1. Capital budgeting
1.1 The capital budgeting process
The capital budgeting process is used to determine and select the most profitable long-term
(greater than one year) projects. The typical step is as below:
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Step 1:Generating ideas(the most important step in the process)
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Step 2: Analyze project proposals(i.e. forecast cash flows and then evaluating the
project’s profitability)
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Step 3: Planning the capital budget
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Step 4: Monitoring and post-auditing
1.2 Categories of capital budgeting projects
1) Replacement projects
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Replacement decision to maintain the business( due to equipment breaks down or
wears out)Do not need capital budget

Replacement decision for cost reduction purpose(replacing existing old equipment with
newer, more efficient equipment)
Need capital budget
2) Expansion projects （more uncertainties than replacement
projects）

Expansion projects for existing product (如增加一条生产线)
Need capital
budget

Expansion projects for new product or new services Need capital budget
3) Mandatory projects – regulatory, safety and environment
project

Projects are required by a governmental agency, an insurance company,or some other
external party.

Cost of project is sufficiently high

Individual NPV is negative
4) Other projects:
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Pet projects(如 CEO 买了私人飞机)
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Research and development decisions (so risky that is difficult to analyze by the usual
methods)
1.3 Basic principles of capital budgeting
1) Decisions are based on after-tax incremental cash flows, not
accounting income.

注意是 after-tax incremental cash flows，税后的增量现金流，the cash flow with a
decision minus the cash flow without that decision, 即做这个项目时才会产生的税后
现金流量的变化。
2) The timing of cash flow is important.

资本预算与 time value of money 也是息息相关的，即 cash flows received earlier are
worth more than cash flows to be received later, 现金越早收到，项目就越有利。
3) 在评估现金流的时候，我们还需要评估以下几类成本是否需要包
含在现金流的估计中：

Ignore Sunk costs

沉没成本: Today’s decisions should be based on current and future cash flows and
should not be affected by prior cost,即sunk costs. Sunk costs在资本预算中不予
考虑，因为沉没成本指公司已经发生的不可收回的成本，它不应该成为影响未
来决定的因素。

Include Opportunity cost

Opportunity cost（机会成本）: is what a resource is worth in its next-best use. 即
把一定的经济资源用于生产某种产品时，而放弃生产另外一些产品所得到的最
大收益。Opportunity cost需要考虑在资本预算的成本里。

Include Externalities

Externalities（外部性）
：项目的外部性指投资这个项目后，可能对于公司的其
他经营活动的利润产生间接效应，分为positive externality（增加利润）和
negative externality(cannibalization,减少利润). Externalities需要考虑在资本预算
的成本里。

Ignore Financing costs

即利息不需要从增量现金流中减去，因为在评估资本项目时，分母中的discount
rate中已经考虑了firm’s cost of capital，所以financing costs在资本预算中不予考
虑。
4) Conventional cash flows vs. nonconventional cash flows

Conventional cash flows pattern

An initial cash flow outflow followed by a series of inflows. If cash flows change
signs once, the pattern is conventional.

Nonconventional cash flows pattern

If cash flows change signs two or more times, the pattern is nonconventional. 如
果是非传统的现金流，那么就会出现没有 IRR 或者多个 IRR 的问题。
1.4 Types of project interactions
1) Independent vs. mutually exclusive projects

Independent project: projects that are unrelated to each other, 即如果两个项目资本
预算都赢利，就都可以投资。
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Mutually exclusive projects: the project compete with each other.即由于公司的资源有
限，只能选择最优的一个项目投资。
2) Project sequencing

Investing one project creates the option to invest in future projects.只有这个项目做好
了或者是 new economic conditions are favorable，才有条件去投资另外一个项目。
3) Unlimited Funds vs. Capital rationing

Unlimited Funds：the firm can undertake all profitable projects(expected returns> cost
of capital)
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Capital rationing: if profitable project opportunities> the amount of funds available, so
company’s capital expenditures 必须投入可以使得股东利益最大化的项目中去。
1.5 Investment decision criteria
1) Net present value (NPV)




Definition: PV of future after-tax cash flows minus the investment outlay.
NPV equation: NPV= CF + CF1 + CF2 + ... + CFn
0
(1 + k)1 (1 + k)2
(1 + k)n
Decision rule:

For independent projects: accept if NPV>0

For mutually exclusive projects: choose the one with the highest NPV
Advantage:

Shows the amount of gain as a currency amount

Economically realistic discount rate: firm’s cost of capital adjusted for the risk level
of the project.


