Capital Budgeting

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• Capital Budgeting Investment Analysis
• Decisions on acquisition of property, plant
  equipment are called capital budgeting decisions.
  They differ from other decisions cos
• (1) they usually involve large amounts of money,
• (2) once undertaken they are normally
  nonreversible,
• (3) they involve long-run commitments that can
  influence the earnings of the firm for many
  years.
• (4) amount timing of the costs benefits from
  each differ.
• To ensure wise investment decisions mgers must
  have procedures to
• (1) determine the amount of capital required for
  investment,
• (2) develop a forecast of added earnings
  benefits that will occur,
• 3) selecting an objective method to evaluate the
  alternatives.

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• General Considerations or Principles for Managers
• 1. Future Earnings Investments affect firms
  future profitability, thus mgers need to
  determine amount timing of the actual earnings
  costs. This means mgers shld analyze future
  earnings of all capital budgeting using cash flow
  analysis in which
• a. Larger benefits/earnings are preferred to
  smaller ones
• b. Early benefits are preferred to later ones
• c. Safety is preferred to risks.
• Evaluating Investment Alternatives without
  Consideration of the Time Value of Money
• Capital investments affect a firm's earning
  power, growth survival. Mgers can rely on
  techniques that do not consider the time value of
  money to evaluate the acceptability of investment
  opportunities. These include

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• 1. Payback methodIts used to determine number of
  periods required before sum of earnings from an
  investment equals the initial outlay. If net
  earnings are constant each year, then
• Payback period P I (investment)
  E (earnings)
• e.g. a 5,000 investment with yields/benefits of
  1,000/yr will have a payback of 5 yrs (5,000/
  1,000 )
• Mgers normally set MAX length for payback period
  accept all investments with paybacks ? the
  MAX.
• Advantages Easy to use quickly identifies
  investments with most immediate cash returns

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• Disadvantages
• 1. It ignores cash flows occurring after end of
  the payback period.
• 2. It ignores timing of cash flows during the
  payback period. e.g. Selecting A in the
  table below using PB ignores the higher returns
  form B in yrs 56 as well as its greater total
  return.
• Analysis of Investments A B (1000) Using
  Payback Method
• AFTER-TAX BENEFITS
• YEAR A B
• 1 500 100
• 2 400 200
• 3 300a 300
• 4 200 400a MAX payback allowed
• 5 100 500
• 6 - 600
• Total benefits 1,500 2,100
• Payback in years 2.3 4.0
• 3. The PB method does not measure profitability
  but is more a measure of how quickly the
  investment will contribute to the liquidity of
  the business.
• For these reasons PBP can easily lead to poor
  investment decisions is not the best method of
  investment analysis.

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• 2a. Simple Rate of ReturnIt expresses ave.
  annual net revenue as a age of the investment.
• Rate of return average annual net revenue x
  100 cost
  of the investment
• Net Cash Revenue For 2 10,000 Investments (No
  terminal value)
• Net cash revenues
• Year Returns A Investment A Returns
  B Investment B 1 3,000
  8,000 1,000 10,000
  2 3,000 6,000
  2,000 8,000 3
  3,000 4,000 3,000
  6,000 4
  3,000 2,000 4,000
  4,000 5
  3,000 0___ 6,000 0___
  Total 15,000
  20,000 16,000
  20,000 Av after tax return/invest 3,000
  4,000 3,200 4,000
  Less annual depreciation 2,000
  2,000 Ave. Annual Net
  revenue 1,000 1,200
• Simple Rate of Return A 1000/10,000 x 100
  10 B 1200/10,000 x 100 12
• 2b The Average or Accounting Rate of Return Its
  same as the simple rate of return but its
  calculated by dividing the ave. after tax yearly
  benefit by ave. investment.
• Ave. Rate of Return ave. annual after tax
  revenue x 100
  ave. cost of the
  investment
• Ave. Rate of Return A 3,000/4,000 x 100 75
  B 3,200/4,000 x 100 80

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• Advantages Better than the payback cos it
  considers an investment's earnings over its
  entire life.
• Disadvantages 1. It uses ave annual earnings,
  which fails to consider the size timing of
  annual earnings can thus cause errors in
  selecting investments, especially when there are
  increasing or decreasing net revenues
• e.g. A wld have the same 10 rate of return with
  0 cash revenue in the 1st 4 yrs 15,000 in
  5th yr, as ave. return is still 3,000/yr.
• 2. Benefits received in first years are given
  same weight as one received in the last years.
• 3. The method cannot tell which project is most
  profitable as it cannot differentiate btwn
  returns on investment in terms of s.

