ECF 2222 CORPORATE FINANCE II

1
ECF 2222 CORPORATE FINANCE II

• WEEK 2
• NPV EXTENDED APPLICATION OF PROJECT EVALUATION
  METHODS

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ECF 2222 CORPORATE FINANCE II

• WEEK 2 NPV EXTENDED
• SCOPE AND OBJECTIVES
• Understand the steps in the capital expenditure
  process
• Revisit the Discounted Cash Flow Methods
• Identify the two types of Investment Projects
• Issues in defining the relevant cash flows
• Comparing Mutually Exclusive Projects with
  different lives
• Decisions on retirement or replacement decision

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Understand the steps in the capital expenditure
process

• Broadly speaking, the capital expenditure process
  involves the following steps
• STEP 1 The generation of investment proposals
• STEP 2 The evaluation and selection of those
  proposals
• STEP 3 Approval and control of expenditures
• STEP 4 The post-completion audit of investment
  projects

4
Revisit the Discounted Cash Flow Methods

• The two most frequently employed discounted cash
  flow (DCF) methods are
• 1. The net present value (NPV) method
• 2. The internal rate of return (IRR) method

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Net Present Value (NPV)

• Difference between the PV of the net cash flows
  (NCF ) from an investment, discounted at the
  required rate of return, and the initial
  investment outlay.
• Measuring a projects net cash flows
• forecast expected net profit from project, making
  an adjustment for non-cash flow items
• estimate net cash flows directly

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Calculation of NPV

• where
• C0 initial cash outlay on project
• Ct net cash flow generated by project at
  time t
• n life of the project
• k required rate of return

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Net Cash Flow

• Cash inflows
• receipts from sale of goods and services
• receipts from sale of physical assets
• Cash outflows
• expenditure on materials, labour, and indirect
  expenses for manufacturing
• selling and administrative
• inventory and taxes

8
Evaluation of NPV

• NPV method is consistent with the companys
  objective of maximising shareholders wealth.
• A project with a positive NPV will leave the
  company better off than before the project and,
  other things being equal, the market value of the
  companys shares should increase.

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Evaluation of NPV

• Decision rule for NPV method
• Accept a project if its net present value is
  positive when the projects net cash flows are
  discounted at the required rate of return.

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Internal Rate of Return (IRR)

• Discount rate that equates the present value of a
  projects net cash flows with its initial cash
  outlay that is, the discount rate at which the
  net present value is zero.
• The IRR is compared to the required rate of
  return (k ). If IRR gt k the project should be
  accepted.

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Calculation of InternalRate of Return

• where
• C0 initial cash outlay on project
• Ct net cash flow generated by project at
  time t
• n life of the project
• r the internal rate of return

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Multiple and Indeterminate Internal Rates of
Return

• Conventional projects have a unique rate of
  return.
• Multiple or no internal rates of return can occur
  for non-conventional projects with more than one
  sign change in the projects series of cash
  flows.
• Under IRR accept the project if it has a unique
  IRR gt the required rate of return.

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Identify the two types of Investment Projects

• 1. Independent Investments
• Projects that can be considered and evaluated in
  isolation from other projects.
• This means that the decision on one project will
  not affect the outcomes of another project.
• 2. Mutually exclusive investments
• Alternative investment projects, only one of
  which can be accepted.
• For example, a piece of land is used to build a
  factory, which rules out an alternate project of
  building a warehouse on the same land.

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Choosing Between the Discounted Cash Flow Methods

• Independent Investments
• For independent investments, both the IRR and NPV
  methods lead to the same accept/reject decision,
  except for those investments where the cash flow
  patterns result in either multiple or no internal
  rate of return.

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Choosing Between the Discounted Cash Flow Methods

• Evaluating Mutually Exclusive Projects
• NPV and IRR methods can provide different ranking
  order.
• The NPV method is the superior method for
  mutually exclusive projects.
• Ranking should be based on the magnitude of NPV.

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EXAMPLE 1- Choosing DCF MethodsPg. 141,
Business Finance

• Two projects, C and D, have the same initial
  cash outlays and the same lives but different net
  cash flows, as shown in the table below.

What are the IRR and NPV for both projects?
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EXAMPLE 1 - SolutionPg. 141, Business Finance

- Using both IRR and NPV analysis, the projects
should be undertaken in their own right. -
However, NPV method should be used in line with
maximising shareholders wealth.
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Application of the Net Present Value Method

• Focus on incremental cash flows
• Is it a cash item?
• Will the amount of the item change if the project
  is undertaken?
• Exclude sunk costs
• Costs already incurred are irrelevant to future
  decision making.
• Decisions on whether to continue a project should
  be based only on expected future costs and
  benefits.

