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FINC3131Business Finance

Chapter 11: Basics of Capital Budgeting

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Learning objectives1. Explain the purpose and importance of capital

budgeting.2. Determine whether a new project should be

accepted using the: i. net present value (NPV)ii. internal rate of return (IRR)iii. payback period (PBP)iv. discounted payback period

3. Identify the two conditions under which IRR doesn’t work.

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Capital Budgeting Decision 1 Capital budgeting: the process of analyzing

projects and decide which ones to invest in.

Project: any investment that involves cash outflows (costs) made in order to receive cash inflows (benefits). E.g.,: new product, new plant & machinery, cost saving technologies, new accounting software.

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Capital Budgeting Decision 2 Let’s be more specific about the decision to be

made: Given the cash inflows and outflows of a

project, should the firm accept or reject the project.

1. If the firm accepts, it will invest in the project. If the firm rejects, it will not invest in the project.

2. This type of decision is known as a capital budgeting decision.

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Capital Budgeting Decision 3

1. If the firm makes a wrong capital budgeting decision, e.g., invest in the wrong project, then scarce resources are wasted. It also means that firm value and shareholder wealth will be reduced.

2. Thus, to maximize shareholder wealth, it’s vital that firms make correct capital budgeting decisions.

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Capital budgeting rules

We will learn to apply 4 capital budgeting rules:

1. Net present value (NPV)

2. Internal rate of return (IRR)

3. Payback period (PBP)

4. Discounted payback period

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Net present value (NPV) rule

Accept project if

Net present value > 0

What is Net present value?

Net present value

= Benefits minus Costs

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How do we measure benefits & costs?

Benefits, B

= Present value of all cash inflows from the project

=

N

ttt

r

CIF

0 1

Cash inflow at the end of period t

Discount rate for the project’s cash flows

Number of years in the project’s life

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How do we measure benefits & costs?

Costs, C

= Present value of all cash outflows from the project

=

N

ttt

r

COF

0 1Number of years in the project’s life

Cash outflow at the end of period t

Discount rate for the project’s cash flows

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How do we measure benefits & costs?

NPV = B – C =

N

ttt

N

ttt

r

COF

r

CIF

00 11

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Internal rate of return (IRR) rule 1

IRR: the discount rate that will make the PV of cash inflows equal to the PV of cash outflows.

• In other words, IRR is the discount rate such that the NPV is 0.

0

11 00

N

tt

tN

tt

t

IRR

COF

IRR

CIF

PV of cash inflows, discounted at IRR

PV of cash outflows, discounted at IRR

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Internal rate of return (IRR) rule 2

Accept project if

IRR > cost of capital

Intuitively, think of the IRR as the return from the project.

Then the project should be accepted if the return is greater than the required rate of return / cost of capital.

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NPV and IRR

1. NPV and IRR are the two most important capital budgeting techniques. The relationship between the two can be illustrated by the NPV profile.

2. NPV profile is a graph showing the NPV values for different discount rates.

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NPV and IRR

6050403020100-1000

0

1000

2000

3000

4000

5000

Discount Rate (%)

Net

Pre

sent

Va

lue (

$)

IRR

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Apply the NPV and IRR A firm is considering investment in a

project that costs $1,200 and yields cash flows of $500 in the first year, $600 in the second year and $700 in the third year. Compute the NPV and IRR of this project. The appropriate discount rate for this project is 10 percent.

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Computing NPV using BA II Plus1. Press CF, press -1200 and then press ENTER for CF0.

2. Next press “” and enter 500 for C01.

3. Press “” and enter 1 for F01.

4. Similarly enter C02 = 600, F02 = 1, C03 = 700, and F03 = 1. Make sure that all the cash flows later than C03 are zero.

5. Press NPV. Enter the discount rate of 10 percent by pressing 10 and then ENTER.

6. The display will show that I = 10. Next press the “” and press CPT. The calculator will display the NPV of 276.33. Decision: Accept project

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Computing IRR using BA II Plus

1. In order to compute the IRR, follow the same steps as above for entering the cash flows.

2. Then instead of pressing NPV, press the IRR button and then press CPT.

3. The calculator will display the IRR as 21.92 percent.

4. Decision: Accept project

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Normal cash flows 1. In the previous problem, there is ONE cash

outflow at the beginning. After that, we have all cash inflows.

