MBA/MFM 253 Measuring Return on

Investment

The Big Picture

The last 2 chapters discussed measuring the cost of capital – the average cost of financing for the entire firmThis chapter discusses adjusting the cost of capital for an individual project.

The weighted average represents an average across all sources of financing – some projects are more risky some are less riskyEach project should be evaluated at their individual cost of capital

The Big Picture – part II

A general valuation model for any asset:The value of an asset (either real or financial) can be found by based upon the PV of the future cash flows generated from owning the asset.The main questions to be addressed are then:

What future cash flows are generated by the assetWhat is the appropriate discount rate (interest rate) based on the riskiness of the cash flows.

Simple 2 project example

Firm value consists of the sum of the individual parts of the firm. Assume the firm has two assets, A and B, each generates a stream of future cash flows that have the same riskiness and there are no shared costs.The PV of the firm is simply the PV of the cash flows from each set of assets or

Firm Value = PV (A) + PV (B) = sum of separate asset values

Three Stages of a Project

Acquisition StageInitial outlay of cash

Operating StageSales Revenue, Operating Expenses, Taxes etc

Disposition StageSales of fixed assets, Tax consequences

What is a Project?

Major Strategic DecisionsAcquisitions of Other firmsNew Ventures within existing marketsChanges in the way current businesses or ventures are approachedSpending money on components necessary for business (investment in information systems for example)

The Project Continuum

Prerequisite Complementary Independent Mutually Exclusive

Project Risk

Should the WACC be used for all projects in the firm?No - it is a composite of all projects (an average). That means some projects are more risky than the average and some less risky.Each project should also be looked at on an individual basis.

Divisional WACC

The WACC represents the composite cost of capital across all projects. Before we developed a market-wide relationship between risk and return with the security market line. You can use a similar concept idea to relate risk to a projects cost of capital. This is done with a graph of risk vs. return where return is measured by the cost of capital.

Divisional Cost of Capital

Firm H is High Risk with a WACC = 12%Firm L is low Risk with a WACC = 8%

Both Firms are considering two projects with equal risk equal to the average risk of Firm H and Firm L.Project A has an expected return of 10.5%, Project B has an expected return of 9.5%

Which project(s) should each firm accept?

RiskL RiskA RiskH

8.0

10.0

12.0

10.5

9.5 B

A

AcceptanceRegion

Rejection Region

Risk

Return

Determining the Project Cost of Equity

1. Single Business – Project risk is similar across all businesses – use the overall cost of equity and cost of debt

2. Multiple Businesses with different risk profiles – estimate cost of equity using project beta – bottom up beta, accounting beta, or regression on cash flows

3. Projects with different risk profiles – ideally estimate cost of equity for each or use divisional costs of equity if they are fairly close

Project Cost of Debt

Generally the cost of debt reflects default risk – however the possibility of default on a given project is difficult to estimate. Therefore debt financing is generally thought of as a firm value instead of a project value. Whether or not to attempt to measure the cost of debt individually depends upon the size of the project and it impact on the overall default risk of the firm.

Cost of Debt - Summary

Project Characteristi

cs

Cost of Debt Debt Ratio

Small and CF similar to firm

Firm’s Cost of Debt

Firm’s Cost of Equity

Project is large CF different from firm

Cost of debt of comparable firms

Average debt ratio of comparable firms

Stand Alone Project

Cost of debt for project

Debt Ratio for Project

Project cost of capital

The combination of different cost of financing into a cost of capital requires a weighting for each of the types of financing. When the project is large, the financing mix may differ from that of the overall firm. In extreme cases the project may be large enough to issue its own debt in that case your weights for the financing options will vary from the firm weights.

Measuring Returns

Accounting Earnings vs. Cash FlowsAccounting earnings are based on accrual accountingCash flow measures the actual cash generated in a given time period.

Accrual Based

Revenues are realized when the sale is made, and expenses when the purchase or expense occurs, not necessarily when the payment is made.This results in income (earnings) that does not represent cash flow.

Why Cash Flows?

Cash represents the ability of the firm to operate (you can’t spend earnings).