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• Evaluating Investments Using Time Value of Money
• A today is worth more than a at some future
  date. Why?
• 1st Interest Earnings A received today can be
  invested to earn interest thus increase to a
  dollar future interest i.e. its opportunity
  cost of receiving in future rather than now.
• 2nd Consumption If the was be spent on goods
  like TV, car etc we wld prefer to have it now in
  order to enjoy the items now rather later.
• 3rd Risks The risk that unforeseen circumstances
  will prevent us from collecting the in the
  future.
• Terms, Definitions, and Abbreviations
• Present Value (PV) Value of available now or
  the current value of some amount(s) to be
  received at some future time.
• Future Value (FV)value to be received at future
  time or the amount a present value will become at
  future date when invested at a given interest
  rate.
• Payment (PMT) value to be paid/ received at end
  of time periods.
• Interest Rate (i) or discount rate is used to
  find present future values. Its also the
  opportunity cost of capital.

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• Time Periods (n) The number of time periods to
  be used for computing present future values.
• Annuity A term used to describe series of equal
  periodic payments (PMT). The payments may be
  either receipts or expenditures.
• 1. Finding Future Values FV (Compounding)
• FV of money is value of investment at a specific
  future date i.e. interest earned during each
  time period is reinvested at end of each period
  so it will also earn interest in the future.
• Thus, FV original investment interest earned
  interest on the accumulated interest.
• Its used for a one-time lump sum investment (a
  PV) or for investment requiring a series of
  payments (PMT) over time.

FV
FV

?
?
PV
PMT PMT PMT
Time
time
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• FV of PV or CompoundingA procedure for finding
  FV when accumulated interest also earns interest
• The FV of a PV money depends on three things the
  
• 1. PV, 2. interest rate it will earn, 3. length
  of time it will be invested.
• If 100 is invested in savings account earning
  12 interest compounded annually, FV of the 100
  after 2 yrs will be
• Value at Interest Interest Value at yr
  Year start of yr rate earned
  () end
• 1 100.00 12 12.00 112.00
  2 112.00 12 13.00 125.00
• Thus a PV of 100 has a FV of 125 if invested at
  12 interest for 2 years. This is expressed
  mathematically as
• FV PV(1 i)N where i
  interest rate per period
• N number of times interest is paid
• FV PV future present values
• FV 100(l 0.12)2 100(l.25)
  125.00

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• How often interest is paid affects FV of
  investment. If interest is paid twice a year for
  2 yrs in our example then N2 x2 4
• FV PV(1 i/2)Nx2
• FV 100(l 0.12/2)4 100(l.26)
• 126 compared to 125 previously
• Thus the more frequent the payment of interest
  the higher the FV.

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• 2. PV of FV or Discounting. FV is discounted back
  to the PV. Its reverse of compounding -i.e. the
  current value of a sum of money to be received or
  paid in the future. The interest rated used is
  called discounted rate. The PV shld be less
  (discounted) than FV due to interest payments.
• PV can be solved from the FV compounding
  equation
• FV PV (I i)N
• FV PV or PV FV (I
  i)N (1 i)N
• What is PV of 1.25 received in 2 yrs if you can
  earn 12
• PV 1.25 1.25
  1.00 (1 0.12)2 1.25
• i.e. PV of 1.25 to be received in 2 yrs 1.00
  today if the opportunity cost is 12, or
  receiving 1.25 in 2 yrs is same as having 1.00
  today if discount rate (opportunity cost of
  money) is 12 per yr.

