Chapter 10 Cash Flows and Other Topics in Capital Budgeting

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Chapter 10 Cash Flows and Other Topics in Capital Budgeting Powered By Docstoc
					                                CHAPTER 10
        Cash Flows and Other Topics
            in Capital Budgeting
                                ANSWERS TO
                         END-OF-CHAPTER QUESTIONS

10-1. We focus on cash flows rather than accounting profits, because these are the flows that
      the firm receives and can reinvest. Only by examining cash flows are we able to
      analyze the timing of the benefit or cost correctly. Also, we are only interested in these
      cash flows on an after-tax basis, as only those flows are available to the shareholder. In
      addition, it is only the incremental cash flows that interest us, because, looking at the
      project from the point of the company as a whole, the incremental cash flows are the
      marginal benefits from the project and, as such, are the increased value to the firm from
      accepting the project.
10-2. Although depreciation is not a cash flow item, it does affect the level of the differential
      cash flows over the project’s life because of its effect on taxes. Depreciation is an
      expense item, and the more depreciation incurred, the larger are expenses. Thus,
      accounting profits become lower and, in turn, so do taxes which are a cash flow item.
10-3. If a project requires an increased investment in working capital, the amount of this
      investment should be considered as part of the initial outlay associated with the
      project’s acceptance. Since this investment in working capital is never "consumed," an
      offsetting inflow of the same size as the working capital’s initial outlay will occur at
      the termination of the project corresponding to the recapture of this working capital. In
      effect, only the time value of money associated with the working capital investment is
      lost.
10-4. When evaluating a capital-budgeting proposal, sunk costs are ignored. We are
      interested in only the incremental after-tax cash flows to the company as a whole.
      Regardless of the decision made on the investment at hand, the sunk costs will have
      already occurred, which means these are not incremental cash flows. Hence, they are
      irrelevant.
10-5. The payback period method is frequently used as a rough risk screening device to
      eliminate projects whose returns do not materialize until later years. In this way, the
      earliest returns are emphasized, which, in all likelihood, have less uncertainty
      surrounding them.
10-6. The use of the risk-adjusted discount rate assumes that risk increases over time. When


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       using the risk-adjusted discount rate method, we are adjusting downward the value of
       future cash flows that occur later in the future more severely than earlier ones. This
       assumption can be justified, because flows that are expected further out in the future
       are more difficult to forecast and less certain than are flows that are expected in the
       near future.
10-7. The idea behind simulation is to imitate the performance of the project being evaluated.
      This is done by randomly selecting observations from each of the distributions that
      affect the outcome of the project, combining each of those observations and
      determining the final outcome of the project, and continuing with this process until a
      representative record of the project’s probable outcome is assembled. In effect, the
      output from a simulation is a probability distribution of net present values or internal
      rates of return for the project. The decision maker then bases his/her decision on the
      full range of possible outcomes.




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                             SOLUTIONS TO
                       END-OF-CHAPTER PROBLEMS

10-1. a.       Tax payments associated with the sale for $35,000:
                       Recapture of depreciation
                       = ($35,000-$15,000) (0.34) = $6,800
      b.       Tax payments associated with sale for $25,000:
                       Recapture of depreciation
                       = ($25,000-$15,000) (0.34) = $3,400
      c.       No taxes, because the machine would have been sold for its book value.
      d.       Tax savings from sale below book value:
                       Tax savings
                       = ($15,000-$12,000) (0.34) = $1,020

10-2. Initial Outlay
      Outflows:
        Cost of machine                                              $55,000
        Installation                                                   5,000
      Inflows:
        Tax savings ($15,000-$10,000) (.34)                            1,700
        Salvage value—old machine                                     10,000
      Net initial outlay                                             $48,300
      Differential outflows over the project’s life:
                                                       Book Profit        Cash Flow
      Savings:   reduced salary                          $20,000          $20,000
                 reduced defects                            3,000            3,000
      Costs:     increased maintenance                    - 1,000          - 1,000
                 increased depreciation
                   expense (12,000-3,000)*                - 9,000
      Net savings before taxes                           $13,000           $22,000
      Taxes (34%)                                         - 4,420           - 4,420
      Annual net cash flow after taxes                                     $17,580
      *Annual Depreciation is calculated as the cost of the machine ($55,000), plus the cost
      of installation ($5,000), divided by the expected life (5 years).
      Terminal cash flow:
           Salvage value—new machine                                    $ 0




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                                       $48,300
10-3. a. Payback period     =                   = 2.75 years
                                       $17, 580
                                        n      ACF t
      b.            NPV     =          ∑                   - IO
                                       t =1   (1 + k )t
                                 5      $17,580
                    NPV     =   ∑                       - $48,300
                                t =1   (1 +   .15)t
                            =          $17,580 (3.352) - $48,300
                            =          $58,928.16 - $48,300
                            =          $10,628.16
                                        n      ACF t
                                        ∑
                                       t = 1 (1 + k )
                                                      t
      c.     PI             =
                                               IO
                                       $58,928.16
                            =
                                        $48,300
                            =          1.22
                                        n        ACFt
      d.   IO               =          ∑
                                       t = 1 (1 + IRR )
                                                            t

           $48,300          =          $17,580 PVIFAIRR%,5 yrs

           2.75             =          PVIFAIRR%,5 yrs

           IRR              =          Just under 24%
      Yes, the NPV > 0, PI > 1.0, IRR > the required rate of return.
10-4. a.                                                               Initial Outlay
           Outflows:
            Purchase price                                              $ 100,000
            Installation Fee                                                5,000
            Increased Working Inventory                                     5,000
                 Net Initial Outlay                                      $110,000




