5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 1/11

CFA TUTORTIPS, TRICKS, AND TUTORING

Search search

HOME » CFA LEVEL I » CAPITAL BUDGETING RULES: NPV, IRR, PAYBACK, DISCOUNTED PAYBACK, AAR

Capital Budgeting Rules: NPV, IRR,Payback, Discounted Payback, AAR

LEVEL I, II AND III JUNE 2014

DAILY CFA TRIVIA

FOLLOW BLOG VIA EMAIL

Enter your email address to follow

this blog and receive notifications

of new posts by email.

The material in this blog post is useful to the candidates preparing for: Level I of CFA Exams.

Today, we talk about an important topic that appears in corporate finance of level I which is the criteria used for

capital budgeting. That is, we talk about techniques used in deciding whether to accept new projects or not: NPV,

IRR, Payback, Discounted Payback, AAR.

Categories of Plans

1. Replacement Projects: decisions to replace old equipment – those are among the easier of capital budgeting

techniques. It is important to decide whether to replace the equipment when it wears out or to invest in

repairing the machine.

2. Expansion Projects: These are decisions whether to increase the size of business or not – they are more

uncertain than replacement projects.

3. New products and services: These are decisions whether to introduce new products and services or not – they

are more uncertain than both replacement and expansion projects.

4. Safety and environmental projects: These are the projects required by governmental agencies and insurance

companies – these projects might not generate revenue and are not for profits; however, sometimes it is

important to analyze the cash flows because the costs might be very high that they require analysis.

Basic Principles of Capital Budgeting

Capital budgeting usually uses the following assumptions:

1. Decisions are based on cash flows not income

2. Timing of cash flows is important

3. Cash flows are based on opportunity cost: cash flows that occur with an investment compared to what they

would have been without the investment

4. Cash flows are analyzed on after-tax basis:

5. Financing costs are ignored because they are incorporated in WACC – that is why counting them twice would

be considered double counting

Costs Concepts of Capital Budgeting

Some important capital budgeting concepts that managers find very useful are given below:

1. Sunk costs: costs that already incurred (i.e. paid for marketing research study) – Today costs should not be

Home About Author About CFATutor Navigation Posts Daily Trivia Solutions Excel Sheets Testimonials Contact Information

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 2/11

follow

CFA INSTITUTE

ARCHIVES

January 2014 (3)

November 2013 (10) (3)

October 2013 (11) (10) (3)

September

2013 (29) (11) (10) (3)

August

2013 (19) (29) (11) (10) (3)

July

2013 (28) (19) (29) (11) (10) (3)

June

2013 (1) (28) (19) (29) (11) (10)

(3)

CATEGORIES

Select Category

MOST RECENT POSTS

DECEMBER LEVEL I

RESULTS ARE

OUT!

CONGRATULATIONS TO 43% WHO

PASSED AND SHORT POST-

RESULTS SURVEY

The CFA institute has started

emailing December 2013 CFA

level I candidates with their exam

results. The institute has

announced the pass rate to be…

LEVEL III 2013

ESSAY EXAM

NOW AVAILABLE

Just like every year, the CFA

institute has posted level III essay

exam and its solutions (This is the

same exam I have took last…

OVERVIEW OF

DECEMBER

(QUARTER

PERFORMANCE):

CFA LEVEL I EXAM AND DAILY

CFA TRIVIA

As we mentioned in November,

December and January are

months in which no new readings

are going to be posted. Instead, we

are going to…

OVERVIEW OF

NOVEMBER

POSTS: TEXAS

PLUS, COST OF

CAPITAL, AND COMMON EXAM

MISTAKES – THE LAST POST FOR

THE YEAR

12,000 views – This is where we

affected by sunk costs

2. Opportunity costs: what a resource is worth for next-best use – Those costs should be considered (i.e. if you

use a warehouse, the current market value should be considered)

3. Incremental cash flow: the cash flow that is realized with the project – that is, the cash flow with a decision

minus the cash flow without the decision

4. Externality: the effect of an investment on other things apart from the investment. Those can be positive or

negative and should both be considered.

