Ch06_Payback_Period by wpr1947

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									Chapter 6                                                                           8224ffe5-04b7-4c69-9a30-f1b4f2537fd7.xls



Atrill/Hurley
Financial Management for Decision Makers
Canadian Edition
Chapter 6
General Excel Template

Topic: Payback and Discounted Payback Period

A central goal in financial management is to undertake those decisions that create value for
shareholders. Therefore, it is of central importance to develop techniques that enable financial
decision makers to identify those investment opportunities that generate value (as opposed to
those that do not).
The capital budget techniques of payback and discounted payback are widely used, despite
being inferior to the techniques of NPV and IRR.

Payback Period:
The payback period of an investment refers to the length of time an investment will take to
generate cash flows equivalent to the original cost of the investment.
The decision criteria for the payback method are:
 ▪ If the investment achieves payback within a specified timeframe, accept it.
 ▪ If the investment does not achieve payback within a specified timeframe, reject it.
Discounted Payback Period:
The discounted payback period of an investment refers to the length of time an investment will
take to generate discounted cash flows equivalent to the original cost of the investment.
The decision criteria for the discounted payback method are:
 ▪ If the investment achieves discounted payback within a specified timeframe, accept it.
 ▪ If the investment does not achieve discounted payback within a specified timeframe, reject it.




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Suppose your company is attempting to evaluate a particular project with the following cash
flows:

                Year     Cash Flow
                 1           $5,000
                 2          $14,000
                 3          $12,000
                 4          $15,000
                 5           $9,000
                 6          $12,000
                 7          $20,000
                 8          $40,000


The project costs $80,000 today, the required return on investments of this type is 8%, and the
required cut-off is 5 years. Calculate both the payback period and the discounted payback
period for the project and determine whether or not you should undertake the project.




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Calculating Payback:
                          Beginning         Net Cash      Ending
                Year       Balance           Flows       Balance
Immediate        0        -$80,000                  $0   -$80,000   Initially, the investment
cost of                                                             "owes" the entire original
investment                                                          cost of $80,000 (the figure
                                                                    is shown as a negative
                                                                    value to indicate that this
                                                                    amount is owing).
                  1          -$80,000           $5,000     -$75,000 As the investment
                                                                    generates cash flows in the
                                                                    future, the amount that the
                                                                    investment "owes" is
                                                                    reduced by the amount
                                                                    generated by the
                                                                    investment that year.
                  2          -$75,000          $14,000     -$61,000
                  3          -$61,000          $12,000     -$49,000
                  4          -$49,000          $15,000     -$34,000
                  5          -$34,000           $9,000     -$25,000
                  6          -$25,000          $12,000     -$13,000
                  7          -$13,000          $20,000       $7,000 Eventually, the investment
                                                                    achieves payback —the
                                                                    point at which the balance
                                                                    owing from the investment
                                                                    goes from negative to
                                                                    positive.
                  8                            $40,000              The cash flow for the 8th
                                                                    period is not used in
                                                                    determining the payback
                                                                    period since it occurs after
                                                                    payback has been
                                                                    achieved. The fact that the
                                                                    payback method ignores
                                                                    some future cash flows, like
                                                                    this, is seen as a
                                                                    disadvantage of the
                                                                    method.




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Payback Period =                 6.65       Years

                      From the above table, we can determine that payback is achieved at
                      some point over the 7th year (we can make this determination because
                      the balance goes from negative to positive during the 7th year).
                      A related question is then, at what point over this year did payback
                      actually occur?
                      A common assumption of the payback criteria is that each period's cash
                      flow is evenly spread over the period. Using this assumption, we can
                      conclude that payback was achieved 65% of the way through the 7th
                      year (13,000/20,000 = 0.65 = 65%). Therefore, the payback period is a
                      total of 6.65 years.
              Accept or Reject?
                      Given that the cut-off period in the example is stated to be 5 years, this
                      investment does not achieve payback soon enough. Therefore, the
                      payback criteria indicate that this investment should be rejected.




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Calculating Discounted Payback:
The process of calculating discounted payback is identical to that of calculating payback , with
one key exception. In place of using the unadjusted cash flows, the discounted payback
approach first determines the present value of the future cash flows for the given investment
and then uses these discounted values to determine the payback period .
Step 1: Calculate the present value of the future cash flows being generated by the
investment.
                                             Discount rate =               8%

                Year     Cash Flow Discounted
               (nper)      (FV)     Cash Flows           Excel Formula
                 1           $5,000    $4,629.63         =PV($F$59,B62,,-C62)
                 2          $14,000   $12,002.74         =PV($F$59,B63,,-C63)
                 3          $12,000    $9,525.99         =PV($F$59,B64,,-C64)
                 4          $15,000   $11,025.45         =PV($F$59,B65,,-C65)
                 5           $9,000    $6,125.25         =PV($F$59,B66,,-C66)
                 6          $12,000    $7,562.04         =PV($F$59,B67,,-C67)
                 7          $20,000   $11,669.81         =PV($F$59,B68,,-C68)
                 8          $40,000   $21,610.76         =PV($F$59,B69,,-C69)

Step 2: Calculate the discounted payback period using the present value cash flows
determined in Step 1.

                                       Net Cash
                         Beginning       Flows              Ending
                Year      Balance    (discounted)           Balance
                 0       -$80,000.00         $0.00         -$80,000.00 Initially, the investment
                                                                       "owes" the entire original
                                                                       cost of $80,000 (the figure
                                                                       is shown as a negative
                                                                       value to indicate that this
                                                                       amount is owing).
                  1      -$80,000.00         $4,629.63     -$75,370.37
                                                                         As the investment
                                                                         generates cash flows in the
                                                                         future, the amount that the
                                                                         investment "owes" is
                                                                         reduced by the discounted
                                                                         amount generated by the
                                                                         investment that year.
                  2      -$75,370.37        $12,002.74     -$63,367.63
                  3      -$63,367.63         $9,525.99     -$53,841.64
                  4      -$53,841.64        $11,025.45     -$42,816.19
                  5      -$42,816.19         $6,125.25     -$36,690.94
                  6      -$36,690.94         $7,562.04     -$29,128.91
                  7      -$29,128.91        $11,669.81     -$17,459.10
                  8      -$17,459.10        $21,610.76       $4,151.66 Eventually, the investment
                                                                       achieves payback —the
                                                                       point at which the balance
                                                                       owing from the investment
                                                                       goes from negative to
                                                                       positive.




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Discounted Payback Period =                   7.808       Years

                      From the above table, we can determine that payback is achieved at
                      some point over the 8th year (we can make this determination because
                      the balance goes from negative to positive during the 8th year).
                      A related question is then, at what point over this year did payback
                      actually occur?
                      A common assumption of the discounted payback method is that each
                      period's cash flow is evenly spread over each period. Using this
                      assumption, we can conclude that discounted payback was achieved
                      80.8% of the way through the 7th year (17,459.10/21,610.76 = 0.808 =
                      80.8%). Therefore, the discounted payback period is a total of 7.808
                      years.
              Accept or Reject?
                      Given that the cut-off period in the example is stated to be 5 years, this
                      investment does not achieve discounted payback soon enough.
                      Therefore, the discounted payback criteria indicate that this investment
                      should be rejected.




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