Capital budgeting rules npv, irr, payback, discounted payback, aar « cfa tutor

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HOME » CFA LEVEL I » CAPITAL BUDGETING RULES: NPV, IRR, PAYBACK, DISCOUNTED PAYBACK, AAR
Capital Budgeting Rules: NPV, IRR,
Payback, Discounted Payback, AAR
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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
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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

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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

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
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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:
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

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:
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

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:

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

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

← 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.
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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.
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