增量现金流的净现值大于零，则选择后产生大额现金流的项目。
5.6 The Profitability Index 盈利指数法 PI
The Profitability Index (PI) = PV of cash flows subsequent to the initial investment / Initial investment 盈利指数等于 项目初始投资以后的所有现金流的现值之和除以项目初始净现值。
For different kinds of situations
1. Independent Projects 独立项目
Accept an independent project if PI is larger than 1, reject if it Smaller than 1
接受盈利指数大于1的项目。
2. Mutually Exclusive Projects 互斥项目
Incremental analysis : if PI on the incremental cash flows is greater than 1, we should choose the bigger project.
选择盈利指数大的项目。
3. Capital Rationing 资本配置
The firm does not always have enough capital to fund all positive NPV projects.
Example :
D0 D1 D2 12%PV of cash flows PI NPV12% subsequent to
initial investment
A -20 70 10 70.5 3.53 50.5
B -10 15 40 45.3 4.53 35.3
C -10 -5 60 43.4 4.34 33.4
The cash constraint forces the firm to choose either A or B and C 资金有限，只能选A项目一个，或者BC项目组合
Individually, B and C have lower NPVs of projects than A. But when the NPVs of B and C are added together the sum is higher than the NPV of A. Thus, we should accept B and C. 如果单独来分析，B、C项目的净现值都没有A项目高，但是组合起来净现值综合却大于A项目。
In the case of limited funds, we cannot rank projects according to their NPVs. Instead, we should rank them according to the ratio — PI. Both B and C have higher PI ratios than does A. Thus, they should be ranked ahead of A when capital is rationed. 在资金有限时，不能只根据项目的净现值进行排名，要首先考虑盈利指数
4. Indivisibilities 不可分割性 / 团性
If the firm has enough money for A and B or A and C, then calculate the NPV of AB and AC. AB's NPV is greater than AC's. The firm will accept project AB. 如果公司有钱能投资AB组合或者AC组合，自然就能投BC组合。计算后发现投AB组合净现值最高。
But B and C still have higher PI, so PI rule now lead to the wrong decision. 但是B和C项目的盈利指数高，如果选BC组合会有资金剩余。此时盈利指数法则失效。
另：重点总结：
1. 净现值法准则？特点？
2. 回收期法准则？优点？缺点？
3. 内部收益率法准则？独立项目、互斥项目？
4. 内部收益率法在独立项目中存在的问题？
5. 内部收益率法在互斥项目中存在的问题？如何解决？增量现金流法，包括增量净现值和增量内部收益率
6. 盈利指数法准则？
2020.02.14
