Capital Budgeting

Capital Budgeting is the process by which the firm decides which long-term investments to
make. Capital Budgeting projects, i.e.,potential long-term investments, are expected to generate
cash flows over several years. The decision to accept or reject a Capital Budgeting project
depends on an analysis of the cash flows generated by the project and its cost. The following
three Capital Budgeting decision rules will be presented:

 Payback Period
 Net Present Value (NPV)
 Internal Rate of Return (IRR)

A Capital Budgeting decision rule should satisfy the following criteria:

 Must consider all of the project's cash flows.

 Must consider the Time Value of Money
 Must always lead to the correct decision when choosing among Mutually Exclusive
Projects.

Project Classifications
Capital Budgeting projects are classified as either Independent Projects or Mutually
Exclusive Projects.

An Independent Project is a project whose cash flows are not affected by the accept/reject
decision for other projects. Thus, all Independent Projects which meet the Capital Budgeting
critierion should be accepted.

Mutually Exclusive Projects are a set of projects from which at most one will be accepted.
For example, a set of projects which are to accomplish the same task. Thus, when choosing
between "Mutually Exclusive Projects" more than one project may satisfy the Capital
Budgeting criterion. However, only one, i.e., the best project can be accepted.

Of these three, only the Net Present Value and Internal Rate of Return decision rules consider all
of the project's cash flows and the Time Value of Money. As we shall see, only the Net Present
Value decision rule will always lead to the correct decision when choosing among Mutually
Exclusive Projects. This is because the Net Present Value and Internal Rate of Return decision
rules differ with respect to their Reinvestment Rate Assumptions. The Net Present Value decision
rule implicitly assumes that the project's cash flows can be reinvested at the firm's Cost of
Capital, whereas, the Internal Rate of Return decision rule implicitly assumes that the cash flows
can be reinvested at the projects IRR. Since each project is likely to have a different IRR, the
assumption underlying the Net Present Value decision rule is more reasonable.
Cost of Capital
The firm's Cost of Capital is the discount rate which should be used in Capital Budgeting.
The Cost of Capital reflects the firm's cost of obtaining capital to invest in long term assets.
Thus it reflects a weighted average of the firm's cost of debt, cost of preferred stock, and cost
of common stock.

Payback Period

The Payback Period represents the amount of time that it takes for a Capital Budgeting project to
recover its initial cost. The use of the Payback Period as a Capital Budgeting decision rule
specifies that all independent projects with a Payback Period less than a specified number of
years should be accepted. When choosing among mutually exclusive projects, the project with
the quickest payback is preferred.

The calculation of the Payback Period is best illustrated with an example. Consider Capital
Budgeting project A which yields the following cash flows over its five year life.

Cash
Year
Flow
0 -1000
1 500
2 400
3 200
4 200
5 100

To begin the calculation of the Payback Period for project A let's add an additional column to the
above table which represents the Net Cash Flow (NCF) for the project in each year.

Cash Net Cash

Year
Flow Flow
0 -1000 -1000
1 500 -500
2 400 -100
3 200 100
 4 200 300
5 100 400

Notice that after two years the Net Cash Flow is negative (-1000 + 500 + 400 = -100) while after
three years the Net Cash Flow is positive (-1000 + 500 + 400 + 200 = 100). Thus the Payback
Period, or breakeven point, occurs sometime during the third year. If we assume that the cash
flows occur regularly over the course of the year, the Payback Period can be computed using the
following equation:

Thus, the Payback Period for project A can be computed as follows:

Payback Period
Payback Period = 2 + (100)/(200) = 2.5 years

Thus, the project will recoup its initial investment in 2.5 years.

As a decision rule, the Payback Period suffers from several flaws. For instance, it ignores
the Time Value of Money, does not consider all of the project's cash flows, and the accept/reject
criterion is arbitrary.

Example Problems
Find the Payback Period for the project with the
following cash flows.
Year Cash Flow

0 $ -1000

1 $ 500

2 $ 400

3 $ 300

4 $ 200

5 $ 100

Payback: years
Net Present Value

The Net Present Value (NPV) of a Capital Budgeting project indicates the expected
impact of the project on the value of the firm. Projects with a positive NPV are
expected to increase the value of the firm. Thus, the NPV decision rule specifies that
all independentprojects with a positive NPV should be accepted. When choosing
among mutually exclusive projects, the project with the largest (positive) NPV should
be selected.

The NPV is calculated as the present value of the project's cash inflows minus the
present value of the project's cash outflows. This relationship is expressed by the
following formula:

where

 CFt = the cash flow at time t and

 r = the cost of capital.

The example below illustrates the calculation of Net Present Value. Consider Capital
Budgeting projects A and B which yield the following cash flows over their five year
lives. The cost of capital for the project is 10%.

Project A Project B
Cash Cash
Year
Flow Flow
0 $-1000 $-1000
1 500 100
2 400 200
3 200 200
4 200 400
5 100 700
Net Present Value
 Project A:

Project B:

Thus, if Projects A and B are independent projects then both projects should be
accepted. On the other hand, if they are mutually exclusive projects then Project A
should be chosen since it has the larger NPV.

Example Problems
Find the NPV for the following Capital Budgeting project.
Year Cash Flow

0 $ -1000

1 $ 500

2 $ 400

3 $ 300

4 $ 200

5 $ 100

Cost of Capital: 10 %

NPV: $

Internal Rate of Return

The Internal Rate of Return (IRR) of a Capital Budgeting project is the discount rate
at which the Net Present Value (NPV) of a project equals zero. The IRR decision rule
specifies that all independent projects with an IRR greater than the cost of capital
should be accepted. When choosing among mutually exclusive projects, the project
with the highest IRR should be selected (as long as the IRR is greater than the cost of
capital).

where

 CFt = the cash flow at time t and

The determination of the IRR for a project, generally, involves trial and error or a
numerical technique. Fortunately, financial calculators greatly simplify this process.

The example below illustrates the determination of IRR. Consider Capital Budgeting
projects A and B which yield the following cash flows over their five year lives. The
cost of capital for both projects is 10%.

Project A Project B
Cash Cash
Year
Flow Flow
0 $-1000 $-1000
1 500 100
2 400 200
3 200 200
4 200 400
5 100 700
Internal Rate of Return
Project A:

Project B:
Thus, if Projects A snd B are independent projects then both projects should be
accepted since their IRRs are greater than the cost of capital. On the other hand, if
they are mutually exclusive projects then Project A should be chosen since it has the
higher IRR.

Example Problems
Find the IRR for the following Capital Budgeting project.
Year Cash Flow

0 $ -1000

1 $ 500

2 $ 400

3 $ 300

4 $ 200

5 $ 100

IRR: %