Application of Capital Budgeting Techniques

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Application of Capital Budgeting Techniques

• Chapter 8 9 Class 4 through 7

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Topics Covered

• Spreadsheet Method use for (discounted) payback
  period.
• Formula Method use for NPV, IRR, and PI.
• Replacement Projects.
• Sensitivity and Break Even Analysis.
• Unequal lives

• Cash Flow Issues Chap 7 post-tax CFs provided
  Chap 8 Not!
• Depreciation CCA (Capital Cost Allowance).
• Terminal Cash Flows.
• Salvage.
• Disposition CCA.

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Some cash flow issues
1. Cash outflows 2. Incremental cash flows firm
with vs. without project 3. Sunk costs -
ignore 4. Opportunity cost take account 5.
Externalities 6. Inflation 7. Financing charges
not in cash flows 8. The opportunity to abandon
and to expand 9. Tax effects 10. Terminal cash
flows
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1. Cash Outflows

• 1. Expenditures on fixed assets are cash
  outflows.
• Includes shipping installation.
• 2. Change in working capital ( current assets -
  current liabilities) is a cash flow.
• New projects increase current assets and current
  liabilities. Increase in WC is outflow decrease
  in WC is inflow
• Only change in WC is a cash flow
• NWC A/R Inventory A/P

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2.Think Incrementally

• Consider only incremental costs, i.e., costs
  resulting from project. Ignore costs incurred in
  past or costs that would be incurred regardless.
• Incremental approach equivalent to comparing two
  valuations of firm with the new project and
  without. If difference positive then accept new
  project.

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Example Samurai Tailors Inc.

• Samurai Tailors Inc. has C cash and expects
  after tax cash flows of 200 in each of the next
  2 years. The cost of capital is 5 
• Samurai Sam is considering buying a new sword for
  C, which will increase his tailoring speed and
  increase annual cash flows to 300 gt 200
• He should buy the sword if the value of the firm
  with the sword is greater than the value without

• If the NPV of incremental cash flows is positive
  undertake project.

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3.Ignore Sunk/Irrelevant Costs

• Costs incurred prior to the project should not be
  allocated to the project.
• Sunk costs are ancient history, i.e. irrevocable.
  Ergo, ignore them.
• If a future cost will be incurred regardless of
  project acceptance, that cost is irrelevant and
  should be ignore.

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4. Opportunity Costs

• The cost of any chosen act is the most valuable
  forsaken alternative opportunity.
• The use of assets that do not have a direct
  price, i.e., machines that the firm already owns,
  have an opportunity cost equal to the profit
  foregone on the best alternative production
  opportunity.

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Opportunity Costs

• The selling price of an asset is an opportunity
  cost that must be considered
• An example
• Assume a machine has an after-tax market value of
  60,000, which is an opportunity cost.

• Using the machine further will generate a stream
  of cash flows with a present value of 55,000.
• Thus, we should sell the machine. NPV 60,000 -
  55,000 5,000.

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5. Externalities

• Externalities are costs borne or benefits
  captured by others.
• Externalities are costs if they affect other
  parts of the firm.
• Externalities can be positive.

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6. Treat Inflation Consistently

• Inflation affects both cash flows and the
  opportunity cost of capital
• Nominal cash flow should be discounted at nominal
  rates. Real Cash flow should be discounted at
  real rates. Dont mix real with nominal!

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Example Inflation

• Economists at Microsoft predict that the sales of
  the Windows operating system will continue in
  perpetuity. They forecast 100M in after-tax cash
  flows (in todays dollars) each year starting one
  year from now. Assume year-end cash flows.
  Inflation is forecast at 4. The nominal cost of
  capital is 10.
• What is the real rate?
• What is the PV of the after-tax cash flows?

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Inflation Example Solution

• Real cash flow 100M must be discounted with
  real cost of capital
• (1 realCoC)(1inflation rate)(1nominalCoC)
• (1realCoC)(14) (110)
• realCoC 5.769
• PV of after cash flows 100M/.05769 1,733.33M
• Note Some time must elapse for there to be a
  difference between real and nominal. Thus, PV is
  both real and nominal as no time has elapsed.

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7. Financing Charges

• Exclude costs of capital (cost of debt, equity
  etc) in cash flow estimates.
• They are already included in WACC.
• No double counting!
• Example Project acceptance requires that firm
  take out a loan that will require annual payments
  to the bank of 1M. Will the project cash flows
  reflect -1M? No! Since the cost of debt is in
  the discount rate.

