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					Capital Budgeting
Decision Methods




  October 27, 2008

                     1
Learning Objectives
 • The capital budgeting process.
 • Calculation of:
       Payback
       Net Present Value (NPV) $
       Internal Rate of Return (IRR) %
   for proposed projects, for decision
   making.
 • Capital rationing, when funds are
   limited.                              2
The Capital Budgeting Process
• Capital Budgeting is the process of
  evaluating proposed investment projects for
  a firm.
• Managers must determine which projects are
  acceptable from a financial standpoint
• Examples might include:
   – purchase of fixed assets,
   – investments in R & D, or new businesses
   – Advertising; intellectual property
                                             3
Relevant cash flows
 • The relevant cash flows are after-tax
   incremental cash flows – Axiom 4
 • Cash flows that will occur if the project
   is done, and won’t occur if the project
   isn’t done.
 • Remember the brief case example
The Accept/Reject Decision
 Three methods:
 • Payback Period
    – Time expressed in years to recoup
      the initial investment
 • Net Present Value (NPV)
    – change in value of the firm in $ if the
      project is accepted and completed
 • Internal Rate of Return (IRR) = K
    – projected rate of return (%) the          4

      project will earn
Capital Budgeting Methods - Payback
• Consider Projects A and B that have the
  following expected cash flows:

                    P R O J E C T
                Time       A           B
                 0      (10,000)   (10,000)
                 1        3,500        500
                 2        3,500        500
                 3        3,500      4,600
                 4        3,500     10,000



  How long will it take for the firm to recover it’s investment?
                                                                   5
   Capital Budgeting Methods
   • What is the payback for Project A?


                          P R O J E C T
                   Time        A           B
                    0       (10,000)   (10,000)
                    1         3,500        500
                    2         3,500        500
                    3         3,500      4,600         Payback in
                    4         3,500     10,000         *2.86 years

            0         1          2          3           4


       (10,000)     3,500      3,500     3,500        3,500
     Cumulative CF -6,500     -3,000     +500        +4,000       8
*(Yr 1 + Yr 2 + 3000/3500 or 86% of Yr 3)       (or 10,000/3,500 = 2.86)
Capital Budgeting Methods
• What is the payback for Project B?


                  P R O J E C T
              Time         A            B
               0        (10,000)    (10,000)
               1          3,500         500
               2          3,500         500
               3          3,500       4,600      Payback in
               4          3,500      10,000      *3.44 years

        0        1            2           3      4


   (10,000)       500         500      4,600   10,000
 Cumulative CF -9,500      -9,000     -4,400   +5,600      10
     *(Yr 1 + Yr 2 + Yr 3 + 4,400/10,000 or 44% of Yr 4)
Payback Decision Rule
 • Accept project if payback is less than
   the company’s predetermined
   maximum.
 • If company has determined that it
   requires payback in three years or less,
   then you would:
    – accept Project A (2.86 years)
    – reject Project B (3.44 years)
                                              11
Payback - Problems
 • Does not consider cash received after
   the payback period is over
   Example: the remainder of the $10,000
   in year four is ignored in project B
 • Does not consider the time value of
   money
   Example, the $3,500 per year for the
   four years in A may have a higher
   present value than project B, even
   though B pays back more total dollars
   ($15,600 vs. $14,000).
  Capital Budgeting Methods
  Net Present Value
• Present Value of all costs and benefits
  (measured in terms of after-tax incremental
  cash flows) of a project.
• It is the dollar amount of the change in the
  value of a firm as a result of undertaking the
  project.
• A positive NPV increases firm value +$
• A negative NPV decreases the firm’s value -$  12
Financial Calculator:
• Additional Keys used to
  enter Cash Flows and
  compute the Net
  Present Value (NPV)                       P/YR
                                CF    NPV   IRR


                            N   I/Y   PV    PMT    FV




    Key used to enter expected cash flows in
    order of their receipt.
    Note: the initial investment (CF0) must be
    entered as a negative number since it is an         23
    outflow.
Financial Calculator:
• Additional Keys used to
  enter Cash Flows and
  compute the Net
  Present Value (NPV)                       P/YR
                                CF    NPV   IRR


                            N   I/Y   PV    PMT    FV




    Key used to calculate the net present value of
    the cash flows ($) to be received by the company
    that have been entered in the calculator.
                                                        24
Financial Calculator:
• Additional Keys used to
  enter Cash Flows and
  compute the Net
  Present Value (NPV)                        P/YR
  and Internal                   CF    NPV   IRR


  Rate of Return (IRR)       N   I/Y   PV    PMT    FV




       Key used to calculate the internal rate
       of return (%) for the cash flows that
       have been entered in the calculator.
                                                         25
Calculate the NPV for Project B with calculator.

