Comparing payback period and discounted payback period. Nielsen, Inc. is switching from the payback period to the discounted payback period for small-dollar projects. The cutoff period will remain at three years. Given the following four projects' cash flows, LOADING..., and using a discount rate of %, determine which projects it would have accepted under the payback period and which it will now reject under the discounted payback period. Which projects that would have been accepted under payback period method will now be rejected under the discounted payback period method?

Question Completion:

Given the following four projects' cash flows, and using a discount rate of 10%, ...

                                project 1          project 2         project 3         project 4  

Cost                        $10,000           $15,000          $8,000           $18,000  

Cash Flow Year 1      4,000               7,000             3,000             10,000  

Cash Flow Year 2     4,000              5,500             3,500              11,000  

Cash Flow Year 3     4,000              4,000             4,000                0

Determination of Projects Acceptance under Payback Period and NPV:

                             Payback Period           NPV

Project 1                  Accepted                 Rejected

Project 2                 Accepted                 Rejected

Project 3                 Accepted                 Accepted

Project 4                 Accepted                 Accepted

Explanation:

1. Data and Calculations:

                              project 1          project 2         project 3         project 4  

Cost                        $10,000           $15,000          $8,000           $18,000  

Cash Flow Year 1      4,000               7,000             3,000             10,000  

Cash Flow Year 2     4,000              5,500             3,500              11,000  

Cash Flow Year 3     4,000              4,000             4,000                0

Total inflows         $12,000           $16,500         $10,500           $21,000

Discount rate = 10%

Payback period       Year 3               Year 3            Year 3            Year 2

2. Discount factors: Year 1 = 0.909; Year 2 = 0.826; and Year 3 = 0.751

3. PV of Cash Flows:

                               project 1          project 2         project 3         project 4  

Cost                        $10,000           $15,000          $8,000            $18,000  

Cash Flow Year 1      3,636               6,363             2,727               9,090  

Cash Flow Year 2     3,304               4,543             2,891                9,086

Cash Flow Year 3     3,004              3,004              3,004                0

Total PV inflow       $9,944           $13,910            $8,622             $18,176

4. NPV                        ($56)           ($1,090)              $622                 $176

5. Nielsen, Inc.'s payback period is the number of years (or length of time) it takes an investment to reach its break-even point (the point where there is no gain or loss).    Nielsen's NPV is the difference between total cash inflows and cash outflows over some periods.  A positive NPV  for Nielsen shows that the projects should be accepted, while a negative NPV points to some underlying problems with the projects, especially with respect to cash inflows and outflows.

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