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8. The Opportunity to Abandon, Expand, Delay

• Expansion Option If after first year, the
  project turns out to be very profitable, the firm
  may want to expand the projects scale.
• Abandonment Option If after first year, the
  project turns out to be quite unattractive, then
  firm may want to close prematurely the facility.
• Option to Delay Project investment now is
  profitable but investment next year may be even
  more profitable.

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Example Option to Abandon

• You are studying the feasibility of launching a
  new video game. The project will generate
  expected annual after-tax cash flows of 0.75M
  for the next 10 years. The discount rate is
  12and the initial investment, 6M. If the
  project is abandoned at the end of year 1, this
  is will generate an after-tax cash flow of 5M.
• What is the NPV ignoring the option to abandon?
• At the end of year 1, you will be able to
  determine if the project will be a success or
  failure and then exercise the abandon option. If
  success, the project will generate annual
  after-tax cash flows of 1.5M. If failure annual
  after-tax cash flow equals 0. Success and failure
  are equally probable. What is the NPV taking
  account of the option to abandon?

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Solution Option to Abandon

• If ignore option to abandon NPV -6M
  0.75MxPVIFA(12,10) -1.76233M ergo Reject
• Take account of option to abandon
• If success, dont abandon PV
  1.5MxPVIFA(12,10) 8.47533
• If failure, abandon PV 5/1.12 4.4643
• NPV -6M .5(8.47533M4.4643M) 0.4698M ergo
  Accept
• Taking account of the option to abandon at end of
  year 1 turns a Reject decision into an Accept
  decision

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9. Taxation Issues Capital Cost Allowance (CCA)

• CCA or depreciation is a deduction from taxable
  earnings.
• A tax shield or reduction in tax liability is
  created.
• Tax shield from CCA T x CCA claimed.
• CCA itself is not a cash flow. But claiming CCA
  creates a cash flow. The cash inflow is the CCA
  tax shield.

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Example V Operating Cash Flows
With and without CCA

• Depreciation deductibility increases operating
  cash flows by
• TCCA 0.520 10.

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CCA Calculations
See the CCA Primer slides.
CCA-a premier
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10.Terminal Year Cash Flows

• Salvage Value (SV) of asset
• Funds from sale of asset are cash inflows at end
  of last year. (Also known as resale value.)
• Recovery of working capital
• Production ceases but sales from inventory
  continue.
• May or may not equal initial NWC investment.
• Tax Effects of Disposition of fixed (depreciable)
  asset
• Sale of asset will affect future taxes.
• General Rule The only effect of selling an asset
  is to reduce UCC of the pool to which asset
  belongs by the Salvage Value of the asset. This
  reduces ability to claim CCA in future years.
• Exceptions to General Rule (capital gains,
  recapture of depreciation, terminal loss)
  discussed in CCA Primer slides.

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Capital Budgeting

• Take the present value of all cash flows accruing
  to the project.
• Discount rate is k, the cost of capital.
• Components of the project are
• Net cost of acquiring all the assets purchased.
• Annual after-tax net benefits or costs.
• Tax shield generated by purchasing depreciable
  assets.
• Tax shield lost due to the salvage of assets.
• Cash inflow from the salvage of the assets.
• Changes in NWC.
• Exclude financing costs!
• Two methods
• Spreadsheet method for (discounted) payback
  period
• Formula method for NPV, IRR and PI

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Spreadsheet Method (Project XY - Expansion
Example)

• Project XY requires an investment of 1000,
  generates revenues of 600, expenses of 300. The
  CCA rate is .25. Assume all cash flows occur at
  year end.
• The project will last for 5 years at which time
  the machinery will be useless. The firms tax
  rate is 36.
• Find the annual after-tax cash flows.
• What is the projects payback period?
• If the firms cost of capital is 10, what is the
  projects discounted payback period?

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Solution
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Spreadsheet Method Solution

• After-tax cash flow ignoring CCA 300(1-.36)192
• CCA1 (1000/2).25 125
• CCA2 1000(1-.125).25 218.75
• CCA3 1000(1-.125)(1-.25).25 164.06
• CCA4 1000(1-.125)((1-.25)2).25 123.05
• CCA5 1000(1-.125)((1-.25)3).25 92.29
• CF1 192 .36(125) 237
• CF2 192 .36(218.75) 270.75
• CF3 192 .36(164.06) 251.06
• CF4 192 .36(123.05) 236.30
• CF5 192 .36(92.29) 225.22

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Spreadsheet Method Solution page 2

• Cumulative CF first becomes nonnegative at year
  5. Thus payback period is 5 years.
• PV of CF1 215.5
• PV of CF2 223.8
• PV of CF3 188.6
• PV of CF4 161.4
• PV of CF5 139.8
• Cumulative PV of CF never becomes nonnegative.
  Thus project will never payback the investment
  inclusive of cost of capital.