Cannibalization is an example of an externality where an investment takes customers and sales from another

part of the company – those should be considered in the analysis because they are incremental cash flows

(i.e. they wouldn’t occur unless for the project)

More about projects…

Some important comparisons in capital budgeting are:

Conventional versus nonconventional cash flows:

Conventional: Initial outflow followed by series of inflows (i.e. change of sign only occurs once). That is, you

can have – + + + + + +, – - – + + +, or – - – - – + and still be considered conventional cash flows because the

sign changes only once.

Nonconventional: Initial outflow followed by series of inflows and outflows (i.e. change of sign occurs more

than once). Examples of those include – + + + -, – - – + + -, or – + – + – +.

Independent versus mutually exclusive projects:

Independent projects: Cash flows are independent of each other. You can use both A and B; there isn’t

overlap between projects. Projects here are being evaluated that could potentially all be selected as long as

their projected cash flows will produce a positive NPV or generate an IRR greater than the firm’s hurdle rate.

Mutually exclusive projects: Projects that compete directly with each other (i.e. you own some

manufacturing equipment that must be replaced. Two different suppliers present a purchase and installation

plan for your consideration). Sometimes there are more than two projects and you select one from group.

Unlimited funds versus capital rationing

Unlimited funds: It assumes the company can raise funds for all profitable projects.

Capital rationing: It exists when a company has fixed amounts of funds to invest. If the company has more

project than funds, it must allocate the funds among the projects.

Project sequencing:

One last important concept here is project sequencing where many projects are evaluated through time; that

is, investing in one project gives the option to invest for other projects in the future. For example, you can

decide to open a mall this year and if the financial results are favorable after 5 years, you will build a hotel next

to the mall.

Investment Decision Criteria

We need to ask ourselves the following questions when evaluating decision criteria:

1. Does the decision rule adjust for the time value of money?

2. Does the decision rule adjust for risk?

3. Does the decision rule provide information on whether we are creating value for the firm?

Investment Decision Criteria: (1) Payback Period

Payback is the number of periods after which the initial investment is covered. The main question used in the

payback period is: how long does it take to get the initial cost back in a nominal sense?

Computation Method:

1. Estimate the cash flows

2. Subtract the future cash flows from the initial cost until the initial investment has been recovered

Decision Rule:

The decision rule is to accept if the payback period is less than some pre‐set limit.

Pros and Cons:

Pros Cons

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 3/11

stand today after five months of

CFA fun. I am beyond happy with all

the positive feedback and…

READ! LEVEL I

COMMON EXAM

MISTAKES –

PART II

The material in this blog post is

useful to the candidates preparing

for: Level I of CFA Exams. This is

an important post! Please spend…

1. Easy to understand.

2. Biased towards liquidity.

1. Ignores the time value of money.

2. Uses an arbitrary cutoff point.

3. Ignores cash flows beyond the cutoff date.

4. Biased against long-term projects such as R&D and new

projects.

Example:

Estimate the payback period for:

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

Solution:

To find the payback period, we need to find the cumulative cash flows first

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

CCF -10000 -5500 -1000 2000 4000

The payback period occurs when the cumulative cash flows changes from negative to positive. That is, it occurs

between years 2 and 3. Because we still have to recover 1000 after second year, the payback period is: 2 +

1000/3000 = 2.33 years.

Investment Decision Criteria: (2) Discounted Payback Period

Discounted payback is the number of periods for the cumulative discounted cash flows to recover the initial

investment. The main question used in the discounted payback period is: how long does it take to get the initial cost

back in a real sense?

Computation Method:

1. Estimate the cash flows

2. Discount these cash flow

3. Subtract the future discounted cash flows from the initial cost until the initial investment has been recovered

Decision Rule:

The decision rule is to accept all projects with the discounted payback period less than a pre‐set limit.

Pros and Cons:

Pros Cons

1. Considers time value of money.

2. Easy to grasp.

3. Biased towards liquidity.

1. If you discount values, then you might want to use NPV

because discounted payback won’t be easier to analyze.

2. It may reject projects with NPV > 0.

3. Uses an arbitrary cut-off point

4. It ignores cash flows after cut-off point.

5. Biased against long-term projects (new R&D projects).

Example:

Estimate the discounted payback period at 10% discount rate for:

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

Solution:

To find the discounted payback period, we need to find the cumulative discounted cash flows first:

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 4/11

DCF -10,000 4,090.91 3,719.01 2,253.94 1,366.03

CDCF -10,000 -5,909.09 -2,190.08 63.86 1,429.89

The discounted payback period occurs when the cumulative discounted cash flows changes from negative to

positive. That is, it occurs between years 2 and 3. Because we still have to recover 2,190.08 after second year, the

payback period is: 2 + 2190.08/2253.94 = 2.97 years.

