Net Present Value and the Internal Rate of Return - CFA Level 1 _ Investopedia

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Chapter 1 - 5hapter 1 - 5 Chapter 6 - 10hapter 6 - 10 Chapter 11 - 15hapter 11 - 15 Chapter 16 - 17hapter 16 - 17

Quantitative Methods - Net Present Value and theuantitative Methods - Net Present Value and theInternal Rate of Returnnternal Rate of Return

This section applies the techniques and formulas first presented in the time value of money materialhis section applies the techniques and formulas first presented in the time value of money materialtoward real-world situations faced by financial analysts. Three topics are emphasized: (1) capitaloward real-world situations faced by financial analysts. Three topics are emphasized: (1) capital

budgeting decisions, (2) performance measurement and (3)udgeting decisions, (2) performance measurement and (3) U.S..S.Treasury-bill yields.Treasury-bill yields.

Net Preset Valueet Preset Value

NPV and IRR are two methods for makingPV and IRR are two methods for making capital-budgetapital-budgetdecisions, or choosing between alternatedecisions, or choosing between alternate

1. Ethics and Standards

2. Quantitative Methods

3. Microeconomics

4. Macroeconomics

5. Global Economic Analysis

2.6 Net Present Value and the Internal Rate of Return

2.7 Money Vs. Time-Weighted Return

2.8 Calculating Yield

2.9 Statistical Concepts And Market Returns

2.10 Basic Statistical Calculations

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projects and investments when the goal is to increase the value of the enterprise and maximizerojects and investments when the goal is to increase the value of the enterprise and maximize

shareholder wealth. Defining thehareholder wealth. Defining the NPV methodPV methodis simple: the present value of cash inflows minus theis simple: the present value of cash inflows minus the

present value of cash outflows, which arrives at a dollar amount that is the net benefit to theresent value of cash outflows, which arrives at a dollar amount that is the net benefit to the

organization.rganization.

To compute NPV and apply the NPV rule, the authors of the reference textbook define a five-stepo compute NPV and apply the NPV rule, the authors of the reference textbook define a five-step

process to be used in solving problems:rocess to be used in solving problems:

1..Identify all cash inflows and cash outflows.dentify all cash inflows and cash outflows.

2..Determine an appropriate discount rate (r).etermine an appropriate discount rate (r).

3..Use the discount rate to find the present value of all cash inflows and outflows.se the discount rate to find the present value of all cash inflows and outflows.

4..Add together all present values. (From the section on cash flow additivity, we know that this actiondd together all present values. (From the section on cash flow additivity, we know that this action

is appropriate since the cash flows have been indexed to t = 0.)s appropriate since the cash flows have been indexed to t = 0.)5..Make a decision on the project or investment using the NPV rule: Say yes to a project if the NPV isake a decision on the project or investment using the NPV rule: Say yes to a project if the NPV is

positive; say no if NPV is negative. As a tool for choosing among alternates, the NPV rule wouldositive; say no if NPV is negative. As a tool for choosing among alternates, the NPV rule would

prefer the investment with the higher positive NPV.refer the investment with the higher positive NPV.

Companies often use the weighted average cost of capital, or WACC, as the appropriate discount rateompanies often use the weighted average cost of capital, or WACC, as the appropriate discount rate

for capital projects. The WACC is a function of a firm's capital structure (common and preferred stockor capital projects. The WACC is a function of a firm's capital structure (common and preferred stock

and long-term debt) and the required rates of return for these securities. CFA exam problems willnd long-term debt) and the required rates of return for these securities. CFA exam problems will

either give the discount rate, or they may give a WACC.ither give the discount rate, or they may give a WACC.

Examplexample

To illustrate, assume we are asked to use the NPV approach to choose between two projects,o illustrate, assume we are asked to use the NPV approach to choose between two projects,

and our company's weighted average cost of capital (WACC) is 8%. Project A costs $7 million innd our company's weighted average cost of capital (WACC) is 8%. Project A costs $7 million in

upfront costs, and will generate $3 million in annual income starting three years from now andpfront costs, and will generate $3 million in annual income starting three years from now and

continuing for a five-year period (i.e. years 3 to 7). Project B costs $2.5 million upfront and $2ontinuing for a five-year period (i.e. years 3 to 7). Project B costs $2.5 million upfront and $2

million in each of the next three years (years 1 to 3). It generates no annual income but will beillion in each of the next three years (years 1 to 3). It generates no annual income but will be

sold six years from now for a sales price of $16 million.old six years from now for a sales price of $16 million.