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      b.   Differential annual cash flows (years 1-9)

                                                        Book Profit       Cash Flow
           Savings:
             Reduction in labor costs                      $35,000          $35,000
           Costs:
            Increased Depreciation*                         10,500
           Net savings before taxes                        $24,500          $35,000
           Taxes (.34)                                       8,330            8,330
                Annual net cash flow after taxes                            $26,670
           * Annual Depreciation on the new machine is calculated by taking the purchase
             price ($100,000) and adding in costs necessary to get the new machine in
             operating order (the installation fee of $5,000) and dividing by the expected
             life.
      c.   Terminal Cash flow (year 10)
           Inflows:
             Differential flow in year 10                                   $26,670
             Recapture of working capital (inventory)                         5,000
                 Total terminal cash flow                                   $31,670

      d.   NPV = $26,670 (PVIFA15%,9 yr.) + $31,670 (PVIF15%, 10 yr.) - $110,000
                    = $26,670 (4.772) + $31,670 (.247) - $110,000
                    = $127,269 + $7,822 - $110,000
                    = $25,091
10-5. a.   Initial Outlay
           Outflows:
                Purchase price                                    $ 500,000
                Installation Fee                                       5,000
                Training Session Fee                                 25,000
                Increased Inventory                                  30,000
                    Net Initial Outlay                             $560,000
      b.   Differential annual cash flows (years 1-9)
                                                         Book Profit       Cash Flow
           Savings:
               Reduction in labor costs                  $150,000          $150,000
           Costs:
              Increased Depreciation*                       50,500
           Net savings before taxes                        $99,500         $150,000
              Taxes (.34)                                   33,830           33,830
                  Annual net cash flow after taxes                         $116,170
           *Annual Depreciation on the new machine is calculated by taking the purchase
           price ($500,000) and adding in costs necessary to get the new machine in
           operating order (the installation fee of $5,000) and dividing by the expected
           life.


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       c.     Terminal Cash flow (year 10)
              Inflows:
                  Differential flow in year 10                                            $116,170
                  Recapture of working capital (inventory)                                  30,000
                      Total terminal cash flow                                            $146,170
       d.      NPV =          $116,170 (PVIFA15%,9 yr.) + $146,170 (PVIF15%, 10 yr.) - $560,000
                        =     $116,170 (4.772) + $146,170 (.247) - $560,000
                        =     $554,363 + $36,104 - $560,000
                        =     $30,467
10-6. Initial outlay
      Outflows:
                    Purchase price                                           $ 80,000
                    Increased taxes, recapture of depreciation
                      ($15,000-$10,000) (.34)                                   1,700
                        Total outflows                                       $ 81,700
              Inflows:
                  Salvage value of old machine                                            - 15,000
                      Net initial outlay                                                  $ 66,700
       Differential annual cash flows (years 1-4)
                                                                       Book profit        Cash flow
              Savings: cash savings                                    $ 30,000           $ 30,000
                 Costs: increased depreciation
                     ($16,000-2,000)*                                   - 14,000
                  Net savings before tax                                $16,000           $ 30,000
                     Taxes (.34)                                          - 5,440           - 5,440
                         Annual net cash flow after taxes                                 $ 24,560
       Terminal cash flow (year 5)
              Inflows:
                  Differential cash flow year 5                                           $ 24,560
                  Salvage value                                                             40,000
              Outflows
                  Taxes on sale of new machine ($40,000 x .34)                             -13,600
                       Total terminal cash flow                                           $ 50,960
       *Note: Annual Depreciation on the new machine is calculated by taking the purchase
       price ($80,000) and dividing by the expected life (5 years).
       a.     Payback period         =      2.72 years
                                 4        $24,560              $50,960
       b.     NPV         =     ∑                         +                   - $66,700
                                t =1     (1 +   0.20) t       (1 + 0. 20) 5
                          =    $24,560 (2.589) + $50,960 (0.402) - $66,700
                          =    $63,585.84 + $20,485.92 - $66,700
                          =    $17,371.76



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                                $84,071.76
     c.     PI            =                = 1.26
                                 $66,700
     d.     Try 30%
            $66,700       =    $24,560(2.166) + $50,960 (0.269)
                          =    $53,196.96 + $13,708.24
                          =    $66,905.20
            Try 31%
            $66,700       =    $24,560 (2.130) + $50,960 (0.259)
                          =    $52,312.80 + $13,198.64
                          =    $65,511.44
            Thus, IRR is between 30 and 31%.
                          n    ACF t
10-7. NPV        =     ∑                        - I0
                       t = 1 (1 + i *)
                                            t

     NPVA        =    $5,000 (3.605) - $10,000

                 =    $18,025 - $10,000
                 =    $8,025
     NPVB        =    $6,000 (3.352) - $10,000

                 =    $20,112 - $10,000
                 =    $10,112
                      n       ACF t
10-8. NPVA =          ∑                     - I0
                     t = 1 (1 + i *)
                                        t

                 =    $30,000 (.893) + $40,000(.797) + $50,000(.712)
                          + $90,000(.636) + $130,000(.567) - $250,000
                 =    $26,790 + $31,880 + $35,600 + $57,240
                          + $73,710 - $250,000
                 =        - $24,780
                          n    ACF t
     NPVB        =     ∑                        - I0
                       t =1   (1 +    i *) t
                 =    $135,000(3.127) - $400,000
                 =    $422,145 - $400,000
                 =    $22,145



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