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• 2b. Net Present Value
• The NPV or discounted cash flow method is a
  preferred method cos it considers the time value
  of money as well as the stream of cash flows over
  entire life of an investment.
• NPV of an investment is sum of PVs for each
  year's net cash flow (or net cash revenue) less
  initial investment cost.
• The equation for finding NPV of an investment is
• NPV P1 P2 Pn - C
  (1 i)l (1 i)2 (1
  i)n
• where Pn is the net cash flow in year n, i is
  discount rate, C is initial cost of
  investment.

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• Net Present Value Calculations for 2 Investments
  of 10,000 (8 Discount Rate and No Terminal
  Values)
• Investment A Investment B Net
  Present Present Net
  Present Present Year cash flow x
  value factor value cash flow value factor
  value 1 3,000 0.926
  2,778 1,000 0.926 926 2 3,000
  0.857 2,571 2,000 0.857 1,714
  3 3,000 0.794 2,382
  3,000 0.794 2,382 4 3,000 0.735
  2,205 4,000 0.735 2,940 5 3,000
  0.681 2,043 6,000 0.681 4,086
  Total 11,979 Total 12,048
  Less cost 10,000
  Less cost 10,000 Net present
  value 1,979 Net present value 2,048
• Investment with ve NPV is accepted those with
  -ve NPV rejected. Investments with ve NPV are
  accepted cos
• 1st, rate of return on investment gt discount rate
  used or return gt opportunity cost of capital used
  as discount rate.
• 2nd investor can pay more for the investment
  still achieve a rate of return equal to discount
  rate used for the NPV

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• 2c. Internal Rate of ReturnThe IRR provides some
  info not available directly from the NPV method.
  Both investments A B have ve NPV using the 8
  discount rate. But what is the actual rate of
  return on these investments? Its the discount
  rate that makes the NPV 0.
• IRR is also called the marginal efficiency of
  capital or yield on the investment. IRR is found
  from NPV
• 0 P1 P2 Pn - C
  (1 i)l (1 i)2 (1
  i)n
• where 0 NPV equation is solved for i. But
  this is very difficult the IRR is therefore
  found by trial error.
• The IRR computation from investments A B
  requires finding a discount rate that can
  discount the future cash flows until they equal
  10,000.

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• 3. Future Value of an Annuity
• Whats FV of a number of (PMT) made at end of
  each yr for a given number of ys? Each pymyt will
  earn interest from the time it is invested until
  the last pymt.
• e.g. What is the FV of 100 if deposited at end
  of each yr earning 12 interest for 3 yrs. It is
  calculated in the ff manner
• 1st 1,00 1,00(l 0.12)2 125
• 2nd 1,00 1,00(l 0.12)1 112
• 3rd 1,00 1,00(l 0.12)0 100
• Future value 337
• 1st 100 earns interest for only 2 yrs, the 2nd
  100 earns interest for 1yr, 3rd 100 earns no
  interest as is deposited at end of 3rd yr. A
  total of 300.00 is invested a total of 37 of
  interest is earned.

FV
?
PMT PMT PMT
time
?
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• The FV of an annuity can be found using the
  equation
• FV of Annuities PMT x (1 i)n 1
  i
• 4. Present Value (PV) of an Annuity
• Determines the PV of an annuity or number of
  pymts to be received over time.
• e.g. What is the PV of 1,000 if its received at
  end of each yr earning 12 interest for 3 yrs. It
  is calculated in the ff manner
• 1st 100 1,00x(1/0.12)1 100 x 89 89
  PVFV/(1i)1
• 2nd 100 1,00x(l/0.12)2 100 x 80 80
  PVFV/(1i)2
• 3rd 100 1,00x(l/0.12)3 100 x 71 71
  PVFV/(1i)3
• Present value
  240

PV
?
PMT PMT PMT
time
?
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• 1st 100 is discounted for 3 yrs, the 1st 100
  is discounted by 11, the 2nd 100 is discounted
  by 20 and the 3rd 100 is discounted by 29. A
  total of 240 is received a total of 60 is
  discounted.
• PV of an annuity can be found using the equation
  
• PV of Annuities PMT x 1 - (1 i)-n
  i

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