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Application of the Net Present Value Method
(cont.)

• Beware of allocated costs
• Any costs that will not change as a result of the
  project should be excluded from the analysis.
• Exclude financing charges
• The required rate of return used to discount cash
  flows incorporates the cost of equity and debt.
  Including financing charges in the cash flows
  would be double counting.

20
Application of the Net Present Value Method
(cont.)

• Include residual values
• This will provide a cash flow at end of project.
• Consistency in the treatment of inflation
• Estimate cash flows based on anticipated prices,
  and discount the cash flows using a nominal rate
  or
• Estimate cash flows without adjusting them for
  anticipated price changes, and discount the cash
  flows using a real rate.

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Application of the Net Present Value Method
(cont.)

• Recognise the timing of the cash flows
• Just as in the valuation of debt securities such
  as bonds, the exact timing of cash flows can
  affect the valuation of an investment project.
• A simplifying assumption is that net cash flows
  are received at the end of a period.

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Application of the Net Present Value Method
(cont.)

• Include residual values
• This will provide a cash flow at end of project.
• Consistency in the treatment of inflation
• Estimate cash flows based on anticipated prices,
  and discount the cash flows using a nominal rate
  or
• Estimate cash flows without adjusting them for
  anticipated price changes, and discount the cash
  flows using a real rate.

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EXAMPLE 2 Incorporating InflationPg. 162,
Business Finance

• Assume that an investment of 1000 is expected
  to generate cash flows of 500, at constant
  prices, at the end of each of 3 years. Assume
  also that prices are expected to increase at the
  rate of 10 p.a and that the nominal required
  rate of return is 15. What is the projects NPV?

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EXAMPLE 2 SolutionPg. 162, Business Finance

• There are two approaches
• 1. Adjust the net cash flows according to the
  inflation rate,

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EXAMPLE 2 Solution (cont) Pg. 162, Business
Finance

• 2. The second approach uses the REAL rate of
  return to discount the net cash flows,
• The real rate of return may be expressed in
  terms of nominal rate as follows
• Where i real rate of return p.a i
  nominal rate of return p.a
• p anticipated rate of inflation p.a

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EXAMPLE 2 Solution (cont) Pg. 162, Business
Finance

• Therefore,
• The NPV is calculated as follows

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EXAMPLE 3 Solution Pg. 163, Business Finance

• Net Cash Flows (000)
• ITEM Yr0 Yr1 Yr2 Yr3 Yr4 Yr5
• 1. Initial Outlay (400)
• 2. Sale of Equipment 157.5
• 3. Factory
• (a) Cancel Lease (15)
• (b) Rent forgone (15) (15) (15) (15) (15)
• 4. Market Research (50)
• 5. Addns to Cur. Assets (22.5) 22.5
• 6. Net Cash flows 200 250 325 300 150
• Total (437.5) 135 235 310 285 315
• Discount factor (10) 1.00000 0.90909 0.82645 0.7
  5131 0.68301 0.62092
• PV of NCF (437.5) 122.73 194.21 232.91 194.66 19
  5.59
• NPV 502.60
• Therefore, the company should add this new
  product to its product line.

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Mutually Exclusive Projectswith Different Lives

• One project may end before the other.
• How to compare?
• Assume that the company will reinvest in a
  project identical to that currently being
  analysed Constant Chain of Replacement
  Assumption.
• OR
• Make assumptions about the reinvestment
  opportunities that will become available in the
  future.

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Mutually Exclusive Projectswith Different Lives
(cont.)

• The second approach is the most realistic and
  could be implemented where the future investment
  opportunities are known.
• However, in practice, this approach would be
  impossible to implement unless managers have
  extraordinary foresight.
• Therefore, the constant chain of replacement
  approach is often used.

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Constant Chain of Replacement Assumption

• Each project is assumed to be replaced at the end
  of its economic life by an identical project.
• Valid comparison only when chains are of equal
  length.
• This can be achieved by
• lowest common multiple method
• constant chain of replacement in perpetuity
• equivalent annual value method

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Chain of Replacement and Inflation

• Chain of replacement methods assume that at the
  end of the projects life, it will be replaced by
  an identical project.
• In an inflationary environment the nominal cash
  flows will obviously not be the same.
• All cash flows and the required rate of return
  should be expressed in real terms.

