CHAPTER12: CAPITAL INVESTMENT DECISIONS

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CHAPTER12CAPITAL INVESTMENT DECISIONS
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INTRODUCTION

• Linear programming models
• company has finite production capacity
  (machinery resource constraints)
• If the demand suddenly increase, the company
  would be unable to meet this extra demand without
  increasing the amount of machine time that is
  available for production
• One way of meeting the additional product demand
  is for the company to buy a piece of machinery
  with greater production capacity.
• Buying new equipment involves decisions making
  over future planning time periods

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• Break-Even model
• Production capacity of the company is limited
  (250 units of output per production time period).
  
• If the demand for the company's product is
  greater than 250 units, then the company would be
  faced with the dilemma of how to handle this
  excess demand.
• For a short-term increased demand
• Introducing overtime working
• Raising the price of the product
• For a long-term increased demand
• Expanding the existing production facilities
• Building a bigger scale production plant.
• Company is faced with a decision which involves
  the costs and benefits that will accrue to the
  company over some future time horizon.

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COMPOUNDING

• Notation for different time periods (yearly
  basis)
• t0 --- to stands for time period zero and
  represents right now
• t1 ---to stands for time period one and
  represents 1 year into the future
• t2 ---to stands for time period two and
  represents 2 years into the future
• tn ---to stands for time period n and represents
  n years into the future , where n can take on any
  value from 0,1,2...

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• Initial capital or lump sum
• A financial investor has a sum of money to
  invest in time period t0, for example 100
• If the investor deposits his 100 in an interest
  bearing bank account, how much will he have after
  1 year.
• Suppose the going rate of interest is 10.

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• For year 1, the value of the investment to the
  investor
• (what he starts with) (the interest on what he
  starts with)
• 100 10x100 100(110) 110
• t010gtt1
• 100 gt 10010 of 100
• 100(110)
• 110

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• For year 2, the value of the investment to the
  investor
• (what he starts with at the beginning of year 2)
  (the interest earned over year 2)
• 110 10xl 10 110(110) 121
• t0 10 gt t1 10 gt t2
• 100 gt 10010xl00
• 100(110)
• 110 gt
  11010x l10
• 
  110(110)
• 
  121
• 110(110) 100(l10)(l10)
• 100(l10)2
• 121

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• For year 3, the value of the investment to the
  investor
• t0 10gt t1 10gt t2 10gt t3
• 100 gt 10010xl00
• 100(110)
• 110 gt 11010xll0
• 
  110(110)
• 
  100(110)2
• 
  121 gt 12110xl21
• 
  121(110)
• 
  100(l10)3
• 
  133.1

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• The value of the investment at different time
  periods can be summarised as follows
• t0 ----------gt t1 -------------gt t2
  -------------gt t3
• 100 100(l10)1 100(l10)2 100(l10)3
• For year n, General compounding idea as follows
• For a given initial lump sum A
• For a given term of investment n
• For a given rate of interest i
• Future value (FV) of the investment is given by
• FV A(li)n

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DISCOUNTING

• Discounting is the reverse side of the coin to
  compounding
• With discounting the time direction is reversed.
• For the value of a sum of money in the future, we
  want to know what this future sum is worth to us
  right now.
• Considering the position of a money lender, A
  client would like to borrow some money in order
  to finance some immediate expenditure, however
  the client does have an asset that will be
  available , not to-day, but in 1 years time. At
  this time the asset will have a value of 100.
  Thus the client has an asset - 100 available in
  one years time -but unfortunately for him he
  wants money NOW. The client can thus pose the
  following question to the money lender

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• How much will you be prepared to lend me right
  now given that I can pay you back 100 in one
  year time?
• For money lender, its a compounding problem for
  1 year, which can be represented as
• t010gtt1
• ? gt ?(110) 100
• ?100/(110) 90.91
• 90.91 is called the discounted value or the
  present value (PV) of 100 in 1 year.

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• The inverse relationship between the present
  value of a future sum of money and the going rate
  of interest
• If the interest rate increases, the denominator
  in the expression for ? increases, and results
  in a fall in the PV.
• If the rate of interest falls, the denominator
  falls , and results in the PV of a future sum of
  money will rise.
• For 2 years,
• t0 ------gt t1-----gt t2
• ?-----------------gt ?(l10)2 100
• ?100/(110)2
  82.65

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• t0 lt10 t1 lt10t2
• 90.91 lt --- 100
• 82.65 lt --------------------100
• 100 in 1 year is worth 90.91 to-day
• 100 in 2 years is worth 82.65 to-day.
• General rule for discounting can be represented
  as follows
• t0 lt --------------------t1 lt --------------t2
• 100 /(l10)1 lt---- 100
• 100 / (l10)2 lt ----------------------100
• For 3 year, PV 100/(l10)3
• For 4 year, PV 100/(l10)4

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• For a given sum of money A, due to be paid n
  years into the future, and a going rate of
  interest of i per year, then the PRESENT VALUE
  of this future amount is given by
• i) numerator --- the fixed amount of money that
  is being promised in the future.
• ii) denominator ---one plus the going rate of
  interest in brackets and the brackets are raised
  to a power determined by how far in the future
  the money is promised.