2. A project with such a cash flow pattern is a project with normal cash flows.

3. So what? For projects with NORMAL CASH FLOWS, the NPV, IRR rules will give the SAME decision. This is exactly what happened in the problem we solved.

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Apply NPV, IRR Assume a discount rate of 11%. Compute the

NPV, IRR and decide whether the project should be accepted or rejected.

Project C0 C1 C2 C3 C4 C5

T=0 T=1 T=2 T=3 T=4 T=5

A -1000 400 400 400 500 500

Verify that NPV = 603.58, IRR = 31.79%,

Since NPV>0, IRR>11%, accept the project

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Another questionA five-year project, if taken, will require an initial investment of

$120,000. The expected end-of-year cash inflows are as follows:

If the appropriate cost of capital for this project is 11%, which of the following is a correct decision?

a. Reject the project because NPV = -$30,507, which is less than 0.b. Reject the project because IRR is 10.04%, which is less than the

cost of capital, 11%.c. Both a and b are correct.d. Accept the project because IRR is positive.e. None of the above is correct.

C1 C2 C3 C4 C5

30,000 42,000 42,000 28,000 12,000

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Conceptual problem: NPV and IRR Consider a project with an initial outflow at time 0 and

positive cash flows in all subsequent years. As the discount rate is decreased the _____________.

A. IRR remains constant while the NPV increases.B. IRR decreases while the NPV remains constant.C. IRR increases while the NPV remains constant.D. IRR remains constant while the NPV decreases.E. IRR decreases while the NPV decreases.

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Computational problem: NPV and IRR You are attempting to reconstruct a project analysis of

a co-worker who was fired. You have found the following information:

1. The IRR is 12%.2. The project life is 4 years.3. The initial cost is $20,000.4. In years 1, 3 and 4 you will receive cash inflows of

$6,000.5. You know there will be a cash flow in year 2, but the

amount is not in the file.6. The appropriate discount rate is 10%.7. What is the NPV of the project?

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Which of the following statements is incorrect?

A. Assuming a project has normal cash flows (that is, the initial cash flow is negative, and all other cash flows are positive), the NPV will be positive if the IRR is less than the cost of capital

B. Assuming a project has normal cash flows, (that is, the initial cash flow is negative, and all other cash flows are positive), any independent project acceptable by the NPV method will also be acceptable by the IRR method

C. If IRR = the cost of capital, then NPV = 0D. NPV can be negative, even if the IRR is positiveE. If the NPV of a normal project is greater than 0, the

company should accept the project

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Project with identical cash inflows Compute the NPV, IRR of the following project

that a firm is considering. The firm’s cost of capital for this project is 12 percent. The project will require an initial investment of $6 million and it will generate cash flows $750,000 per year for ever.

Verify that NPV=$250,000, IRR=12.5%

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Warnings about IRR criterion The IRR criterion cannot give the correct

accept/reject decision under the following conditions:

1. Cash inflows (benefits) occur BEFORE cash outflows (costs).

2. Cash flows change signs more than once. E.g., cash outflow at t=0, cash inflow at t=1, cash outflow at t=2.

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Condition 1: Cash inflows occur before cash outflows

1. Thus far, we have considered projects with normal cash flows, (i.e., a single cash outflow in year 0 followed by cash inflows in all future years).

2. With normal cash flows, IRR works fine. 3. However, if you have cash inflow first, followed

by cash outflow, then IRR will be negative. 4. Result: You cannot use IRR to make the

accept/reject decision. 5. Use NPV to get the correct decision.

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Consider the project that yields a cash flow of $120 at t = 0 and requires a cost of $100 to be paid at t = 1. The discount rate is 10%.