For each project, find NPV = (PV inflows) - (PV outflows).or each project, find NPV = (PV inflows) - ( PV outflows).

Project Aroject A: The present value of the outflows is equal to the current cost of $7 million. TheThe present value of the outflows is equal to the current cost of $7 million. The

inflows can be viewed as an annuity with the first payment in three years, or an ordinarynflows can be viewed as an annuity with the first payment in three years, or an ordinary

annuity at t = 2 since ordinary annuities always start the first cash flow one period away.nnuity at t = 2 since ordinary annuities always start the first cash flow one period away.

Over-The-Counter - OTCver-The-Counter - OTC

Quarter - Q1, Q2, Q3, Q4uarter - Q1, Q2, Q3, Q4

Weighted Average Cost Of Capital - WACCeighted Average Cost Of Capital - WACC

Basis Point (BPS)asis Point (BPS)

Sharing Economyharing Economy

Unlevered Betanlevered Beta

HOT DEFINITIONSOT DEFINITIONS

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PV annuity factor for r = .08, N = 5: (1 - (1/(1 + r)V annuity factor for r = .08, N = 5: (1 - (1/(1 + r)N)/r = (1 - (1/(1.08)/r = (1 - (1/(1.08)5)/.08 = (1 - (1/(1.469328)/.08 =/.08 = (1 - (1/(1.469328)/.08 =

(1 - (1/(1.469328)/.08 = (0.319417)/.08 =1 - (1/(1.469328)/.08 = (0.319417)/.08 = 3.99271.99271

Multiplying by the annuity payment of $3 million, the value of the inflows at t = 2 is ($3ultiplying by the annuity payment of $3 million, the value of the inflows at t = 2 is ($3

million)*(3.99271) = $11.978 million.illion)*(3.99271) = $11.978 million.

Discounting back two periods, PV inflows = ($11.978)/(1.08)iscounting back two periods, PV inflows = ($11.978)/(1.08)2= $10.269 million.= $10.269 million.

NPV (Project A) = ($10.269 million) - ( $7 million) = $3.269 million.PV (Project A) = ($10.269 million) - ($7 million) = $3.269 million.

Project Broject B: The inflow is the present value of a lump sum, the sales price in six years discountedThe inflow is the present value of a lump sum, the sales price in six years discounted

to the present: $16 million/(1.08)o the present: $16 million/(1.08)6== $10.083 million10.083 million.

Cash outflow is the sum of the upfront cost and the discounted costs from years 1 to 3. We firstash outflow is the sum of the upfront cost and the discounted costs from years 1 to 3. We first

solve for the costs in years 1 to 3, which fit the definition of an annuity.olve for the costs in years 1 to 3, which fit the definition of an annuity.

PV annuity factor for r = .08, N = 3: (1 - (1/(1.08)V annuity factor for r = .08, N = 3: (1 - (1/(1.08)3)/.08 = (1 - (1/(1.259712)/.08 =/.08 = (1 - (1/(1.259712)/.08 =

(0.206168)/.08 = 2.5770970.206168)/.08 = 2.577097. PV of the annuity = ($2 million)*(2.577097) = $5.154 million.PV of the annuity = ($2 million)*(2.577097) = $5.154 million.

PV of outflows = ($2.5 million) + ($5.154 million) = $7.654 million.V of outflows = ($2.5 million) + ($5.154 million) = $7.654 million.

NPV of Project B = ($10.083 million) - ($7.654 million) = $2.429 million.PV of Project B = ($10.083 million) - ($7.654 million) = $2.429 million.

Applying the NPV rule, we choose Project A, which has the larger NPV: $3.269 million versus $2.429pplying the NPV rule, we choose Project A, which has the larger NPV: $3.269 million versus $2.429

million.illion.

