Managerial Finance
Finance 6335
Lecture 5
Chapter 6 & 7
Alternative Decision Rules
Fundamentals of Capital
Budgeting
Ronald F. Singer
6.1 NPV and Stand-Alone
Projects
• Consider a take-it-or-leave-it investment
decision involving a single, stand-alone
project for Fredrick Feed and Farm (FFF).
– The project costs $250 million and is
expected to generate cash flows of $35
million per year, starting at the end of the first
year and lasting forever.
NPV Rule
• The NPV of the project is calculated as:
35
NPV   250 
r
• The NPV depends on the discount rate, r
• The Internal Rate of Return (IRR) is that discount rate that
makes the NPV = 0
Alternative Rules Versus the
NPV Rule
• Sometimes alternative investment rules
may give the same answer as the NPV
rule, but at other times they may disagree.
– When the rules conflict, the NPV decision rule
should be followed.
6.2 Alternative Decision Rules
• The Payback Rule
– The payback period is amount of time it
takes to recover or pay back the initial
investment. If the payback period is less than
a pre-specified length of time, you accept the
project. Otherwise, you reject
the project.
• The payback rule is used by many companies
because of
its simplicity.
• However, the payback rule does not always give a
reliable decision since it ignores the time value of
money.
NPV Rule
• The NPV of the project is calculated as:
35
NPV   250 
r
• Therefore the Internal Rate of Return (IRR) is
14%
Figure 6.1 NPV of FFF’s New
Project
• If FFF’s cost of capital is 10%, the NPV is $100 million and they
should undertake the investment.
Measuring Sensitivity with IRR
• For FFF, if their cost of capital estimate is
more than 14%, the NPV will be negative,
as illustrated on the previous slide.
– In general, the difference between the cost of
capital and the IRR is the maximum amount
of estimation error in the cost of capital
estimate that can exist without altering the
original decision.
When does IRR work?
• You can take all or no project (stand alone
project)
• “Normal Project” Negative Cash flows
first, followed by positive cash flows
• In other cases, the IRR rule may disagree
with the NPV Rule. If that is the case
always go with the NPV Rule
See excel File IRR, NPV versus
Payback
Practical Problems in Capital
Budgeting
• We have stated that we want the firm to
take all projects that generate positive
NPV and reject all projects that have a
negative NPV. Capital budgeting
complications arise when you cannot,
either physically or financial undertake all
positive NPV projects. Then we have to
devise methods of choosing between
alternative positive NPV projects.
Mutually Exclusive Projects
• IF,AMONG A NUMBER OF PROJECTS, THE
FIRM CAN ONLY CHOOSE ONE, THEN THE
PROJECTS ARE SAID TO BE MUTUALLY
EXCLUSIVE.
• For example: Suppose you have the choice of
modifying an existing machine, or replacing it
with a brand new one. You could not do both
and produce the desired amount of output.
Thus, these projects are mutually exclusive.
Given the cash flows below, which of these
projects do you choose?
Mutually Exclusive Projects
Time
0
1
2
IRR
Modify
-100,000
105,000
49,000
.40
Replace
-250,000
130,000
253,500
.30
• Suppose the cost of capital is 10%
Difference
-150,000
25,000
204,500
.25
Mutually Exclusive Projects
Time
Modify
0
-100,000
1
105,000
2
49,000
IRR
.40
NPV(@ 10%) 36,000
Replace
-250,000
130,000
253,500
.30
77,700
Difference
-150,000
25,000
204,500
.25
41,700
• Notice the conflict that can exist between NPV and IRR.
CAPITAL BUDGETING COMPLICATIONS
• Capital Budgeting Complications occur
when you cannot take all positive NPV
PROJECTS. Thus, the firm is faced with
the choice of two possibilities.
• Remember: Goal is still Max NPV of all
possibilities
Differences in Scale
• If a project’s size is doubled, its NPV will
double. This is not the case with IRR.
Thus, the IRR
rule cannot be used to compare projects of
different scales.