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Formula Method (Use to calculate NPV, IRR and PI)

• 6 Step Method
• PV of initial investment (EE is equipment
  expenditure).
• PV of operating cash flows.
• PV of CCA tax shields.
• PV of tax shield.
• Lost of tax shields from selling asset at end of
  project.
• PV of salvage.
• PV of net working capital (- initial IncreaseNWC
  PV of DecreaseNWC at a later date)

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1. PV of Initial Outlay

• I initial (or time 0) investment.
• Cost of equipment, facilities and land purchased.
• All other costs related to investment.
• Increase in net working capital.
• Not all of these costs are depreciable land and
  net working capital are not depreciable, fixed
  assets are depreciable.

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2. PV of Operating Cash Flows

• t - tax rate
• k is firms cost of capital
• OCF1, OCF2...OCFn - before tax annual cash
  flows.
• Increased revenues, expenses
• Need to calculate after tax flows.
• Deviate from text and consider CCA tax shields
  separately.
• Present value of cash flows is

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3. PV of CCA Tax Shields Declining Balance

• Assume that there are always other assets in
  pool. This is the default assumption.
• PV of tax shields is a 2 step calculation
• PV of tax shields forever less
• PV of tax shields lost after disposition

Second term adjusts for half-year rule.
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4. Present Value of Salvage

• Present value of salvage is

• If the salvage price (S) is above the purchase
  price (P) the firm pays taxes on the capital
  gain. But since this is a rare event, we wont
  consider this in the NPV formula. Refer to CCA
  Primer.

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5 6. PV of Net Working Capital and Inventories

• NWC accounts receivable inventories
  accounts payable
• INWC0 increase in NWC at time 0 (negative CF)
• DNWCn decrease in NWC at time n (positive CF)
• Present value of any changes in NWC

• E.g. inventories increase by 1M at time 0 and
  decrease by 0.3M at time n INWCo 1M DNWCn
  0.3M

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Putting it All Together An Expansion Project

• Equations needed to calculate a project's NPV

NPV Initial cash flows PV of
after-tax cash operating income PV of CCA tax
shields PV of salvage PV of NWC changes
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Putting it All Together An Expansion Project
(Continued)
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Formula Method IRR and PI

• IRR Calculation
• In Excel Write NPV formula in one cell
  referencing discount rate in another cell.
• Use Goal-Seek Set NPV 0, find discount rate.
• That discount rate IRR
• PI Calculation
• Use formula PI (NPV/I) 1 where I is initial
  investment.
• NPV, IRR and PI all use same NPV Formula.

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Project XY (provided earlier) Find NPV, PI and
IRR

• NPV -I PVOCF PVCCATS
• I 1000
• PVOCF 300(1-.36)PVIFA(10,5) 727.83
• PVCCATS 1000((.25x.36)/(.25.10))(1.05/1.1)
  245.45
• NPV -26.72 consistent with discounted payback
  period calculation
• IRR Note where unknown discount rate is present
  in NPV formula.
• IRR 9 using Excels Goal Seek.
• PI (-26.72/1000) 1 0.973
• 3 criteria are consistent as expected
  independent project with only one cash flow sign
  change.

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Oddflew Example Expansion

• Oddflew Co. is considering investing 10M in a
  project. Its tax rate is 40 and its cost of
  capital is 12.33.
• 80 of the 10 million investment will be used to
  purchase machinery upon which CCA can be taken at
  30.
• The remaining 2 M represents the required
  increase in inventory and accounts receivable.
  This amount will not be liquidated upon project
  termination.
• The machinery is expected to have a salvage value
  of 2.5 million at the end of 6 years.
• The project is expected to produce pre-tax
  operating income of 1.5M at the end of the first
  year, and this amount is projected to increase by
  10 a year over the remaining 5 years of the
  project.
• Should Oddflew undertake this project?

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Oddflew Solution (see 2.3.Spreadsheets)

• Use NPV to answer question.
• I 10M
• PV after-tax operating CFs 4.564776M
• PVCCATS 1.7906M
• PVSV 1.244416M
• NPV -2.4M
• Calculate PI and IRR for practice.
• PI (-2.4/10) 1 0.76
• IRR 4.14
• All 3 criteria tell you that the project should
  be rejected. Why? Independent project with only
  one sign change in cash flows.