Exam Tips and Tricksxam Tips and Tricks

Problems on the CFA exam are frequently set up so that it is tempting to pick a choice that seemsroblems on the CFA exam are frequently set up so that it is tempting to pick a choice that seems

intuitively better (i.e. by people who are guessing), but this is wrong by NPV rules. In the case wentuitively better (i.e. by people who are guessing), but this is wrong by NPV rules. In the case we

used, Project B had lower costs upfront ($2.5 million versus $7 million) with a payoff of $16sed, Project B had lower costs upfront ($2.5 million versus $7 million) with a payoff of $16million, which is more than the combined $15 million payoff of Project A. Don\'t rely on what feelsillion, which is more than the combined $15 million payoff of Project A. Don\'t rely on what feels

better; use the process to make the decision!etter; use the process to make the decision!

The Internal Rate of Returnhe Internal Rate of Return

The IRR, orThe IRR, or internal rate of returnnternal rate of return, is defined as the discount rate that makes NPV = 0. Like the NPVis defined as the discount rate that makes NPV = 0. Like the NPV

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process, it starts by identifying all cash inflows and outflows. However, instead of relying on externalrocess, it starts by identifying all cash inflows and outflows. However, instead of relying on external

data (i.e. a discount rate), the IRR is purely a function of the inflows and outflows of that project. Theata (i.e. a discount rate), the IRR is purely a function of the inflows and outflows of that project. The

IRR rule states that projects or investments are accepted when the project's IRR exceeds a hurdleRR rule states that projects or investments are accepted when the project's IRR exceeds a hurdle

rate. Depending on the application, the hurdle rate may be defined as the weighted average cost ofate. Depending on the application, the hurdle rate may be defined as the weighted average cost of

capital.apital.

Examplexample

Suppose that a project costs $10 million today, and will provide a $15 million payoff threeuppose that a project costs $10 million today, and will provide a $15 million payoff three

years from now, we use the FV of a single-sum formula and solve for r to compute the IRR.ears from now, we use the FV of a single-sum formula and solve for r to compute the IRR.

IRR = (FV/PV)RR = (FV/PV)1/N/N -1 = (15 million/10 million)1 = (15 million/10 million)1/3/3 - 1 = (1.5)1 = (1.5)1/31/3 - 1 = (1.1447) - 1 = 0.1447, or 14.47%1 = (1.1447) - 1 = 0.1447, or 14.47%

In this case, as long as our hurdle rate is less than 14.47%, we green light the project.n this case, as long as our hurdle rate is less than 14.47%, we green light the project.

NPV vs. IRRPV vs. IRR

Each of the two rules used for making capital-budgeting decisions has its strengths and weaknesses.ach of the two rules used for making capital-budgeting decisions has its strengths and weaknesses.

The NPV rule chooses a project in terms of net dollars or net financial impact on the company, so ithe NPV rule chooses a project in terms of net dollars or net financial impact on the company, so it

can be easier to use when allocating capital.an be easier to use when allocating capital.

However, it requires an assumed discount rate, and also assumes that this percentage rate will beowever, it requires an assumed discount rate, and also assumes that this percentage rate will be

stable over the life of the project, and that cash inflows can be reinvested at the same discount rate.table over the life of the project, and that cash inflows can be reinvested at the same discount rate.

In the real world, those assumptions can break down, particularly in periods when interest rates aren the real world, those assumptions can break down, particularly in periods when interest rates are

fluctuating. The appeal of the IRR rule is that a discount rate need not be assumed, as theluctuating. The appeal of the IRR rule is that a discount rate need not be assumed, as the

worthiness of the investment is purely a function of the internal inflows and outflows of thatorthiness of the investment is purely a function of the internal inflows and outflows of that

particular investment. However, IRR does not assess the financial impact on a firm; it only requiresarticular investment. However, IRR does not assess the financial impact on a firm; it only requires

meeting a minimum return rate.eeting a minimum return rate.

The NPV and IRR methods can rank two projects differently, depending on thesize of the investment.he NPV and IRR methods can rank two projects differently, depending on thesize of the investment.

