Time Value of Money

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. A plant engineer is considering two machines to purchase:

Item                                  Model A                          Model B

Initial Cost                        $8,000                             $9,000

Annual Savings                $1,750                             $2,000

Annual Maintenance        $200                                $350

Expected Life                   8 years                            8 years

Salvage Value                  $800                                $900

The firm’s MARR is 10%. On the basis of the IRR criterion, which machine is the better choice?



Initial cost

Annual savings

Annual Maintenance

Expected life

Salvage value

Model A

year 1year 2year 3year 4year 5year 6year 7

Initial cost-8000

Annual savings175017501750175017501750

Annual Maintenance-200-200-200-200-200-200

Salvage value

Net cash flow-8000155015501550155015501550

Model B

year 1year 2year 3year 4year 5year 6year 7

Initial cost-9000

Annual savings200020002000200020002000

Annual Maintenance-350-350-350-350-350-350

Salvage value

Net cash flow-9000165016501650165016501650

Given MARR = 10%, we accept project A (IRR 10%) and reject project B (IRR 8%)


Given: Purchasing cost of Tesla Model = $35,000

Downpayment = $5000

Monthly Repayment = $ 775 for 48 Months

Find ARR

Amount of Repayments = $775 * 48 37200

Down Payment5000

total value42200

Profit on sale=9200

ARR =(Profit/Initial cost)/Number of years(9200/35000)/2


3     Period                                                  Net Cash Flow

         n                            A                   B                  C                 D

         0                       $45,000       -$15,000        -$12,500      $10,000

         1                      -$15,000       -$15,000         $5,000       -$9,000

         2                      -$15,000       -$15,000         $5,000       -$11,500

         3                      -$20,000        $60,000         $3,000        $10,000

     a)      Which of the projects represent simple investments?

     b)      Which of the projects represent nonsimple investments?

     c)      Compute the i* for each project.

     d)     Which of the projects has no rate of return?

a) A simple investment is an investment in which the initial cash flow is a negative value, 

in addition, it has only one sign change in the net cash flow series.

Project C is a simple investment

b) A non simple investment is one where the cahs flow has more than one sign change, 







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