Differences in Scale (cont'd)
• Identical Scale
– Consider two projects:
Initial Investment
Cash FlowYear 1
Annual Growth Rate
Cost of Capital
Girlfriend’s
Business
$1,000
$1,100
-10%
12%
Laundromat
$1,000
$400
-20%
12%
Differences in Scale (cont'd)
• Identical Scale
– Girlfriend’s Business
NPV   1000 
1100
1100
  1000 
 $4000
r  0.1
0.12  0.1
1000 
1100
implies r  100%
r  0.1
Differences in Scale (cont'd)
• Identical Scale
– Laundromat
NPV   1000 
400
400
  1000 
 $250
r  0.2
0.12  0.2
• IRR = 20%
– Both the NPV rule and the IRR rule indicate
the girlfriend’s business is the better
alternative.
Figure 6.5
NPV of Investment
Opportunities
• The NPV of the girlfriend’s business is always larger than the NPV of
the single machine laundromat. The IRR of the girlfriend’s business is
100%, while the IRR for the laundromat is 20%.
Differences in Scale (cont'd)
• Changes in Scale
– What if the laundromat project was 20 times
larger?
400


NPV  20  1000 
  $5000
0.12  0.2 

• The NPV would be 20 times larger, but the IRR
remains the same at 20%.
– Give an discount rate of 12%, the NPV rule indicates you
should choose the 20-machine laundromat (NPV =
$5,000) over the girlfriend’s business (NPV = $4,000).
Figure 6.6 NPV of Investment
Opportunities
with the 20-Machine Laundromat
• The NPV of the 20-machine laundromat is larger than the
NPV of the girlfriend’s business only for discount rates less
than 13.9%.
Differences in Scale (cont'd)
• Percentage Return Versus Impact on
Value
– The girlfriend’s business has an IRR of 100%,
while the 20-machine laundromat has an IRR
of 20%, so why not choose the girlfriend’s
business?
• Because the 20-machine laundromat makes more
money
– It has a higher NPV.
Differences in Scale (cont'd)
• Percentage Return Versus Impact on
Value
– Would you prefer a 200% return on $1 dollar
or a 10% return on $1 million?
• The former investment makes only $2, while the
latter opportunity makes $100,000.
• The IRR is a measure of the average return, but
NPV is a measure of the total dollar impact on
value, and thus stockholders’ wealth.
Timing of Cash Flows
• Another problem with the IRR is that it can
be affected by changing the timing of the
cash flows, even when that change in
timing does not affect the NPV.
– It is possible to alter the ranking of projects’
IRRs without changing their ranking in terms
of NPV.
– Hence you cannot use the IRR to choose
between mutually exclusive investments.
Timing of Cash Flows (cont'd)
• Assume you are offered a maintenance
contract on the laundromat machines
which would cost $250 per year per
machine. With this contract, you would not
have to pay for maintenance
and so the cash flows from the machines
would not decline.
– The expected cash flows would then be:
$400 – $250 = $150 per year per machine
Timing of Cash Flows (cont'd)
• The time line would now be:
150 

NPV  20  1000 
  $5000
r 

– The NPV of the project remains $5,000 but
the IRR falls to 15%.
Figure 6.7 NPV With and
Without
the Maintenance Contract
Timing of Cash Flows (cont'd)
• The NPV without the maintenance contract
exceeds the NPV with the contract for discount
rates that are greater than 12%.
– The IRR without the maintenance contract
(20%)
is larger than the IRR with the maintenance
contract (15%).
• The correct decision is to agree to the contract if
the cost of capital is less than 12% and to
decline the contract if the cost of capital exceeds
12%. With a 12% cost of capital, you are
indifferent.
Capital Rationing
• In this situation, the decision maker is faced with a
limited capital budget (or limitations on some other
input). As a result, it may not be possible to take all
positive net present value projects. Under this scenario,
the problem is to find that combination of projects (within
the capital budgeting constraint) that leads to the highest
Net Present Value.
• The problem here is that the number of possibilities
become very large with a relatively small number of
projects. Thus, in order to make the problem
"manageable", we can systematize the search.
Capital Rationing
• Since we have a constraint, what we want to do
is invest in those projects which gives us the
highest BENEFIT per dollar invested. (The
highest bang per buck). What is the benefit?, it
is the Present Value of the Cash Flows. So that
we would want to choose that set of projects
within the capital budgeting constraint that gives
the highest:
Net Present Value
INVESTMENT
• This ratio is called the profitability Index.
Capital Rationing
• For example, suppose we have a $13 million capital
budgeting constraint, with 7 alternative capital budgeting
projects with the following projections.