Investment Decision Criteria: (3) Average Accounting Return

There are many different definitions for average accounting return. The most commonly used one is the average

net income to average book value. Note, however, that the average book value depends on how the asset is

depreciated.

Computation Method:

1. Estimate the net incomes

2. Estimate the book values

3. Estimate average net incomes

4. Estimate average book value (i.e. for straight-line depreciation, average book value is [historical value –

salvage value]/2)

Decision Rule:

We accept the project if the AAR is greater than a pre‐set rate.

Pros and Cons:

Pros Cons

1. Easy to calculate.

2. Needed information will usually be available.

1. It is not a true rate of return.

2. Time value of money is ignored.

3. Uses an arbitrary cut-off point.

4. Based on accounting net income and book values, not cash

flows and market values.

Example:

Assume a company invests 400,000 in project depreciated using straight-line method over 4 years with zero salvage

value. The following table shows the revenues and operating expenses. Calculate AAR using 40% tax rate:

Year 1 2 3 4

Revenue 200,000 250,000 300,000 320,000

Operating Expenses 90,000 100,000 120,000 90,000

Solution:

First, we find the net income where depreciation = (book value – salvage value)/ useful life. Deprecation is

400,000/4 = 100,000

Year 1 2 3 4

Revenue 200,000 250,000 300,000 320,000

Operating Expenses 90,000 100,000 120,000 90,000

Depreciation 100,000 100,000 100,000 100,000

Taxes = 0.4 (R-OE-D) 4,000 20,000 32,000 52,000

Net Income 6,000 30,000 48,000 78,000

Average net income = (6,000 + 30,000 + 48,000 + 78,000)/4= 40,500

Average book value = (400,000-0)/2= 200,000

Follow

Follow “CFA Tutor”

Get every new post delivered

to your Inbox.

Join 537 other followers

Enter your email address

sign me up

Pow ered by WordPress.com

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 5/11

Investment Decision Criteria: (4) Net Present Value (NPV)

The net present value (NPV) is the present value of future after-tax cash flows minus initial investment. It reflects the

difference between the market value of the project and its cost.

Computation Method:

1. Estimate the expected future cash flows.

2. Estimate the required return for projects of this risk level.

3. Find the present value of the cash flows and subtract the initial investment.

Where CF is the cash flow at time t, r is the discount rate for the investment and outlay is the investment cash flow

at time 0.

Decision Rule:

We accept the project if the NPV is greater than zero. A positive NPV means that the project is expected to add

value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth,

NPV is a direct measure of how well this project will meet our goal.

Pros and Cons:

Pros Cons

1. NPV gives importance to the time value of money.

2. In the calculation of NPV, both after cash flow and before

cash flow over the life span of the project are considered.

3. Profitability and risk of the projects are given high priority.

4. NPV helps in maximizing the firm’s value.

1. NPV is difficult to use.

2. NPV can’t give accurate decision if the amount of investment

of mutually exclusive projects is not equal.

3. It is difficult to calculate the appropriate discount rate.

4. NPV may not give correct decision when the projects are of

unequal life.

Example:

Estimate the NPV at 10% discount rate for:

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

Solution:

Investment Decision Criteria: (5) Profitability Index (PI)

The profitability index (PI) is very closely related to net present value (NPV). It is the present value of cash flows

dividend by the initial investments.

Computation Method:

1. Estimate the expected future cash flows.

2. Estimate the required return for projects of this risk level.

3. Find the present value of the cash flows and divide by the initial investment.

t

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 6/11

Where CF is the cash flow at time t, r is the discount rate for the investment and outlay is the investment cash flow

at time 0.

Decision Rule:

We accept the project if the PI is greater than one. PI greater than one means that the project is expected to add

value to the firm and will therefore increase the wealth of the owners.