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Constant Chain of Replacement in Perpetuity

• Assumes both chains continue indefinitely
• where NPV0 net present value of each
  replacement

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Equivalent Annual Annuity (EAA)

• Unequal lives could do LCM, bit messy
• Convert to annuity equivalent over life of
  project what the effective cost is each year
• EAA method assumes projects can be repeated to
  (at least) the lowest common multiple of their
  lives.
• We can extend to repeating indefinitely

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Equivalent Annual Value Method (EAV)

• Involves calculating the annual cash flow of an
  annuity that has the same life as the project and
  whose present value equals the net present value
  of the project.

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EXAMPLE 4 LCMPg. 165, Business Finance

• Assume that a company is considering the
  purchase of two different pieces of equipment, A
  and B, that will perform the same task and
  generate the same cash inflows. Therefore, A and
  B can be compared on the basis of their cash
  outflows.
• Assuming a required rate of return of 10,
  calculate the PV of costs of A and B.

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EXAMPLE 4 SolutionPg. 165, Business Finance

• The present values of the costs of A and B are as
  follows
• PV of costs for A 15000 6000/1.1
• 20455
• PV of costs for B 20000 10000
• 44869
• Since A would incur the smaller costs, it should
  be purchased. However, this ignores the fact that
  the projects have unequal lives.

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EXAMPLE 4 Solution (cont)Pg. 165, Business
Finance

• Assuming a constant chain of replacement,
• In this case,
• PV of costs for A 15000 21000/1.1
  21000/(1.1)2 6000 (1.1)3
• 55954
• Based on this comparison, the PV of costs for A
  (55954) gtPV of cost for B (44869), therefore B
  shhould be purchased.

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EXAMPLE 5 CCR and EAVPg. 168, Business
Finance

• Suppose that two machines A and B are mutually
  exclusive projects and have the characteristivs
  shown in the table below. Assuming a required
  rate of retrun of 10 p.a, which machine should
  be purchased?

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EXAMPLE 5 SolutionPg. 168, Business Finance

• The NPV of Machine A at time zero is
• NPVA0 -1000010000/1.123000/(1.1)225000/(
  1.1)3
• 36882.04
• The NPV of Machine B at time zero is
• NPVB0 -1000012000/1.115000/(1.1)225000/(
  1.1)3
• 30000/(1.1)430000/(1.1)5
• 51206.70
• The NPV of infinite chains of replacement are
• NPVA8 (36882.04)(1.1)3/(1.1)3-1
  148308.14
• NPVB8 (51206.70) (1.1)5/(1.1)5-1
  135081.98
• Therefore, Machine A should be accepted although
  its NPV (over its 3-year life) is less than the
  NPV of Machine B.

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EXAMPLE 5 Solution (cont)Pg. 168, Business
Finance

• Using the equivalent value method, it is found
  that
• EAVA 14830.81
• or kNPVA8
• (0.1)(148308.14)
• 14830.81

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EXAMPLE 5 Solution (cont)Pg. 168, Business
Finance

• For Machine B
• EAVB 13508.20 or kNPVA8
• (0.1)( 135081.98)
• 13508.20
• Therefore, Machine A would provide the investor
  with receiving payments of 36882.04 every 3
  years, a single payment of 148308.14 now or
  14830.81 forever.

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EXAMPLE 6 CCR Pg. 169, Business Finance

• Assume that Madison Company, which operates a
  fleet of trucks, is considering replacing them
  with a new model.
• ITEM Old Trucks New Trucks
• 1.Net cash flows 45000p.a 50000p.a
• 2.Estimated life 2 years 4 years
• 3.Disposal (a) at present 10000
• (b) in 4 years NIL 10000
• 4.Cost of new trucks 60000
• Real required rate of return 10 10
• Advise management on these two proposals
• (a) Replace old trucks now and assume that the
  trucks are operated for 4 years and replaced in
  perpetuity or
• (b) Replace the old trucks in 2 yrs time and
  assume that the new trucks are operated for 4
  years, and replaced in perpetuity.

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EXAMPLE 6 Solution Pg. 169, Business Finance

• (a) Replace the old trucks now, operate new
  trucks for 4 years in perpetuity.
• The NPV of a new truck is
• 105323.43

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EXAMPLE 6 Solution (cont)Pg. 169, Business
Finance

• The PV of an infinite chain of these trucks is
  therefore
• In addition, at the start of this chain Madison
  Company receives a cash inflow of 10000 from the
  disposal of the old truck. Therefore, the total
  NPV for this porposal is 33226510000342265.