Project
NPV
Investment
A
10
15
B
8
10
C
4
2.5
D
6
5
E
5
2.5
F
7
5
G
4.5
3
Capital Rationing
• Rank by Profitability Index {(NPV/INV}
Project
Profitability Index Investment Total
E
C
G
F
D
B
A
2.0
1.6
1.5
1.4
1.2
.8
.667
2.5
2.5
3
5
5
10
15
2.5
5.0
8.0
13.0
• COMBINATION WITH HIGHEST PROFITABILITY INDEX WITHIN
THE CAPITAL BUDGET
• (E,C,G,F) has a NPV of $20.5 million, and a cost of $13 million.
See Spreadsheet
Capital Rationing
• However, if the budget were 15 million rather than 13
million we would have a problem. Adding D would go
over the budget and be infeasible, but the combination
CDEF has a higher NPV ($22 million) than the chosen
combination of ECGF. This is because the amount spent
was only 13 million leaving 2 million in unspent funds. In
this case, we are better off choosing a combination
which spends all the funds.
• THE ONLY WAY TO DO THIS RIGHT IS TO DO A FULL
BLOWN LINEAR PROGRAMING PROBLEM WITH
CONSTRAINTS.
Capital Budgeting
• We are now ready to consider the capital
budgeting decision.
• As we said repeatedly, the idea is to invest
in such a way that you maximize the Net
Present Value of your decision.
• What we mean by the NPV is the Present
Value of the Cash Flow from Operations
generated by the project less the initial
Cash Investment
Cougar Enterprises
Pro-Forma Income Statement
(Year ending December 31, 2006)
($ thousand)
Sales
$5,000
Less: Operating Expenses (COGS)
2,000
Depreciation & Amortization
500
Allocated G & A Costs
300
Operating Income (EBIT)
$2,200
Less: Interest Expense
770
Earnings Before Tax(taxable income)
1,430
Less Tax (@ 40%)
572
Net Income (Earnings after Tax)
$858
Earnings per Share (EPS) = Net Income/Shares = $0.858
Cougar Enterprises
Pro-Forma Cash Flow Statement
(Year ending December 31, 2006)
($ thousand)
Earnings Before Interest and Taxes
Less: Tax on Operations (@ 40%) (Note: not $572)
Operating Income after Tax (EBIT(1-t) )
Plus: Non-Cash Expenses (Depreciation & Amortization)
Less: Change in Working Capital
(Change a/c receivable
200
Change in Inventory
100
Change other ST Assets
100
Less: Change in a/c payable
150
Change in ST Liabil.
(50)
Change in Working Capital
Free Cash Flow from Operations
Plus Interest Tax Shield
(707 times 0.40)
CASH FLOW
Less: Net New Investment (net of capital gains tax)
Less: Cash Flow to Bondholders (Interest, principal, Bond Repurchase, Call)
Less: Cash Flow to Preferred stockholders
Free Cash Flow to Common Stockholders
EBITDA
$2,200
880
1,320
500
300
$1,520
308
$1828
400
770
100
558
2,700
38
Capital Budgeting Decisions Check List
1.
Net Present Value is the "Discounted value of
incremental cash flow”
2.
Cash flow is:
CASH MONEY IN - CASH MONEY OUT
Capital Budgeting Decisions Check List
3. Consider only if it is an incremental cash flow,
and consider all incremental cash flows:
(a) not historical, or averages;
(b) consider only cash flows that appear as a
result of the project
(c) consider the impact of the project on cash
flows from other projects
(d) exclude fixed or sunk costs
(e) exclude allocated overhead unless it will
change as a result of the project.
Capital Budgeting Decisions Check List
4. Treat inflation consistently:
Make sure that you have considered the impact
of inflation on Cash Flows
5. All Cash Flow should be on an After-Tax basis.
Use actual tax changes when paid!
Don't forget to allow for the tax on capital gains
Use future marginal tax rates applied to future
taxable
income
Capital Budgeting Decisions Check List
6. Include the opportunity cost of the project, even if there
is no explicit cash flow realized
Account for assets sold and not sold as a result of
adoption of a project.
7. Account for changes in working capital and only
changes in working capital. Recognize that working
capital will in general be re-cooped at the end of the
project.