A positive NPV project is expected to increase shareholder wealth

Can be used both in conventional cash flow and unconventional cash flow.
Disadvantage:

Size of projects ignored
2) Internal rate of return (IRR)

Definition:IRR is the discount rate that makes NPV equal to zero.

Decision rule:


If IRR> the required rate of return, accept the project;

If IRR<the required rate of return, accept the project.
The multiple IRR problem and no IRR problem:

The multiple IRR problem: more than one IRR will make NPV=0

No IRR: There is no IRR will make NPV=0

一旦出现了 nonconventional cash flow pattern, 就会出现这样的问题。

注意，没有 IRR，不代表是一个不好的投资。没有 IRR，代表在所有的 discount
rate 下，NPV 一直是大于 0 的。
3) Payback period

Definition: is the number of years required to recover the original investment in a
project(based on cash flow). 即多长时间可以回本。
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Drawbacks：

Not a measure of value, only measure liquidity.

Ignores the time value of money and the risk of the project.

Ignores cash flows after the payback period is reached.
必做习题：

P13-Example 1， Drawbacks of the payback period.
4) Discounted Payback period

Definition: is the number of years it takes for the cumulative discounted cash flows
from a project to recover the original investment(based on discounted cash flow).

A negtive NPV
it will not have a discounted payback period(因为永远无法回本)

Drawbacks：等同于 payback period
5) Average accounting rate of return

AAR= Average net income/ average book value

注意，这个几乎不考，因为是基于 net income 的指标，而不是 cash flow.
6) Profitability index

Definition:PI is the ratio of the PV of future cash flows to the initial investment.
PI=

PV of future cash flows
NPV
= 1+
initial investment
initial investment
PI is closely related to the NPV. NPV is the difference between the PV of future cash
flows and the initial investment. Whenever the NPV is positive, the PI will be greater
than 1.0.

Decision rule:Invest if PI>1.0, Do not invest if PI <1.0

Although PI is used less frequently than the NPV and IRR, it is sometimes used as a
guide in capital rationing.因为 PI 体现了 benefit and cost 的 relationship，反应了一个
效率。
7) NPV profile

定义：NPV profile show a project’s NPV graphed as a function of various discount rates.
就是在不同的折现率下绘制出的 NPV 的曲线。

NPV 曲线特征：NPV profile is convex from the origin（凸向原点的曲线）, 即 NPV
declines at a decreasing rate as the discount rate increases.

NPV profile 与纵轴和横轴交点的经济含义（纵轴为 NPV，横轴为 discount rate）
：

NPV profile 与纵轴的交点数值为 Undiscounted future cash flow- initial
investment outlay
或者是 the sum of all the undiscounted cash flow，如图中的 project B 的 NPV
profile 与纵轴的
交点为 200=-200+0+0+0+400

NPV profile 与横轴的交点数值为 IRR，即 NPV=0 时的 discount rate. 从图中可以
看出是 project A 的 IRR 10%大于 project B 的 IRR 8%。
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Decision rule:如果两个项目是互斥的，即如上图显示的mutually exclusive projects，
而且两个项目是different cash flow pattern, 那么会出现NPV与IRR的决策矛盾。在考
试中我们要记住是在crossover rate之前，会有decision rule conflict出现。如果有矛
盾，则以NPV决策为主，即做NPV大的项目。


在 Crossover rate 6% 的时候，两个项目的 NPV 是相等的。
Project B realizes its cash payoffs later than project A. Project B’s NPV profile is more
steeper than project A. 项目 B 更晚地收到现金，所以 project B 的 NPV profile 是更
加陡峭的。
WMI 提示：
NPV profile 是考试的重点，希望大家熟练掌握。
 Independent and conventional projects: NPV and IRR give the same
accept/reject decisions.
 Mutually exclusive projects: NPV and IRR sometimes may result in conflicting
rankings, due to:
1）These projects have different cash flows patterns(or timing) ；
2）These projects have different scale(or size)即期初投资额不一样. Choosing
a large project with a lower rate of return or a smaller project with a larger
rate of return? 一般是选择 a large project with a lower rate of return，因 NPV
高。
必做习题：
 P19-Example 4,
 P21-Example 5,
Ranking conflict due to differing cash flow patterns
Ranking conflict due to differing project scale
1.6 Relationship between NPV and stock price

In theory, a positive NPV project should cause a proportionate increase in a company’s
stock price.

Changes in the stock price will result more from changes in expectations about a firm’s
oositive NPV projects.

Estimated increase in share value= NPV/ number of shares
必做习题：
 P27-Example 6,
NPVs and stock prices