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Smith Example Expansion

• Smith Industries Ltd. is purchasing a fleet of
  trucks for 105,000 and will also pay 5,000
  acquisition costs.
• The trucks will be part of their class 10 pool of
  assets that has a CCA rate of 30.
• They have a useful life of 3 years and a net
  resale value of 10,000 at that time.
• Cash inflows and outflows are 80,000 and 20,000
  per year, respectively.
• T 40 and k 14.
• Should the fleet be purchased? Use NPV, PI and
  IRR.

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Smith Solution (see 2.3.Speadsheets)

• I 110K
• PV of after tax operating cash flows 83.5788K
• PVCCATS 26.31706K
• PVSV 6.749715
• NPV 6.6455K
• IRR 17
• PI 1.06
• All 3 criteria tell you that the project should
  be undertaken. Why the consistency? Independent
  project with only one cash flow sign change.

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Replacement Projects

• Think Incremental!
•  STEP 1 Incremental Initial Investment
• ?EE0 Equipment ExpenditureNEW Salvage
  ValueOLD, at time 0.
• ?NWC0
•  STEP 2 Incremental Operating Cash Flows
• ?Before tax OCF.
• STEP 3 Incremental Ending Cash Flows
• Change in Salvage ?SSNEW -SOLD, at time n
  (plus any tax effects).
• ?NWC0

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Putting it All Together Replacement Project
Were not going to consider terminal loss,
capital gains , and recapture of depreciation in
the formula..
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Replacement Projects contd.

• The incremental cash flows that are important
• Cash flows related to the new equipment less cash
  flows related to the old equipment
• For incremental initial flows, consider
• The cost of new equipment, facilities and land
  purchased
• Opportunity costs net of taxes
• The increase in net working capital
• Funds realized from the sale of replaced assets
  plus tax effects of the sale or disposal of the
  replaced asset
• For after-tax incremental operating flows
  consider
• The changes in cash inflows
• The changes in cash outflows
• The changes in capital cost allowance
• In calculating the incremental after-tax ending
  flows consider
• Funds from reselling any asset
• Tax benefits and liabilities from resale
• Funds if working capital is released
• If the NPV of the incremental cash flows is
  positive, the existing asset should be replaced

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Jones Example Replacement

• Jones Industries owns old machinery that was
  purchased 3 years ago at a cost of 250,000.
• It belongs in CCA class 8, with a CCA rate of
  20. The equipment will last 5 more years, at
  which time its net resale value will be 7,500,
  but it could be sold now to net the firm 20,000.
• The new machinery will reduce yearly expenses
  from 255,000 to 100,000, but would require a
  10,000 increase in inventory. This increase in
  inventory will be liquidated at the end of 5
  years.
• The new machinery costs 500,000 and belongs in
  class 8. It has a life of 5 years, and its net
  resale value then will be 25,000.
• T 40 and k 15. Should Jones Industries
  replace their old machinery?

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Jones Solution (see 2.3.Spreadsheets)

• All NPV components are incremental.
• Incremental means new minus old.
• I 480K 500K 20K
• PVOCF 311.7504K PV after-tax of(255K-100K)
• PVCCATS 100.5703K
• PVWCE (working capital effects) -5.02833K
• PVSV 8.700593 PV of (25K 7.5K)
• NPV -64.0069K
• IRR 10
• PI 0.869 (-64.0069/(48010)) 1

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POS Bid Example

• A large retailer has asked you to submit a bid to
  supply POS credit checking systems. 20 systems
  are required per year for 3 years.
• To manufacture the POS systems you will need to
  invest in new equipment that costs 1M, on which
  you will claim CCA at a rate of 25. No salvage
  value is envisioned. Assume that there are other
  assets in the pool.
• Labour and material cost per POS system equals
  0.1M. The tax rate is 44.
• What price should you bid per POS system if you
  need a 16 return on you investment?

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POS Bid Solution

• Write down NPV formula involving P (bid price per
  system).
• Set NPV 0 and solve for P.
• PVCCATS 0.2497897M
• NPV -1M PVCCATS 20M(P-0.1)(1-.44)PVIFA(16,
  3)
• P .129825M satisfies NPV 0 requirement.
• Bid price per system 129,825

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Sensitivity vs. Scenario Analysis

• NPV calculations can be used to for break even
  calculations.
• Discover sensitivity of NPV to key project inputs
  such as project life, number of units sold, cost
  of capital.
• Scenario analysis is sensitivity analysis with
  more than one variable changing in value. Values
  of the variables are correlated. E.g., in an
  economic boom scenario price per unit sold and
  of units sold will both be high while in an
  economic recession scenario both of these
  variables will be low.