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EXAMPLE 6 Solution (cont)Pg. 169, Business
Finance

• (b) Replace the old trucks in 2 years time,
  operate the new trucks for 4 years, and replace
  them in perpetuity.\
• For the new trucks the NPV 8 is equals to the NPV
  8 from (a) discounted by two time periods to Year
  0
• 332265/1.12 274599.17
• NPV of operating the old truck for first two
  years
• 45000/1.1 45000/1.12
• 78099.177
• Total NPV 274599.17 78099.17 352698.34
• Therefore, since (b) has a higher NPV than (a),
  management should replace trucks in 2 years
  time.

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Is The Chain of Replacement Method Realistic?

• The assumption that the machines replaced and the
  services they provide are identical in every
  aspect is unrealistic.
• The impact of such assumptions is reduced by the
  fact that their cash flows are years in the
  future and will be discounted to a present value.
• However, it may be more unrealistic for
  management to make predictions on replacement
  projects years into the future.

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Deciding When to Retire (Abandon) or Replace a
Project

• Retirement Decisions
• Situations where assets are used for some time,
  and then it is decided not to continue the
  operation in which the assets are used.
  Therefore, the assets are sold and not replaced.
• Replacement Decisions
• Situations where a particular type of operation
  is intended to continue indefinitely. The company
  must decide when its existing assets should be
  replaced.

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Retirement Decisions

• Want to determine, during the life of a project,
  whether the project is still worthwhile.
• NPV rule is the appropriate tool for retirement
  decisions.
• A project should be retired if the NPV of all its
  future net cash flows is less than zero.

49
EXAMPLE 7 Retirement DecisionsPg. 172,
Business Finance

• Mortlake Ltd owns a machine that is 6 years old
  and has an estimated remaining physical life of
  nomore than 2 years. The table below shows the
  net cash flow and residual value estimates for
  the machine.
• The required rate of return is 10. When should
  the machine be retired?

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EXAMPLE 7 SolutionPg. 172, Business Finance

• To run the machine for 1 more year,
• NPV -12000 (80006000)/1.1
• 727
• To run the machine for 2 years,
• NPV -120008000/1.1 5000/1.12
• -595
• Therefore, the machine should be retired at the
  end of the seventh year.

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Replacement Decisions

• The constant chain of replacement method may be
  used to evaluate replacement decisions.
• Two cases of replacement
• identical replacement
• non-identical replacement
• Identical Replacement
• Choose the replacement frequency that maximises
  the projects net present value for a perpetual
  chain of replacement, or maximises its equivalent
  annual value.

52
EXAMPLE 7 Replacement DecisionsPg. 173,
Business Finance

• A machine costs 20000 and has an estimated
  useful life of 5 years. The net cash flows are
  12000 in the first year, decreasing by 500 each
  year as a result of higher maintenance costs.
  Also, as the machine becomes olders, its residual
  value will decline as shown in the table below.
  The required rate of return is assumed to be 10.
  Management wishes to know when the machine
  should be replaced,
• Year Inflows Residual Value (4)
• 1 12000 16000
• 2 11500 14000
• 3 11000 12000
• 4 10500 6000 5 10000 NIL

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EXAMPLE 7 SolutionsPg. 173, Business Finance

• The NPVs for the respective years in use are as
  follows
• NPV1 -20000 (12000 16000)/1.1
• 5455
• NPV2 -20000 12000/1.1 (11500
  14000)/(1.1)2
• 11983
• NPV3 -20000 12000/1.1 11500/1.12
  (1100012000)/1.13
• 17693
• NPV4 -20000 12000/1.1 11500/1.12
  11000/1.13 (105006000)/1.14
• 19947
• NPV5 -20000 12000/1.1 11500/1.12
  11000/1.13 10500/1.14 10000/1.15
• 22059

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EXAMPLE 7 Solutions (cont)Pg. 173, Business
Finance

• However, the NPV cannot be compared because they
  are based on different lives. This can be
  overcome by assuming a constant chain of
  replacement.
• Using the formula,
• NPV(1, 8) 60000
• NPV(2, 8) 69048
• NPV(3, 8) 71148
• NPV(4, 8) 62928
• NPV(5, 8) 58190
• These results show that the machine should be
  replaced after 3 years.

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Replacement Decisions (cont.)

• Non-identical ReplacementWhen should the old
  machine be discarded in favour of the new one?
• First, determine the optimum replacement
  frequency for the new machine, based on identical
  replacement.
• Second, the equivalent annual value (EAV ) of the
  new machine at its optimum replacement frequency
  is compared with the NPV of continuing to operate
  the old machine.

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Replacement Decisions (cont.)

• The changeover should be made when the NPV of
  continuing to operate the old machine for one
  more year is less than the EAV of the new
  machine.