Pros and Cons:

Pros Cons

1. PI helps in maximizing the firm’s value.

2. PI is useful in cases of capital rationing.

1. PI can’t give accurate decision if the amount of investment of

mutually exclusive projects is not equal.

2. It may not be easy to understand.

Example:

Estimate the PI at 10% discount rate for:

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

Solution:

Investment Decision Criteria: (6) Internal Rate of Return (IRR)

This is the most important alternative to NPV; it is often used in practice and is intuitively appealing. It is based

entirely on the estimated cash flows and is independent of interest rates found elsewhere.

Computation Method:

1. Estimate the expected future cash flows.

2. Estimate using trial and error the discount rate that makes NPV = 0

Written out in an equation form,

Decision Rule:

Accept the project if the IRR if it is greater than the required return.

Pros and Cons:

Pros Cons

1. Knowing a return is intuitively appealing – managers like to

hear returns.

2. It is a simple way to communicate the value of a project to

someone who does not know all the estimation details.

3. If the IRR is high enough, you may not need to estimate a

required return, which often is a difficult task.

1. Unrealistic assumption of reinvestment at IRR – unlike NPV

which assumes reinvestment at WACC which is a realistic

assumption.

2. IRR is not good for comparing two mutually exclusive

investments.

Example:

t

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 7/11

Estimate the IRR at 10% discount rate for:

Year 0 1 2 3 4

CF -10,000 4,500 4,500 3,000 2,000

Solution:

Using trial and error, if we start with discount rate of 17%

We find:

So we use a higher discount rate; let’s say we apply a discount rate of18%, we find:

Therefore, the discount rate that makes NPV = 0 is between 17% and 18%. Keeping trial and error, then IRR =

17.43%

IRR Alert

When using the IRR rule you have to be very careful from which standpoint you evaluate the investment: investor or

financier.

EXCEL FILE

This file can be used to solve problems related to capital budgeting techniques. In the first sheet, and after

entering conventional stream of cash flows for maximum of 15 periods, the file will solve for payback period,

discount payback period, NPV and IRR; it also shows the NPV profile. In the second sheet, you can find average

accounting return for a project given its estimated revenues, operating expenses and book value.

Which investment decision criteria to use?

Whenever in conflict, always use NPV. This is because NPV (1) is based on cash flows not accounting data, (2)

assumes reinvestment rate at WACC and (3) does not require arbitrary cut-off point. These all are improvements

over the other capital budgeting techniques. It is important to note that NPV and IRR will generally give us the same

decision except when:

1. Non‐conventional cash flows – cash flow signs change more than once

2. Mutually exclusive projects

Initial investments are substantially different

Timing of cash flows is substantially different

Before showing the conflict between NPV and IRR, we must first discuss the concept of NPV profile.

NPV Profile

NPV profile is a project’s NPV (y-axis) graphed as a function of discount rates (x-axis). For the data shown in the

previous example, the next graph shows the NPV profile:

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 8/11

Two important properties here are:

1. The point in which the profile goes through the vertical axis is the sum of undiscounted cash flows

2. The point in which the profile goes through the horizontal axis is the IRR

Conflicts between NPV and IRR: (1) Nonconventional Cash Flows

When the cash flows are nonconventional, there are two possible problems for IRR: ‘multiple IRR’ problem or ‘no

IRR’ problem. When the cash flows change signs more than once, there is either none or more than one IRR. When

you solve for IRR, you are solving for the root of an equation and when you cross the x‐axis more than once, there

will be more than one return that solves the equation. If you have more than one IRR, which one do you use to make

your decision? For example, assume a project with a discount rate of 15% has initial outlay of 800 and will return

875 in year 1, 1,210 in year 2, and will cost 1300 in year 3. Would you accept or reject the project using the IRR

method?