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Some Complications- Unequal lives

• Suppose firm is deciding between 2 mutually
  exclusive projects with different project lives?
• Choose 1 of 2 machines to upgrade production
  Machine L has a useful life of 5 years and
  Machine S has a useful life of 3 years.
• If comparison is between one Machine L versus one
  Machine S, calculate NPV as before.
• But if comparison is between two policies Always
  use Machine L versus always use Machine S, must
  use either Replacement Chain or EANPV.
• Replacement Chain approach Replicate projects
  over common time horizon then calculate the NPV
  of the chain.
• Equivalent Annual NPV Convert NPV to an annuity.

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L vs. S Example Unequal Lives

• A firm needs to decide between 2 mutually
  exclusive projects. The firm wants to compare 2
  policies always use L versus always use S. The
  after-tax CFs are

• Which project should it undertake if its cost of
  capital is 9?

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Unequal Lives The EANPV Criterion

• Problem with comparing the NPVs of the 2
  projects You are comparing one S versus one L.
  Thats not the issue!
• Instead, use the equivalent annual NPV approach
• Replace the uneven stream of cash flows over a
  projects lifetime with a level annuity, such
  that the two streams have the same present value.
• For a j year project with a present value of
  NPVj, the equivalent annual annuity Aj solves

• Compare the equivalent annual NPVs of both
  projects and pick the project with the higher
  EANPV.

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EANPV applied to L vs. S Problem

• NPVL 6.344769K vs. NPVS 5.5633K. If compare
  one L versus one S, L is better.
• But this comparison does not address the issue.
• We need to compare continuing commitments to L
  versus S. Correct criterion is EANPV.
• EANPVL 6.344769K/PVIFA(9,5) 1.631K
• EANPVS 5.5633K/PVIFA(9,3) 2.1978K
• A continuing commitment to L is an annuity of
  1.631K whereas continuing commitment to S is an
  annuity of 2.1978K.
• If comparing policies, S is better.

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Equivalent Annual NPV (EANPV) versus Replacement
Chain Method

• EANPV approach is necessary when comparing
  mutually exclusive policies.
• However, this approach does not allow for the
  impact of inflation or changes in technology.
• If there are changes in project cash flows in the
  future (1st L differs from 2nd L), you must use
  replacement chain method rather than EANPV.
• In replacement chain method, repeat one or both
  projects until both project chains run for the
  same length of time, and then compare the NPV of
  the two chains of projects.
• Common time horizon is lowest common multiple.

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L vs. S Replacement Chains

• Dont need replacement chains since no changes in
  project cash flows 1st L identical to 2nd L,
  etc.
• Used purely to illustrate replacement chains.
• Compare chain of 3 Ls with chain of 5 Ss.
• NPV of chain of 3 Ls 6.344769K ( 1
  (1.09)-10) 13.148K
• NPV of chain of 5 Ss 5.5633K (1
  (1.09)-12) 17.713K
• Policy S is better (same answer as EANPV).
• Replacement chain approach consistent with EANPV
  if no changes in project CFs (1st L identical to
  2nd L, etc.)

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Example Replacement Chain Method

• A firm, with a cost of capital of 10, is
  submitting a bid to the government to produce
  widgets for 4 years. 2 options are available to
  the firm.
• Machine A has an after tax installation cost of
  50,000, but is expected to generate after tax
  returns of 20,000 a year for 4 years. After 4
  years, the machine has no salvage value.
• Machine B has only a 2 year lifetime, and its
  after tax installation cost is 30,000. For the 2
  years, it is expected to produce after tax
  returns of 20,000 a year. When it is replaced
  after 2 years at a cost of 30,000, the firm
  expects to generate after tax returns of 22,000
  a year for 2 years because of expertise gained in
  the first 2 years.
• Should the firm submit a bid for the contract?
  If yes, should they plan to use machine A or
  machine B?

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Replacement Chain Solution

• EANPV is not viable 1st and 2nd Bs not
  identical.
• Note presence of qualifier after-tax. Dont do
  CCA!
• NPV of 1 A 13,397
• NPV of 2 Bs 4,710.7 6,761.8 11,473
• 6.761.8 Present value of 8,181.8 (the NPV of
  the 2nd B that is generated at start of 3rd year)
• Conclusion A is better than B.