                                   P R O J E C T
                                Time      A           B
                                 0     (10,000)   (10,000)
                                 1       3,500        500
                  P/YR
                                 2       3,500        500
     CF     NPV   IRR            3       3,500      4,600
                                 4       3,500     10,000
 N   I/Y    PV    PMT    FV




           Note: First step is to press the CF
           button. Then press 2nd and CE/C to
           clear all prior data                              26
Calculate the NPV for Project B with calculator.

                               Keystrokes for TI BAII PLUS:
     CF0 =         -10,000
                               CF 10000    +/- ENTER
                   P/YR
       CF    NPV   IRR


 N     I/Y   PV    PMT    FV




                                                      27
Calculate the NPV for Project B with calculator.

                               Keystrokes for TI BAII PLUS:
     C01 =               500
                               CF 10000    +/- ENTER
                  P/YR               500       ENTER
      CF    NPV   IRR


 N    I/Y   PV    PMT     FV




                                                     28
Calculate the NPV for Project B with calculator.

                                  Keystrokes for TI BAII PLUS:
     F01 =               2
                                  CF 10000     +/- ENTER
                  P/YR                  500       ENTER
      CF    NPV   IRR
                                           2       ENTER
 N    I/Y    PV   PMT        FV




F stands for “frequency”. Enter 2 since there
are two adjacent payments of 500 in periods 1
and 2.
                                                           29
Calculate the NPV for Project B with calculator.

                                Keystrokes for TI BAII PLUS:
     C02 =               4600
                                CF 10000     +/- ENTER
                  P/YR                500       ENTER
      CF    NPV   IRR
                                         2       ENTER
 N    I/Y   PV    PMT     FV
                                     4600        ENTER




                                                     30
Calculate the NPV for Project B with calculator.

                                  Keystrokes for TI BAII PLUS:
     F02 =               1
                                  CF 10000     +/- ENTER
                  P/YR                  500       ENTER
      CF    NPV   IRR
                                           2       ENTER
 N    I/Y    PV   PMT        FV
                                       4600        ENTER
                                           1       ENTER


                                                         31
Calculate the NPV for Project B with calculator.

                                 Keystrokes for TI BAII PLUS:
     C03 =               10000
                                 CF 10000     +/- ENTER
                  P/YR                 500       ENTER
      CF    NPV   IRR
                                          2       ENTER
 N    I/Y   PV    PMT     FV
                                      4600        ENTER
                                          1       ENTER
                                     10000        ENTER

                                                          32
Calculate the NPV for Project B with calculator.

                                  Keystrokes for TI BAII PLUS:
     F03 =               1
                                  CF 10000     +/- ENTER
                  P/YR                  500       ENTER
      CF    NPV   IRR
                                           2       ENTER
 N    I/Y    PV   PMT        FV
                                       4600        ENTER
                                           1       ENTER
                                      10000        ENTER
                                           1       ENTER
                                                           33
Calculate the NPV for Project B with calculator.

                               Keystrokes for TI BAII PLUS:
     I =                 10
                               NPV      10      ENTER

                   P/YR
       CF    NPV   IRR

                                     k = 10%
 N     I/Y   PV    PMT    FV




                                                      34
Calculate the NPV for Project B with calculator.

                               Keystrokes for TI BAII PLUS:
     NPV =         1,153.95
                               NPV      10      ENTER

                   P/YR                CPT
      CF     NPV   IRR


 N     I/Y   PV    PMT    FV



     The net present value of Project B =
     $1,154 as we calculated previously.
     Note: If you press the IRR key, and
                                                     35
     CPT, it will calculate the IRR for you,
     i.e. 13.5%
Calculate the NPV for project A with calculator

 • CF             -10,000           ENTER
     down arrow
 • CO1              3,500           ENTER
     down arrow

 • FO1                 4            ENTER
 • Down arrow
 •   CO2                            NPV
 •   I=                10           ENTER
 •   NPV =                          CPT
 •   NPV =        $1,094.53
      For IRR, punch the IRR key and then CPT
NPV Decision Rule
 • Accept the project if the NPV is greater than
   or equal to 0.

 Example:
 NPVA = $1,095      >0      Accept
 NPVB = $1,154      >0      Accept

 •If projects are independent, accept both projects.
 •If projects are mutually exclusive, or you don’t
 have enough money to do both, accept the project
                                                 36

 with the higher NPV, in this case project B.
 Capital Budgeting Methods
• IRR (Internal Rate of Return) = K
   – IRR is the discount rate (K) that forces the NPV
     to equal zero.
   – It is the rate of return on the project given its
     initial investment and future cash flows.
      • We use the same equation as for NPV, except that
        NPV = zero, and we solve for k
      • Using the table method, and you have unequal
        amounts of cash flow, it can only be done by trial and
        error. For example, substitute values for k until the
        NPV comes out to zero. Ugh! So don’t even try.
                                                           37
      • Use your financial calculator! 
  Calculate the IRR for project A using the
  financial calculator – an annuity
• If the payments are $3,500 each for four periods, and
  the present value is $10,000, the initial outlay, then
• IRR = $3,500(PVIFA k, 4), solving for k
• N=4
• PMT = 3,500
• PV = -10,000
• FV = 0
• CPT I/Y = 14.96%
• You can also use Cash Flow method
Calculate the IRR for Project B with calculator.
Not an Annuity

                                      P R O J E C T
                                   Time      A           B
                                    0     (10,000)   (10,000)
                                    1       3,500        500
                 P/YR
                                    2       3,500        500
     CF    NPV   IRR                3       3,500      4,600
                                    4       3,500     10,000
 N   I/Y   PV    PMT    FV




                             See slides 17 – 23 for entering
                             the unequal amounts in project B
                                                           39
  Calculate the IRR for Project B with calculator.