Accounting earnings are often manipulated to impress shareholders.

Cash Flow vs. Accounting Earnings

GAAP is based on accrual accountingRevenues are realized at the time of the sale, not when cash is received (Expenses are realized at the time acquired, not when paid forOperating ExpendituresProduce benefits only in the current period

Capital Expendituresproduce benefits over multiple periods

Non - Cash Charges (depreciation etc)Reduce accounting income, but cash exists

Free Cash Flows

FCFE (Cash Flow to Equity) = Net Income + Depreciation& Amortization -Changes in Non-Cash Net Working Capital - Capital Expenditures - Principal

Repayments + New Debt IssuesFCFF (Cash Flow to Firm) = EBIT(1-t) + Depreciation& Amortization - Changes in Non-Cash Net Working Capital - Capital Expenditures

Incremental Cash Flow

Cash flow changes that result from a particular projectRelevant Cash Outflows Increase Cash outflow Elimination of cash inflow Investment in Assets

Relevant Cash Inflow Increase in cash inflow Elimination of cash outflow Liquidation of assets

Applying the NPV Rule

Discount only Incremental Cash FlowsIncremental cash flows represent changes that are a result of the project under consideration

Be careful about InflationDo not double count inflation. If you price estimates and future cash flows include inflation, then the correct discount rate should be a REAL rate not the nominal rate.

Steps in estimating Cash Flow

Estimate the Income StatementEstimate the Balance SheetCombine the income statement and balance sheet into a cash flow statementMake a decision

Steps in the planning process

1. Pro Forma Financial Statements and NPV2. Determine the funds needed to support

the plan3. Forecast the funds available4. Establish controls5. Plan for other contingencies6. Establish a performance based

compensation plan

Capital Budgeting Decision Rules

Balance between subjective assessment and consistency across projectsReinforces the main goal of corporate finance – Maximize the value of the firmBe applicable to a wide range of possible investments.

Capital Budgeting Decision Rules

Accounting Returns

Return on Capital – the return earned by the firm on its total investment

Accept the project if ROC > Cost of CapitalMore difficult for multiyear projects

Invested) Capital of ValueBook (Average

EBITROC

Capital Budgeting Decision Rules

Accounting Returns

Return on Equity on the project

If ROE > Cost of Equity Accept the project

Projectin InvestmentEquity of ValueBook Average

IncomeNet ROEProject

Problems with Accounting Returns

Accounting choices cause the balance between subjective judgment and consistency to be called into question. Based on Earnings (Net Income) – so acceptance of a project may or may not add value to the firm (PV of expected future cash flows)Works best for projects with large upfront costs (large capital invested)

Accounting returns for entire firm

Both ROE and ROC can provide good intuition about the overall quality of projects accepted by the firm. Both can be calculated for the aggregate firm using book value of equity and book value of capital.

Economic Value Added

A measure of the surplus value created by a firm’s projects.

EVA and ROE

capital)equity ofcost -OEcapital)(R(equity

capitalequity ofcost CapitalEquity

IncomeNet capital)(equity

captial)equity ofcost (capital)(equity IncomeNet

capital ofcost

percentage

taxAfter

captial operating

supplied-investor

Total

-T)EBIT(1

Charge Capital - NOPAT EVA

Capital Budgeting Decision Rules

Payback Period and Discounted Payback

Net Present Value

Internal Rate of Return & Modified IRR

Profitability Index and Modified Profitability index

Payback Period

Intuition: Measures length of time it takes for the firm to payback the original investment.Simple example:

Cost = 100,000 Cash Flow = 20,000 a year

Payback = Cost / Cash Flows = 100,000 / 20,000 = 5 years

Payback Period

Most problems do not work out even….

You need to look at the cumulative cash flow and compare to the initial cost.