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NET PRESENT VALUE

• an investment project
• A large amount of money is spent RIGHT NOW
• Operational benefits are spread out over a number
  of years into the future.
• How long will the investment project last?
• A 'new PC ---life of 3 years
• A 'new' football star---future of 8 years
• An offshore oil rig--- for 40 years.
• In general terms we can model a project that has
  a life span of N years, that ist0 ----gt t1----gt
  t2----gt t3---gt t4 ---gt tN

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Project Costs

• Initial set-up cost or CAPITAL EXPENDITURE
• a single payment to get the project started
• construction of a factory.
• Operational costs
• Labour costs
• Material costs
• and son on

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• In general terms we can indicate this as
  follows
• Time t0 t1 t2 t3 ... tN0
• Costs C0 C1 C2 C3 ... CN
• Co ---costs in time period 0
• C1 ---costs in time period 1
• C2 ---costs in time period 2
• CN, the costs involved in the final year of the
  capital project.

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Project Benefits

• Project revenues are called as BENEFITS
• Generally, the benefits in period 0 will be 0
• Bi--- Benefit in period I
• Grevs---Gross Revenues

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• Profit Taxes---T represents the tax rate on
  company profits.
• Payment of tax is CONDITIONAL
• GRevs gt 0, pay taxes
• GRevs lt 0, pay no taxes

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• Notation (Bt-Ct)
• If GRevs is positive for any particular period ,
  then tax has to be paid. hence NRev will be less
  than GRevs.
• If GRevs is zero or negative, then no tax is
  paid. NRev will be the same as GRev.

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• NET REVENUE (NRevs)
• NRevs GRevs Tax
• NRevs (Bn-Cn) - T(Bn-Cn), for n 1,2,3...,N
• NRevs (Bn-Cn) - T(Bn-Cn)
  (Bn-Cn)(1-T)

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Sensitivity Issues

• Costs
• Inverse relationship between OPERATIONAL COSTS
  and project PROFITABILITY
• For example Labour costs.
• If the cost of labour rises, GRevs and hence
  NRevs will fall, the project will become less
  profitable.
• If a decrease in labour costs, NRevs will rise
  thus making the project more profitable.

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• Revenues
• a higher price can be charged for the same
  output, revenue will rise an increase in Grevs
  and Nrevs, hence an increase in the
  profitability of the project.
• Tax
• If the tax rate goes up, NRevs will decrease and
  lead to a reduction in the overall profitability
  of the project.

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THE NET PRESENT VALUE IDEA .

• In order to work out the value of a future amount
  of money in terms of the base period t0, we have
  to DISCOUNT or find the PRESENT VALUE of that
  future sum.

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• The idea of NET PRESENT VALUE can be written as
  THE FUNDAMENTAL NPV FORMULA

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• The NPV value is a measure of the overall
  profitability of the investment project. The NPV
  figure can be positive or negative. In terms of a
  decision making rule we have the following
• If NPV gt 0, then the project is a worthwhile
  investment opportunity.
• If NPV lt 0 , then the project is NOT a worthwhile
  investment opportunity.

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• The interpretation of NPV a net profitability
  figure what the project will actually earn for
  the company after all costsinitial capital costs
  
• future interest payment costs
• yearly operating costs
• yearly tax bills
• have been paid in full.
• The higher is the NPV value then the more
  profitable, and hence more desirable, is the
  capital investment project.

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• Important input the rate of interest (i)
• If i rises, NPV will fall.
• If i falls, NPV will rise.
• An inverse relationship between the level of the
  rate of interest and the NPV of an investment
  project.

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A PRACTICAL EXAMPLE

• A company is considering making a line extension
  to its range of products.
• Lump Sum 165,000.
• A market life of 5 years.
• Benefits
• 105,000 after 1 year
• After year 1, to grow at 20 per annum.

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• Operating costs
• Budget in the first year 25,000
• After year 1, to grow annually at 4.5.
• Tax rate
• Current Pay tax of 30 on any profits
• In future, in the range (27 - 33 )
• The rates of interest
• Current 12
• In future, in the range ( 10 - 14 )

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• Conceptual Paper Worksheet

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• IF function
• IF( CONDITION, A, B)
• IF(D4 gt 0, A2D4,0)
• A2D4 is the Tax Rate G-REV and is the tax
  payable if G-REV is gt0
• 0 is the tax payable if G-REV is NOT gt 0

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• NPV function
• NPV1NPV(A5, E6I6)
• NPV NPV1 D6

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For this project the Net Present Value is
145,130, so is positive. By the NPV decision
rule this project is viable.
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MODELLING THE UNCERTAINTY IN THE PROBLEM

• Tax Rate Sensitivity
• If the Tax-Rate varies between 27 and 33 in
  step 1, How does NPV change?
• ToolTable submenu
• CWP for sensitivity
• Interpretation For all Tax-Rates the NPV
  remains positive, so that for Tax-Rates in the
  range 27 to 33 the project remains viable.

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• Interest Rate Sensitivity
• Interest rates varies between 10 and 14 in
  steps of 0.5 , how does NPV changes?

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• Combined sensitivity in Tax and Interest Rates
• A two way table can be set up quite easily, with
  the Interest Rates along the row and the
  Tax-Rates down the columns as shown in the
  partial CPW below

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• Interpretation
• At all combinations of Tax-Rates and
  Interest-Rates the NPV remains positive, by the
  NPV decision rule the project is viable at all
  combinations of Tax-Rate and Interest-Rate within
  the ranges 27-33 and 10.0 to 14.0. Further
  since NPV is quite large this suggests a robust
  project

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