                                          P R O J E C T
       IRR =                13.5%   Time       A           B
                                     0      (10,000)   (10,000)
                                     1        3,500        500
                     P/YR
                                     2        3,500        500
        CF     NPV   IRR             3        3,500      4,600
                                     4        3,500     10,000
   N     I/Y   PV    PMT     FV



                                    Enter Cash Flows as for NPV

                                    IRR    CPT
Calculate IRR for project A
with calculator. = 14.96%                                         40
IRR Decision Rule
 • Accept the project if the IRR is greater than
   or equal to the required rate of return (k).
 • Reject the project if the IRR is less than the
   required rate of return (k).

 Example:
 If k = 10%
 IRRA = 14.96% > 10%             Accept
 IRRB = 13.50% > 10%             Accept
                                                    41
What if NPV and IRR give different results?

 • Which project(s) should the firm accept?
      NPV         IRR
 • A $1,095       14.96%
 • B $1,154       13.5%




                                              48
NPV/IRR Decision Rules
 •If projects A & B are independent, and you
 have enough money, accept both projects
 •If projects A & B are mutually exclusive,
 meaning you can only pick one or the other,
 or you don’t have enough money to do
 both,
 •Always choose the project with the highest
 NPV. See page 257 (280), mid-page             49
What is capital rationing?
 • Capital rationing is the practice of
   placing a dollar limit on the total size of
   the capital budget.
 • This practice may not be consistent
   with maximizing shareholder value but
   may be necessary for other reasons,
   like lack of cash.
 • Choose between projects by selecting
   the combination of projects that yields
   the highest total NPV without exceeding
   the capital budget cash outlay limit.
                                            54
Capital Rationing example p. 261 (284)
 • Project        Cash Outlay        NPV
    –A            $20,000            $8,000
    –B            $50,000            $7,200
    –C            $40,000            $6,500
    –D            $60,000            $5,100
    –E            $50,000            $4,200
    –F            $30,000            $3,800
    –G            $30,000            $2,000
                 $280,000
   If cash outlay spending limit is $200,000,
     which combination of projects should be
     chosen to maximize NPV?
Capital Rationing example p. 261 (284)
 • Project     Cash Outlay    NPV
   A,B,C,D     $170,000       $26,800
   A,B,C,D,F   $200,000       $30,600
   A,B,C,D,G   $200,000       $28,800
   B,C,D,E     $200,000       $23,000
   B,C,E,F,G   $200,000       $23,700
   A,C,D,E,F   $200,000       $27,600
   A,C,D,E,G   $200,000       $25,500
Mutually Exclusive Projects With
Unequal Lives
 • Mutually exclusive projects with unequal
   project lives can be compared by using
   the Replacement Chain method




                                         68
Replacement Chain Approach
 • Assumes each project can be replicated
   until a common period of time has
   passed, allowing the projects to be
   compared.
 • Example
    – Project Cheap Talk has a 3-year life,
      with an NPV of $4,424.
    – Project Rolles Voice has a 12-year
      life, with an NPV of $12,000.
                                         69
Replacement Chain Approach
 • Project Cheap Talk could be repeated
   four times during the life of Project
   Rolles Voice. (4 x $4,424 = $17,696?)

 • The NPVs of Project Cheap Talk, in
   years t3, t6, and t9, need to be
   discounted back to year t0.


                                           70
Replacement Chain Approach
 • The NPVs of Project Cheap Talk, in years t3,
   t6, and t9, are discounted back to year t0,
   which results in an NPV of $12,121. So
   choose project Cheap Talk
              k=10%
          0           3      6      9

        4,424    4,424    4,424   4,424

       3,324
       2,497
       1,876
                                                  71
      12,121
Disparate sizes

 •   Suppose capital budget is $10,000
 •   Project A: $2,000 with NPV of $1,000
 •   Project B: $10,000 with NPV of $3,000
 •   Which should you choose? Say you
     only have $10,000 and can’t do both.
Disparate Sizes
 • Ans: depends on what you can earn on
   the extra $8,000 if you choose Project
   A. If the combined NPV’s for project A
   plus what you earned on the other
   $8,000 exceeds the NPV of project B,
   then do project A plus others.
 • Otherwise, choose project B
 • Always choose the option with the
   highest NPV!

				
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