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
firm
This 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 risky
Each 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 asset
What 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 Stage
Initial outlay of cash
Operating Stage
Sales Revenue, Operating Expenses, Taxes etc
Disposition Stage
Sales of fixed assets, Tax consequences
What is a Project?
Major Strategic Decisions
Acquisitions of Other firms
New Ventures within existing markets
Changes in the way current businesses or
ventures are approached
Spending 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?
Acceptance
Region
Return
12.0
A
10.5
10.0
9.5
B
Rejection
Region
8.0
RiskL
RiskA
RiskH
Risk
Determining the Project
Cost of Equity
1.
2.
3.
Single Business – Project risk is similar across all
businesses – use the overall cost of equity and
cost of debt
Multiple Businesses with different risk profiles –
estimate cost of equity using project beta –
bottom up beta, accounting beta, or regression
on cash flows
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
Characteristics
Small and CF
similar to firm
Cost of Debt
Firm’s Cost of
Debt
Debt Ratio
Firm’s Cost of
Equity
Project is large
Cost of debt of
Average debt
CF different from comparable firms ratio of
firm
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 Flows
Accounting earnings are based on accrual
accounting
Cash 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 accounting
Revenues are realized at the time of the sale, not when
cash is received (Expenses are realized at the time
acquired, not when paid for
Operating Expenditures
Produce benefits only in the current period
Capital Expenditures
produce 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 Issues
FCFF (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
project
Relevant 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 Flows
Incremental cash flows represent changes that
are a result of the project under consideration
Be careful about Inflation
Do 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 Statement
Estimate the Balance Sheet
Combine the income statement and balance
sheet into a cash flow statement
Make a decision
Steps in the planning process
1.
2.
3.
4.
5.
6.
Pro Forma Financial Statements and NPV
Determine the funds needed to support the
plan
Forecast the funds available
Establish controls
Plan for other contingencies
Establish a performance based compensation
plan
Capital Budgeting Decision Rules
Balance between subjective assessment and
consistency across projects
Reinforces the main goal of corporate finance –
Maximize the value of the firm
Be 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
EBIT
ROC 
(AverageBook Value of CapitalInvested)
Accept the project if ROC > Cost of Capital
More difficult for multiyear projects
Capital Budgeting Decision Rules
Accounting Returns
Return on Equity on the project
P rojectROE 
Net Income
AverageBook Value of EquityInvestmentin P roject
If ROE > Cost of Equity Accept the project
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
EVA  NOP AT- CapitalCharge
Total

 After  tax 



 EBIT(1 T) -  investor- supplied percentage 
 operatingcaptial  cost of capital



 Net Income  (equitycapital) (cost of equitycaptial)
 Net Income

 (equitycapital)
 cost of equitycapital
 EquityCapital

 (equitycapital)(ROE - cost of equitycapital)
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
YR
1
2
3
4
Yearly
Cumulative
Cash Flow Cash Flow
40,000
40,000
30,000
70,000
25,000
95,000
20,000
115,000
Remaining
Cash Flow
60,000
30,000
5,000
-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
YR
1
2
3
4
5
r = 10%
Yearly
PV
Cumul
Remaining
CF
CF
CF
CF
40,000 36,364
36,364
63,636
30,000 24,793
61,157
38,843
25,000 18,783
79,940
20,060
20,000 13,660
93,600
6,400
15,000
9,314 102,914
-2,914
Payback = 4 + 6400/9314 = 4.687
Discounted Payback
Weakness: Still ignores cash flows after
payback
Strengths: Accounts for time value of money,
easy to understand and calculate, risk measure
Accept / 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

CFt
 
t
 t 1 (1  WACC)
n

  Initial Cost

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 = 510.14
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 project
IF 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 zero
If the (cost of capital) < IRR accept the
project, this also implies a positive NPV
If the (cost of capital) > IRR reject the project ,
this also implies a negative NPV
IRR
Benefits
Intuitive
Measure of risk compared to Cost of Capital
Weaknesses
Ignores size and amount of wealth created
Ignores project life
It is possible to have multiple IRR’s
Multiple IRR’s
Time
0
1
2
Cash Flow
-100
275
IRR = 7.4% and 67.6%
-180
Time
0
1
2
Cash Flow
100
-275
IRR = 7.4% and 67.6%
180
Multiple IRR’s vs. NPV
Time
0
1
2
Cash Flow
-100
275
NPV @ 15% = $3
-180
Time
0
1
2
Cash Flow
100
-275
NPV @ 15% = -$3
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 project
Terminal Value = the FV of the positive Cash
flows compounded at the cost of capital
Example Cost of Capital = 10%
Time
0
1
2
3
4
Cash Flow
-1000
500
400
-150
500
PV
-1000.00
-112.69
FV
665.50
484.00
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

CFt 

t 
NPV
t 1 (1  r) 

PI
 1
I0
I0
n
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
Reject
Payback Payback < cutoff Payback>cutoff
Disc. Payback Same as Payback
NPV
NPV > 0
NPV < 0
IRR
IRR > WACC
IRR < WACC
MIRR
MIRR >WACC
MIRR < WACC
PI
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
A
B
C
D
(65,420.56)
122,307.28
129,478.56
117,224.21
PI
0.9346
1.1023
1.1439
1.1066
Discounted
Paback
0.07
1.5512
1.8472
1.6110
Pay
IRR
1.0000
1.2468
1.7268
1.3478
0.0000
0.1604
0.1521
0.1610
1.0000
1.2468
1.7268
1.3478
0.0000
0.1604
0.1521
0.1610
0.12
A (107,142.86)
B
51,831.63
C
47,385.20
D
50,031.89
0.8929
1.0433
1.0527
1.0455
1.7916
1.9387
1.8181
IRR vs. NPV revisited
Investment
A
B
Cost
10,000
15,000
YR 1
12,000
17,700
IRR
20%
18%
NPV@12%
NPV@16%
A
714
344.82
B
803.50
258.60
NPV@14%
526.31579 for both
On the Graph
Asset B
526.32
Asset A
14%
18%
20%
Summary
Use NPV as the first rule
The other criteria can provide secondary
information
Which criteria is most often used by managers?
Identifying Good Projects
Creation of Barriers to competitors and their
Maintaining the barriers
Economies of Scale
Cost Advantages
Capital Requirements
Product Differentiation
Access to Distribution Channels
Legal and Government Barriers
Putting it all together:
The Value of a Share
Market Value
of the Firm
 PV of Free Cash Flows
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
The Share Price
Value
Market Value of Equity
of one 
# of common Shares Outstandin
g
share
EVA and Share Price
EVA  equtiycaptial(ROE - Cost of equitycapital)
The market value of the firm should represent the
book value of the firm plus a claim on all future EVA
created or:
Market Value
of the Firm
 BookValue PV of future EVAs
Economic Value Added
Market Value Added = Present Value of Future EVA™
Market
Value
Share Price
x
Shares
Outstanding
+
Debt
Market
Value
Added
Capital
EVA IS a trademark of Stern Stewart
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EVA™ = NOPAT – Capital Charge
Market Price
Can analysts forecast future EVA and FCF?
Information and market problem
Agency Problems
Short Term vs. Long Term (Bounded Self
Control?)
Valuing Strategic Options
Other Problems
Identifying Good Projects
Creation of Barriers to competitors and their
Maintaining the barriers
Economies of Scale
Cost Advantages
Capital Requirements
Product Differentiation
Access to Distribution Channels
Legal and Government Barriers