Consider the case presented below, with an NPV of 6%:onsider the case presented below, with an NPV of 6%:

Projectroject Initial outflownitial outflow Payoff after oneayoff after one

yearear

IRRRR NPVPV

A $250,000250,000 $280,000280,000 12%2% +$14,151$14,151

B $50,00050,000 $60,00060,000 20%0% +66046604


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Next:ext Money Vs. Time-Weighted Returnoney Vs. Time-Weighted Return

By the NPV rule we choose Project A, and by the IRR rule we prefer B. How do we resolve the conflicty the NPV rule we choose Project A, and by the IRR rule we prefer B. How do we resolve the conflict

if we must choose one or the other? The convention is to use the NPV rule when the two methodsf we must choose one or the other? The convention is to use the NPV rule when the two methods

are inconsistent, as it better reflects our primary goal: to grow the financial wealth of the company.re inconsistent, as it better reflects our primary goal: to grow the financial wealth of the company.

Consequences of the IRR Methodonsequences of the IRR Method

In the previous section we demonstrated how smaller projects can have higher IRRs but will haven the previous section we demonstrated how smaller projects can have higher IRRs but will have

less of a financial impact. Timing of cash flows also affects the IRR method. Consider the exampleess of a financial impact. Timing of cash flows also affects the IRR method. Consider the example

below, on which initial investments are identical. Project A has a smaller payout and less of aelow, on which initial investments are identical. Project A has a smaller payout and less of a

financial impact (lower NPV), but since it is received sooner, it has a higher IRR. Wheninancial impact (lower NPV), but since it is received sooner, it has a higher IRR. When

inconsistencies arise, NPV is the preferred method. Assessing the financial impact is a morenconsistencies arise, NPV is the preferred method. Assessing the financial impact is a moremeaningful indicator for a capital-budgeting decision.eaningful indicator for a capital-budgeting decision.

Projectroject Investmenvestme

ntt

Income in future periodsncome in future periods IRRRR NPVPV

t1 t2 t3 t4 t5

A $100k100k $125k125k $00 $00 $00 $00 25.0%5.0% $17,92517,925

B $100k100k $00 $00 $00 $00 $200k200k 14.9%4.9% $49,45249,452

INVESTING BASICSNVESTING BASICS

Capital Budgeting: Capital Budgeting Decision Toolsapital Budgeting: Capital Budgeting Decision ToolsOnce projects have been identified, management then begins the financialnce projects have been identified, management then begins the financial

process of determining whether or not the project should be pursued. The threerocess of determining whether or not the project should be pursued. The three

common capital budgeting decision tools ...ommon capital budgeting decision tools ...

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PERSONAL FINANCEERSONAL FINANCE

An Introduction To Capital Budgetingn Introduction To Capital BudgetingWe look at three widely used valuation methods and figure out how companiese look at three widely used valuation methods and figure out how companies

justify spending.ustify spending.

FUNDAMENTAL ANALYSISUNDAMENTAL ANALYSIS

Calculating the Internal Rate of Return Using Excelalculating the Internal Rate of Return Using ExcelThe internal rate of return on investments is explained and illustrated in differenthe internal rate of return on investments is explained and illustrated in different

investment scenarios.nvestment scenarios.


Return on Investment (ROI) Vs. Internal Rate of Return (IRR)eturn on Investment (ROI) Vs. Internal Rate of Return (IRR)Read about the similarities and differences between an investment's internal rateead about the similarities and differences between an investment's internal rate

of return (IRR) and its return on investment (ROI).f return (IRR) and its return on investment (ROI).


Internal Rate Of Return: An Inside Looknternal Rate Of Return: An Inside LookUse this method to choose which project or investment is right for you.se this method to choose which project or investment is right for you.

TERMERM

What is the Equivalent Annual Annuity Approach?hat is the Equivalent Annual Annuity Approach?Companies use the equivalent annual annuity approach to compare the returnsompanies use the equivalent annual annuity approach to compare the returns

of two projects that have different lifespans.f two projects that have different lifespans.

INSURANCENSURANCE

How to Compare Permanent Life Insurance Policiesow to Compare Permanent Life Insurance Policies

How you can use the internal rate of return to compare and purchase aow you can use the internal rate of return to compare and purchase apermanent life insurance policy.ermanent life insurance policy.