1. NPV = 120 – (100/1.1) = 29.09

2. IRR = -16.67

3. For this type of project, use NPV to get the correct accept/reject decision.

4. IRR is NOT appropriate for this type of project!

Condition 1: Cash inflows occur before cash outflows

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Condition 2: Cash flows change signs more than once

Consider the following project cash flows: t = 0, -$400, t = 1, $2,500, t = 2, -$3,000. Suppose that the company’s cost of capital is 70 percent.

NPV = $32.53. The project is, acceptable. There are two IRR’s for this project: 61.98%, 363%.

Look at the NPV profile (next slide). When there are multiple IRRs, the IRR method

loses meaning and is NOT appropriate. However, the NPV method still gives the correct

accept/reject decision.

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Condition 2: Cash flows change signs more than once

Figure 11.3: Project NPV profile. Cash flows at t = 0, 1, 2 are -$400, $2,500, -$3,000.

6005004003002001000-1000

-800

-600

-400

-200

0

200

Discount rate

NP

V

IRR?

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Payback Period (PBP) Criterion Payback period: the number of periods it takes

the cash inflows from a project to recover the original cost of the project.

Decision rule: 1. Firm specifies an arbitrary number of years as

the critical number (x).2. If payback period < x, then accept the project.

Otherwise, reject the project. Note: unless otherwise stated, assume that

cash flows are received evenly throughout the year.

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Applying the PBP criterion

1. Compute the payback periods for the following two projects.

Project C0 C1 C2 C3 C4 C5

A -9000 2000 3000 4000 5000 6000

B -11000 2000 3000 4000 5000 6000

Verify that PBP for A = 3 years, PBP for B = 3.4 years (assume cash flows occur evenly throughout the year)

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Which of the following statements is most correct?

A. If the NPV of a project is positive then the payback rule will always accept the project.

B. If the NPV of a normal cash flow project is negative then the IRR will always be greater than cost of capital.

C. For projects in which the cash flows switch direction (i.e. from positive to negative or vice-versa) more than once, the NPV criteria may give multiple solutions.

D. For independent projects with normal cash flows, the NPV, IRR rules are equally valid and give the same accept/reject decision.

E. If the NPV of a project is greater than zero, then the IRR will always be less than the required rate of return.

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NPV + PBP Problem Bantam Industries is considering a project which has

the following cash flows:Year Cash flow

0 ? 1 $2,000 2 $3,000 3 $3,000 4 $1,500

The project has a payback period of 2 years. The firm's cost of capital is 12%.

What is the project's net present value?Verify that NPV = 2,265.91

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Problems with the payback period criterion

1. It is an arbitrary decision rule since the critical number is arbitrarily chosen.

2. It ignores the cash flows that occur after the critical number.

3. It ignores the time value of money. Future cash inflows are directly compared with the project’s cost without discounting those future cash flows.

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PBP does not consider cash flows after the critical number

Project C0 C1 C2 C3

A -1000 500 510 10

B -1000 0 0 99,000,000

A firm uses two years as the critical number for the payback period.

This firm is faced with two projects whose cash flows are:

According to the payback rule, project A will be accepted and B will be rejected.

But, if you consider all cash flows, including those after 2 years, then project B is more attractive.

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Discounted payback back period criterion

1. Address the fact that PBP ignores the time value of money.

2. To apply the discounted PBP criterion, use discounted value of cash flows. Everything else is the same as the original PBP criterion.

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Example of discounted payback period criterion

Example: Suppose that the discount rate is 10 percent. Project A has the following cash flows and discounted cash flows. Find A’s discounted PBP.

Project A C0 C1 C2 C3

Cash flow -9000 3000 6000 9000

Discounted cash flow 2727 4959 6762

Verify that discounted payback period = 2.194 years

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Why PBP exists

1. It is used quite widely by corporations.

2. It is used primarily as a secondary project selection criterion.

3. For example, a firm may require a project to have positive NPV first and also satisfy some payback criterion.

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SummaryTechniques Accept project if Reject project if

NPV NPV > 0 NPV < 0

IRR IRR > cost of capital, r IRR < cost of capital, r

PBP PBP < arbitrary no. of years

PBP > arbitrary no. of years

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Assignment

Problems: 1, 2, 4, 5, 6, 7, 10, 11, 12,

MIRR is NOT required in this course.