Calculating Payback Period

Calculate the cumulative cash flow (total cash flow received)

Calculate the Remaining Cost (Total Cost - Cumulative Cash Flow) Repeat 1 and 2 until remaining cost is less

than zero In last positive year divide remaining cash

flow by yearly cash flow in next year Calculate total payback

Example: Initial Cost = 100,000

Yearly Cumulative RemainingYR Cash Flow Cash Flow Cash Flow1 40,000 40,000 60,0002 30,000 70,000 30,0003 25,000 95,000 5,0004 20,000 115,000 -15,000

Payback = 3 + 5,000/20,000 = 3.25

Payback Period: Benefits

Easy to Understand and Interpret

Reject / Accept based on a Minimum payback

Provides measure of risk

Payback Period Weaknesses

Ignores Time Value of Money

Ignores all cash flows after the payback

Discounted Payback Period

Attempts to account for time value of money by evaluating the yearly cash flows in their present value.

Calculating Discounted Payback Period

Calculate the PV of each cash flow Calculate the cumulative present value of the

cash flows (total cash flow received) Calculate the Remaining Cost

(Total Cost - Cumulative PV Cash Flow) Repeat 1 & 2 until remaining cost is less than 0 In last positive year divide remaining cash flow

by yearly cash flow in next year Calculate total payback

Initial Cost=100,000 r = 10%

Yearly PV Cumul RemainingYR CF CF CF CF1 40,000 36,364 36,364 63,636 2 30,000 24,793 61,157 38,8433 25,000 18,783 79,940 20,060 4 20,000 13,660 93,600 6,4005 15,000 9,314 102,914 -2,914

Payback = 4 + 6400/9314 = 4.687

Discounted Payback

Weakness: Still ignores cash flows after paybackStrengths: Accounts for time value of money, easy to understand and calculate, risk measureAccept / Reject -- Set Minimum payback and compare

Net Present Value

The sum of the PV of the positive cash flows minus the PV of negative cash flows

or

Cost InitialWACC)(1

CFn

1tt

t

Incremental Cash Flows

The cash flows used should represent any changes to Free Cash Flow that result from undertaking the project.

The Required Return

What interest rate should be used to discount the cash flows?

The project cost of capital

NPV Accept or Reject(The NPV Rule in Detail)

If the NPV is positive the PV of the benefits is greater than the PV of the cost -- You should accept the project (The value of the firm will increase if the project is accepted)If the NPV is negative, The PV of the benefits is less than the PV of the cost -- You should reject the project (The value of the firm would decrease if the project is accepted)

NPV Example

Assume a cost of capital of 10% (the WACC) Year Cash Flow Present Value

0 -1,000 -1,000.00 1 1,000 909.90 2 -2,000 -1,652.89 3 3,000 2,253.94

NPV = 510.14NPV = 510.14

Calculator

HP 10B-1,000 <CFj>

1,000 <CFj>

-2,000 <CFj>

3,000 <CFj>

10 <I/Y> <NPV>

NPV

Note, as in the case of our bond and stock valuation models there will be an inverse relationship between the required return and the NPV.A lower WACC increases the NPV of the project (And the value of the firm)

Internal Rate of Return(The Rate of Return Rule in detail)

The IRR is the required return that makes the NPV of a project equal to zero.If IRR is greater than the hurdle rate (the cost of capital) Accept the projectIF IRR is less than the hurdle rate (the cost of capital) Reject the project

IRR and NPV

IRR and NPV will always provide the same accept / reject decision WHY????IRR is the rate that makes NPV zeroIf the (cost of capital) < IRR accept the project, this also implies a positive NPVIf the (cost of capital) > IRR reject the project , this also implies a negative NPV

IRR

BenefitsIntuitiveMeasure of risk compared to Cost of Capital

WeaknessesIgnores size and amount of wealth created

Ignores project life

It is possible to have multiple IRR’s

Multiple IRR’s

Time Cash Flow 0 -100 1 275 IRR = 7.4% and 67.6% 2 -180

Time Cash Flow 0 100 1 -275 IRR = 7.4% and 67.6% 2 180

Multiple IRR’s vs. NPV

Time Cash Flow 0 -100 1 275 NPV @ 15% = $3 2 -180

Time Cash Flow 0 100 1 -275 NPV @ 15% = -$3 2 180

Multiple IRR’s

An easy check for Multiple IRR’s

Mathematically the largest number of IRR’s that is possible equals the number of sign changes in the cash flow stream