INVESTINGNVESTING

Understanding The Discounted Payback Periodnderstanding The Discounted Payback Period
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Its similar to a simple payback, but a discounted payback period accounts forts similar to a simple payback, but a discounted payback period accounts for

moneys time value. Its a more precise estimate of when investors will recoveroneys time value. Its a more precise estimate of when investors will recover

their total investment.heir total investment.

FOREX EDUCATIONOREX EDUCATION

Time Value Of Money: Determining Your Future Worthime Value Of Money: Determining Your Future WorthDetermining monthly contributions to college funds, retirement plans or savingsetermining monthly contributions to college funds, retirement plans or savings

is easy with this calculation.s easy with this calculation.


Calculating the Present Value of an Annuityalculating the Present Value of an AnnuityThe present value of an annuity is the current, lump sum value of periodic futurehe present value of an annuity is the current, lump sum value of periodic future

payments as calculated using a specific rate.ayments as calculated using a specific rate.

Net Present Value - NPVet Present Value - NPVNet Present Value (NPV) is the differenceet Present Value (NPV) is the difference

between the present ...etween the present ...

Internal Rate Of Return - IRRnternal Rate Of Return - IRRA metric used in capital budgeting measuringmetric used in capital budgeting measuring

the profitability ...he profitability ...

Net Present Value Ruleet Present Value RuleA rule stating that an investment should berule stating that an investment should be

accepted if its net ...ccepted if its net ...

IRRRRThe currency abbreviation or currency symbolhe currency abbreviation or currency symbol

for the Iranian ...or the Iranian ...

Modified Internal Rate Of Return ...odified Internal Rate Of Return ...While the internal rate of return (IRR) assumeshile the internal rate of return (IRR) assumes

the cash flows ...he cash flows ...

Capital Budgetingapital BudgetingThe process in which a business determineshe process in which a business determines

whether projects such ...hether projects such ...

RELATED TERMSELATED TERMS

Q:: How much debt is too much when calculating capital budgeting?ow much debt is too much when calculating capital budgeting?

earn how companies determine how much debt is acceptable when funding a new project by using the net

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Learn how companies determine how much debt is acceptable when funding a new project by using the netearn how companies determine how much debt is acceptable when funding a new project by using the net

present value to estimate ...resent value to estimate ... Read Answer >>ead Answer >>

Q:: How do you use discounted cash flow to calculate a capital budget?ow do you use discounted cash flow to calculate a capital budget?

Learn how discounted cash flows are used in creating capital budgets as a part of the net present value andearn how discounted cash flows are used in creating capital budgets as a part of the net present value and

internal rate ...nternal rate ... Read Answer >>ead Answer >>

Q:: What is the formula for calculating net present value (NPV) in Excel?hat is the formula for calculating net present value (NPV) in Excel?

Understand how net present value is used to estimate the anticipated profitability of projects or investments andnderstand how net present value is used to estimate the anticipated profitability of projects or investments and

how to ...ow to ... Read Answer >>ead Answer >>

Q:: Do you discount working capital in net present value (NPV)?o you discount working capital in net present value (NPV)?

Learn why changes in net working capital (NPV) should be included in net present value calculations for analyzingearn why changes in net working capital (NPV) should be included in net present value calculations for analyzing

a project's ...project's ... Read Answer >>ead Answer >>

Q:: What are the disadvantages of using net present value as an investment criterion?hat are the disadvantages of using net present value as an investment criterion?

While net present value (NPV) calculations are useful when you are valuing investment opportunities, the processhile net present value (NPV) calculations are useful when you are valuing investment opportunities, the process

is by no ...s by no ... Read Answer >>ead Answer >>

Q:: What's the difference between net present value and internal rate of return? How ...hat's the difference between net present value and internal rate of return? How ...

Both of these measurements are primarily used in capital budgeting, the process by which companies determineoth of these measurements are primarily used in capital budgeting, the process by which companies determine

whether a new ...hether a new ... Read Answer >>ead Answer >>
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Net Present Value and the Internal Rate of Return - CFA Level 1 _ Investopedia

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