Anew operating system for an existing machine is expected to cost $620,000 and have a useful life of six years. the system yields an incremental after-tax income of $265,000 each year after deducting its straight-line depreciation. the predicted salvage value of the system is $14,200. a machine costs $520,000, has a $38,000 salvage value, is expected to last eight years, and will generate an after-tax income of $62,000 per year after straight-line depreciation. assume the company requires a 12% rate of return on its investments. compute the net present value of each potential investment. (pv of $1, fv of $1, pva of $1, and fva of $1) (use appropriate factor(s) from the tables provided.)

             1st Investment

Year    Cashflow    [email protected]%    PV

0          (620,000)      1            (620,000)

1-6        365,967    4.1114         1,504,637

6          14,200      0.5066      71,937

                                   NPV      956,574                                                                                                                                                                                                                                                                                                                                                                                                                                                      

Annual cashflow = Annual net income + Depreciation

Annual cashflow = $265,000 + $100,967

Annual cashflow = $365,967

Depreciation = Cost - Residual value

                         Estimated useful life

                      = $620,000 - $14,200

                                 6 years

                       = $100,967                                  

                2nd Investment

Year    Cashflow    [email protected]%    PV

0          (520,000)      1             (520,000)

1-8        122,250     4.9676       607,289                                                                                                                                                                                                                                                                                                          

8          38,000       0.4039       15,348

                                     NPV     102,637

Annual cashflow = $62,000 + $60,250

Annual cashflow = $122,250

Depreciation = Cost - Residual value

                         Estimated useful life

                      = $520,000 - $38,000

                                 8 years

                       = $60,250  

Explanation:

In this case, the initial outlay of each investment is the cashflow for year 0.

The annual cash inflow of each investment is the addition of annual net income and depreciation.

The cashflow at the end of each investment is the residual value of each machine.

Then, we will obtain the NPV by deducting the present value of initial outlay from the present value of cash inflow.

The present value of annual  cash inflow of the 1st investment is obtained by discounting the annual cash inflow at present value of annuity factor of 12% for 6 years and the present value of the residual value is obtained by discounting the residual value at the present value factor at 12% for 6 years.                                                                              

The present value of annual cash inflow of the 2nd investment is determined by discounting the annual cash inflow at present value of annuity factor of 12% for 8 years and the present value of the residual value is calculated by discounting the residual value at the present value factor at 12% for 8 years

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