Modified IRR

The discount rate that makes the PV of the projects costs equal the PV of the terminal value of the projectTerminal Value = the FV of the positive Cash flows compounded at the cost of capital

Example Cost of Capital = 10%

Time Cash Flow PV FV0 -1000 -1000.001 500 665.502 400 484.003 -150 -112.694 500 500.00

-1,112.69 1,649.50

1112.69 = 1649.50/(1+MIRR)4 MIRR = 10.34%

Profitability Index

Measures the value created per dollar invested

00

1t

t

I

NPV1

I

r)(1CF

PI

n

t

PI

If the PI is greater than 1 accept the project (NPV is positive)If the PI is less than 1 reject the project (NPV is negative)If PI = 1.45 it would imply that the project will produce $1.45 for each $1 invested.

Quick Review

Method Accept RejectPayback Payback < cutoff

Payback>cutoffDisc. Payback Same as PaybackNPV NPV > 0 NPV < 0IRR IRR > WACC IRR < WACCMIRR MIRR >WACC MIRR < WACCPI PI > 1 PI < 1

Mutually Exclusive

NPV provides the best ranking when comparing between mutually exclusive investments, The rest can produce inconsistent rankings.

Example

Project Initial Cost YR1 CF YR2 CF A 1,000,000 1,000,000 0 B 1,200,000 1,119,000 312,000 C 900,000 195,000 970,000 D 1,100,000 980,000 345,000

Compare the different methods for both 7% and 12% (in Class)

Comparison of results

NPV PIDiscounted

Paback Pay IRR

A (65,420.56) 0.9346 1.0000 0.0000B 122,307.28 1.1023 1.5512 1.2468 0.1604C 129,478.56 1.1439 1.8472 1.7268 0.1521D 117,224.21 1.1066 1.6110 1.3478 0.1610

A (107,142.86) 0.8929 1.0000 0.0000B 51,831.63 1.0433 1.7916 1.2468 0.1604C 47,385.20 1.0527 1.9387 1.7268 0.1521D 50,031.89 1.0455 1.8181 1.3478 0.1610

0.07

0.12

IRR vs. NPV revisited

Investment Cost YR 1 IRRA 10,000 12,000 20%B 15,000 17,700 18%

NPV@12% NPV@16% A 714 344.82B 803.50 258.60NPV@14% 526.31579 for both

On the Graph

14%

526.32

Asset A

Asset B

20%18%

Summary

Use NPV as the first ruleThe other criteria can provide secondary informationWhich criteria is most often used by managers?

Identifying Good Projects

Creation of Barriers to competitors and their Maintaining the barriers

Economies of ScaleCost AdvantagesCapital Requirements Product DifferentiationAccess to Distribution Channels Legal and Government Barriers

Putting it all together: The Value of a Share

This definition includes value of equity and debt. If you subtract the value of debt (and preferred stock) you would have a measure of the Market Value of Equity or the Market Value of the claims of the shareholders

FlowsCash Free of PVFirm theof

ValueMarket

The Share Price

gOutstandin Sharescommon of #

Equity of ValueMarket

share

one of

Value

EVA and Share Price

The market value of the firm should represent the book value of the firm plus a claim on all future EVA created or:

capital)equity ofCost -(ROE captialequtiy EVA

EVAs future of PV BookValueFirm theof

ValueMarket

MarketValue

Share Price x

Shares Outstanding

+ Debt

Market Value Added

Capital

Economic Value Added

EVA

EVA

EVA

EVA

EVA

EVA

EVA

EVA

EVA

EVA

Market Value Added = Present Value of Future EVA™

EVA™ = NOPAT – Capital Charge

EVA IS a trademark of Stern Stewart

Market Price

Can analysts forecast future EVA and FCF?

Information and market problemAgency ProblemsShort Term vs. Long Term (Bounded Self Control?)Valuing Strategic OptionsOther Problems

Identifying Good Projects

Creation of Barriers to competitors and their Maintaining the barriers

Economies of ScaleCost AdvantagesCapital Requirements Product DifferentiationAccess to Distribution Channels Legal and Government Barriers