The best way to illustrate the problem in the previous example is to draw the NPV profile for the cash flows:

There is more than one IRR (one lower than discount rate and one higher than discount rate) and therefore, it is

hard to determine a decision rule based on IRR method. The other problem is the ‘no IRR’ problem which we

illustrate below using a graph:

Conflicts between NPV and IRR: (2) Mutually Exclusive Projects

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 9/11

When choosing between mutually exclusive projects, an overlap between NPV and IRR decisions could occur due

to:

1. Differences in cash flow scale – Initial investments are substantially different

2. Differences in cash flow time – Timing of cash flows is substantially different

Given the following two mutually exclusive projects with discount rate of 10%:

Year 0 1 2 3 4 5

Project A-20,000 7,000 7,000 7,000 7,000 7,000

Project B -5,000 2,000 2,000 2,000 2,000 2,000

The following graph shows the NPV profile for both projects A and B:

The point at which project A and project B interacts is called the cross-over rate. For mutually exclusive projects:

1. Below cross-over, there is different decision between IRR/NPV

2. Above cross-over same, the same decision happens between IRR/NPV

NPV and stock prices

What are the effects of new projects on share prices? It appears that NPV is the most directly related criteria to

value-addition. If a corporation invests in positive NPV projects, wealth must increase for shareholders.

Example:

Given:

Project’s Investment = $400 million

PV of after-tax CFs = $500 million

Outstanding shares = 100 million

Price = $40

What is the project’s effect on the stock price?

Solution:

NPV = 500 – 400 = 100

MV(before project) = 100 * 40 = 4000

MV(after project) = 4000 + 100 = 4100

Price after project = 4100/100 = $41

Or can be found as price after project = 40 + 100/100 = 41

Practitioners

Recent surveys show that:

1. European companies prefer payback method

2. Large companies prefer NPV/IRR

3. Private companies use payback more than public companies

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 10/11

← THE FINAL CHAPTER IN BLACK-SCHOLES WORLD: HOW TO

DERIVE THE GREEKS?

HOW TO USE TEXAS PLUS FOR CAPITAL BUDGETING RULES? NPV,

IRR, PAYBACK AND DISCOUNTED PAYBACK →

4. Companies managed by MBA holders prefer NPV/IRR

Tomorrow, I am going to show how to use the Texas Plus calculator to calculate the previous measures.

For Typos/Questions:

Name (required)

Email (required)

Exam level (required)

Level I

Please type down the typo or question (required)

submit »

Disclaimer:

Some of the material contained within the text of the blog posts is the copyrighted property of CFA Institute. The

following is the copyright disclosure for these materials: “Copyright, 2013, CFA Institute. Reproduced and

republished from 2013 Learning Outcome Statements, Level 1, 2, and 3 questions from CFA® Program Materials,

CFA Institute Standards of Professional Conduct, and CFA Institute’s Global Investment Performance Standards

with permission from CFA Institute. All Rights Reserved.”The material written in the blog posts are produced to the

best knowledge of the blogger. Best efforts are made to ensure the accuracy of the blog posts. However, this is

not a guarantee that these blog posts will result to ultimate exam success.

Blog posts do not represent the opinions or ideas of the CFA institute. These blog posts are not meant to replace

the original readings produced by the CFA Institute. Rather, blogs should be used in conjunction with original

readings set forth by CFA Institute.

These blog posts are based on original CFA curriculum provided by CFA instituted for the sole purpose to help

candidates prepare for the exam and are not produced for profit.

The blog posts may not be copied and reproduced elsewhere without written permission from the original author.

Share this:

TAGS: AAR, CASH FLOWS, CFA, CFA 1, CFA HELP, CFA INSTITUTE, CFA PREPARATION, IRR, MUTUALLY EXCLUSIVE, NPV, PAYBACK, PI,

PROJECT, RETURN

BY OMAR ALISMAIL IN CFA LEVEL I, CORPORATE FINANCE - LEVEL I ON JULY 27, 2013.

3

1

Related

How to use Texas Plus for Capital

Budgeting Rules? NPV, IRR,

Payback and Discounted Payback

Capital Budgeting: Cash Flow

Projections, Project Analysis and

Evaluation, and Income

Measures.

Overview of July Posts: Equity

Valuation Methods, Analysis of

Inventory and Long-Lived Assets,

Option Pricing, and Capital

Budgeting.

In "CFA Level I"

In "CFA Level II"

In "Monthly Archives"

5/26/2014 Capital Budgeting Rules: NPV, IRR, Payback, Discounted Payback, AAR « CFA Tutor

http://cfatutor.me/2013/07/27/capital-budgeting-rules-npv-irr-payback-discounted-payback-aar/ 11/11

Leave a Reply

Blog at WordPress.com. / Customized Academica Theme.

Enter your comment here...