8. Ignore financing including the tax shield on interest
Capital Budgeting Decisions Check List
9. Include Asset's Entire Life
10. Include the depreciation tax shield, but not
depreciation itself.
Capital Budgeting Decisions Check List
No matter how complicated the decision: What is
important?
MAXIMIZE NPV
PLAN TO TAKE ALL PROJECTS WITH A POSITIVE
NET PRESENT VALUE AND REJECT ALL PROJECTS
WITH A NEGATIVE NET PRESENT VALUE
Application of the NPV Rule and
Capital Budgeting
• For now we are going to assume that the
appropriate discount rate is known.
• The problem we want to tackle is to forecast the
relevant cash flows.
Only Cash Flows Affect Wealth.
What is and is not Cash Flow
-Expenses are cash flow regardless of whether the
accountant capitalizes and depreciates them or
expenses them.
-Capital expenditures are cash outflows regardless of the
fact that accountants depreciate them over a period.
Only Incremental cash flows are
relevant
• Not historical cash flows, not averages, not sunk costs!
• Example 1: Consider a firm having made an investment
one year in the past. The project required an initial
investment of $10,000- with the expectation of $14,000
to be generated within two years. At a discount rate of
10% should the firm have made the investment?
Only Incremental cash flows are
relevant
14,000
-1---------------0-----------------1
10,000
• Of course it should have. The NPV was: NPV = 1,564
Only Incremental cash flows are
relevant
• NOW THINGS CHANGE. A NEW DEVICE
INTRODUCED BY A COMPETITOR MAKES THE
PRODUCT OBSOLETE. THUS EXPECTED CASH
FLOWS DECLINE TO $7,000. THAT IS THE
INVESTMENT, DID NOT PAY OFF AS EXPECTED AND
THE PROJECT IS NOW A LOSER.
• SUPPOSE THAT FOR AN ADDITIONAL INVESTMENT
OF $5,000, YOU CAN REGAIN YOUR COMPETITIVE
POSITION, SO THAT EXPECTED CASH FLOW
INCREASES TO THE ORIGINAL $14,000. SHOULD
YOU MAKE THE NEW INVESTMENT?
Only Incremental cash flows are
relevant
14,000
-1---------------0-----------------1
-10,000
-5,000
• Note that the project, looked at as a whole is still a loser:
NPV(-1) = -10,000 - 5,000 + 14,000
(1.1)
(1.1)2
= - 2,975
BUT the additional investment should be made.
• Determine the incremental cash flows.
• Determine Net Present Value of the incremental cash
flows
Incremental Cash Flow: -5,000 + 7,000/(1.1) = 1,363.65
Only Incremental cash flows are
relevant
• Example 2: Assume that the original cash flow estimates
were accurate. But, that you can, by making an
additional investment of 1,000 generate total second
period cash flow of 15,050. Should the additional
investment be made?
(Still Assume r= 10%)
Only Incremental cash flows are
relevant
14,000
-1---------------------0-----------------------1
-10,000
-5,000
1,050
-1---------------------0-----------------------1
-1,000
NPV (of Additional Investment) = -1000 + 1050
1.1
initial
Incremental
= - 45.45
• Even though, the original project is a winner, do not
make the additional investment
• Y0u must Ignore Sunk Costs, and consider only
incremental cash flows.
Treat inflation consistently
•
MAKE SURE THAT INFLATION IS
ACCOUNTED FOR IN A CONSISTENT
MANNER. EITHER:
1. Revenues and Expenses are not
necessarily effected uniformly by inflation
2. Depreciation expense is not effected by
inflation
Tying up assets uses a valuable
resource and must be accounted for.
• Example: A firm is considering installing a brick
manufacturing kiln. The initial investment will
require $300,000 in building and equipment. The
kiln will be located on a vacant lot having an
estimated market value of $1,000,000. The
project is expected to generate net cash flow of
$50,000 per year for 20 years. After 20 years,
the kiln will be worthless. It is anticipated that
the lot could be sold for $2,653,000 at the end of
20 years. At a 10% discount rate, is this a good
investment? (Ignore taxes)
Tying up assets uses a valuable
resource and must be accounted for.
• ALTERNATIVE ONE
Ignoring the opportunity cost of the (tied-up) land.
