Managerial Finance Finance 6335 Lecture 5 Chapter 6

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Managerial Finance Finance 6335Lecture
5Chapter 6 7Alternative Decision
RulesFundamentals of Capital Budgeting Ronald
F. Singer
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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.

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NPV Rule

• The NPV of the project is calculated as
• The NPV depends on the discount rate, r
• The Internal Rate of Return (IRR) is that
  discount rate that makes the NPV 0

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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.

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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.

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NPV Rule

• The NPV of the project is calculated as
• Therefore the Internal Rate of Return (IRR) is
  14

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Figure 6.1 NPV of FFFs New Project

• If FFFs cost of capital is 10, the NPV is 100
  million and they should undertake the investment.

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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.

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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

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See excel File IRR, NPV versus Payback
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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.

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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?

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Mutually Exclusive Projects

• Time Modify Replace
  Difference
• 0 -100,000 -250,000
  -150,000
• 1 105,000 130,000
  25,000
• 2 49,000
  253,500 204,500
• IRR .40 .30
  .25
• Suppose the cost of capital is 10

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Mutually Exclusive Projects

• Time Modify Replace
  Difference
• 0 -100,000 -250,000
  -150,000
• 1 105,000 130,000
  25,000
• 2 49,000
  253,500 204,500
• IRR .40 .30
  .25
• NPV(_at_ 10) 36,000 77,700
  41,700
• Notice the conflict that can exist between NPV
  and IRR.

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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

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Differences in Scale

• If a projects 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.

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Differences in Scale (cont'd)

• Identical Scale
• Consider two projects

Girlfriends Business Laundromat
Initial Investment 1,000 1,000
Cash FlowYear 1 1,100 400
Annual Growth Rate -10 -20
Cost of Capital 12 12
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Differences in Scale (cont'd)

• Identical Scale
• Girlfriends Business

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Differences in Scale (cont'd)

• Identical Scale
• Laundromat
• IRR 20
• Both the NPV rule and the IRR rule indicate the
  girlfriends business is the better alternative.

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Figure 6.5 NPV of Investment Opportunities

• The NPV of the girlfriends business is always
  larger than the NPV of the single machine
  laundromat. The IRR of the girlfriends business
  is 100, while the IRR for the laundromat is 20.

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Differences in Scale (cont'd)

• Changes in Scale
• What if the laundromat project was 20 times
  larger?
• 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 girlfriends
  business (NPV 4,000).

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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 girlfriends business only
  for discount rates less than 13.9.

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Differences in Scale (cont'd)

• Percentage Return Versus Impact on Value
• The girlfriends business has an IRR of 100,
  while the 20-machine laundromat has an IRR of
  20, so why not choose the girlfriends business?
• Because the 20-machine laundromat makes more
  money
• It has a higher NPV.

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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.

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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.

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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

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Timing of Cash Flows (cont'd)

• The time line would now be
• The NPV of the project remains 5,000 but the IRR
  falls to 15.

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Figure 6.7 NPV With and Without the Maintenance
Contract
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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.

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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.

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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.

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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

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Capital Rationing

• Rank by Profitability Index (NPV/INV
• Project Profitability Index
  Investment Total
• E 2.0
  2.5 2.5
• C 1.6 2.5 5.0
  
• G 1.5 3
  8.0
• F 1.4
  5 13.0 D
  1.2 5
• B .8 10
• A .667 15
• 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.

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See Spreadsheet
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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.

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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

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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 (_at_ 40)
  572
• Net Income (Earnings after Tax)
  858
• Earnings per Share (EPS) Net Income/Shares
  0.858

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Cougar Enterprises

• Pro-Forma Cash Flow Statement
• (Year ending December 31, 2006)
• ( thousand)
• Earnings Before Interest and Taxes 2,200
• Less Tax on Operations (_at_ 40) (Note
  not 572)
  880
• Operating Income after Tax (EBIT(1-t) )
  1,320
• Plus Non-Cash Expenses (Depreciation
  Amortization)
  500
• Less Change in Working Capital
  
  300
• (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 1,520
• Plus Interest Tax Shield
  (707 times 0.40)
  308
• CASH FLOW
  
  1828
• Less Net New Investment (net of capital
  gains tax)
  400
  
• Less Cash Flow to Bondholders (Interest,
  principal, Bond Repurchase, Call) 770

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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

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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.

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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

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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

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Capital Budgeting Decisions Check List

• 9. Include Asset's Entire Life
• 10. Include the depreciation tax shield, but not
  depreciation itself.

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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

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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.

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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.

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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?

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Only Incremental cash flows are relevant

• 
  14,000
• -1---------------0-----------------1
• 10,000
• Of course it should have. The NPV was NPV
  1,564

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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?

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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

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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)

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Only Incremental cash flows are relevant

• 
  14,000
• -1---------------------0-----------------
  ------1 initial
• -10,000 -5,000
• 
  1,050
• -1---------------------0-----------------
  ------1 Incremental
• -1,000
• NPV (of Additional Investment) -1000
  1050 - 45.45
• 
  1.1
• 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.

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Treat inflation consistently

• MAKE SURE THAT INFLATION IS ACCOUNTED FOR IN A
  CONSISTENT MANNER. EITHER
• Revenues and Expenses are not necessarily
  effected uniformly by inflation
• Depreciation expense is not effected by inflation
  

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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)

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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).

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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!

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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.

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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

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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)

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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 tc x (Market Value - Book
  Value)
• On sale
• If Market Value gt Book Value, then tax on gain is
  cash outflow.
• If Market Value lt Book Value, then we have a loss
  on sale, tax is negative, and there is a cash
  inflow.

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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 _at_ 140,000 per year,
  leaving 300,000 when the project ends.

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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 PE 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)

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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

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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