Question

A: A new operating system for an existing machine is expected to cost $580,000 and have a useful life of six years. The system yields an incremental after-tax income of $280,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $24,600.

B: A machine costs $410,000, has a $33,500 salvage value, is expected to last eight years, and will generate an after-tax income of $86,000 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.

Required A: A new operating system for an existing machine is expected to cost $580,000 and have a useful life of six years. The system yields an incremental after-tax income of $280,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $24,600. (Round your answers to the nearest whole dollar.)

Required B: A machine costs $410,000, has a $33,500 salvage value, is expected to last eight years, and will generate an after-tax income of $86,000 per year after straight-line depreciation.

Answer 1

Answer A)

Calculation of Net Present Value

Net Present value = Present value of Cash inflows – Present value of cash outflows

                                  = $ 1,544,239 - $ 580,000

                                  = $ 964,239

Therefore the net present value of the investment is $ 964,239.

Working Notes:

Calculation of Annual Depreciation expense:

Annual depreciation expense = (Original cost of machine – Salvage value of machine)/ number of years of useful life of the asset

                                                                  = ($ 580,000 - $ 24,600)/ 6 years

                                                                   = $ 92,567

Calculation of Annual Incremental cash inflows:

Annual Incremental cash inflows = Incremental after tax income + Annual Depreciation expense

                                                             = $ 280,000 + $ 92,567

                                                             = $ 372,567   

Calculation of Present of Cash inflows:

Present Value of cash inflows = (Annual Incremental cash inflows X Present value of annuity factor at 12% for 6 years) + (Salvage value X Present value factor at 12% for 6 years)

                                                         = ($ 372,567 X 4.11141) + ($ 24,600 X 0.50663)

                                                         = $ 1,531,775.69 + $ 12,463.10

                                                          = $ 1,544,239

Answer B)

Calculation of Net Present Value

Net Present value = Present value of Cash inflows – Present value of cash outflows

                                  = $674,539 - $ 410,000

                                  = $ 264,539

Therefore the net present value of the investment is $ 264,539.

Working Notes:

Calculation of Annual Depreciation expense:

Annual depreciation expense = (Original cost of machine – Salvage value of machine)/ number of years of useful life of the asset

                                                                  = ($ 410,000 - $ 33,500)/ 8 years

                                                                   = $ 47,063

Calculation of Annual cash inflows:

Annual cash inflows = after tax income + Annual Depreciation expense

                                     = $ 86,000 + $ 47,063

                                    = $ 133,063   

Calculation of Present of Cash inflows:

Present Value of cash inflows = (Annual cash inflows X Present value of annuity factor at 12% for 8 years) + (Salvage value X Present value factor at 12% for 8 years)

                                                             = ($ 133,063 X 4.96764) + ($ 33,500 X 0.40388)

                                                             = $ 661,009.08 + $ 13,529.98

                                                              = $ 674,539