NET PRESENT VALUE CALCULATION:
NPV=-300,000 + PMT(50,000, 10%, 20)
=-300,000 + 425,693.05 = 125,693.05
ACCEPT PROJECT
• The problem with this is that you ignore the fact that you
lose the use of $1,000,000 that you could have had if
you had not adopted the project and sold the land (or
used it in an alternative project).
Tying up assets uses a valuable
resource and must be accounted for.
• ALTERNATIVE TWO
Explicitly consider the land as part of the inputs: You
estimate that the land will be worth $2,653,000 in 20
years.
PRESENT VALUE CALCULATION:
NPV = -1,000,000 -300,000 + PMT(50,000, 10%, 20)
+ PV($2,653,000, 10%,20)
= - 1,300,000 + 425,678 + 394,352
= - 479,970
REJECT PROJECT
• NOTICE HOW THE TIED UP LAND IS TREATED!
Rule 4: Tying up assets uses a
valuable resource and must be
accounted for.
• Other Incremental Costs Are
Increases in overhead costs as a result of project.
Increases in working capital as a result of project.
• Notice the reduction in working capital would be a cash
inflow at that time.
• Do not use allocated overhead, or allocated working
capital.
Changes in Working Capital Should be
accounted for
• Example:
Suppose, due to the adoption of the project, the firm is
required to increase working capital from $100,000 to
$110,000 per annum for the life of the project. How do
you account for the working capital?
So you see that this is simply a timing problem
Remember taxes
1. Calculate all cash flows after taxes
2. Include non-cash expenses (depreciation) for its effect on taxes, but
not as a cash flow itself.
•
HOW TO HANDLE THE DEPRECIATION TAX SHIELD
We want the project's AFTER TAX CASH FLOW
Equals: Before Tax Cash Flow Less Corporate Taxes
Taxes = tc [Cash revenue - Cash Expenses - Depreciation]
Therefore, for each year:
After Tax Cash Flow =(Cash Revue - Cash Expenses)(1 - tc)+ tc Depr
Where: tc x Depr is the Depreciation Tax Shield)
Remember taxes on Capital Gains
3. Tax on gains/losses from sale of assets is an
additional negative/positive cash flow
Tax on
Gains/Losses
On sale
= tc x (Market Value - Book Value)
• If Market Value > Book Value, then tax on gain is cash
outflow.
• If Market Value < Book Value, then we have a loss on
sale, tax is negative, and there is a cash inflow.
Remember taxes on Capital Gains
• Example:
• XYZ Corp. has a project which is going to last 5
years. P & E for this project of $1,000,000 can
assume a scrap value of 300,000 at the end of 5
years. On a straight line basis, that means the
firm depreciates the assets @ $140,000 per
year, leaving 300,000 when the project ends.
Remember taxes and the effect
of selling assets
• However, you expect that you can sell the asset
for $500,000 at the end of 5 years. Thus there is
a taxable capital gain of: (MV-BV) = $200,000.
• At a 35% Corporate Capital Gain Tax rate, that
means that after tax cash flow from the disposal
of P&E is
0.35 * $200,000 = $70,000
Thus the Cash flow from selling the asset is:
$500,000 -70,000 = $430,000
(Remember to add back Book Value)
Ignore the means of financing both as a
direct cash flow and as its effect on taxes.
• Interest payment is not a cash flow. Discounting already takes
the value of time into account. To deduct interest would be
double counting.
• Example: Suppose that you borrow $500, and put in $500 of
your money into the following project. (Bank charges 8% on
loan)
0
1
Cash Flow
-1000
1125
Interest
-40
Net
-1000
1085
• To say that we reject the project since NPV (of net cash flow) is
negative at 10% (NPV = -13) is double counting. We penalize
the project twice, one by deducting interest, second by
discounting.
• The NPV of this project is:- 1,000 + (1,125) X (0.909) = 23
STEPS IN PROJECT ANALYSIS
1. MAKE INITIAL PROJECTIONS
Made by operations manager
Generally in form of income statement
Clarify assumptions
2. ADJUST FOR INFLATION IF APPROPRIATE
3. REARRANGE IN CASH FLOW FORM
4. PERFORM NET PRESENT VALUE CALCULATIONS
5. PERFORM "WHAT IF" CALCULATIONS