Question

1. A new operating system for an existing machine is expected to cost $520,000 and have a useful life of six years. The system yields an incremental after-tax income of $175,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $22,600.

2. A machine costs $430,000, has a $33,200 salvage value, is expected to last eight years, and will generate an after-tax income of $66,000 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.

Answer 1

First Investment

Cost of Investment = 520,000

Life = 6 years

Incremental Income = $175,000 (post depreciation)

Salvage value = $22,600

The incremental value is arrived at post depreciation, however, for net present value calculation non cash items are not considered, therefore the depreciation expense which was deducted from yearly income needs to be added back.

Depreciation charged = (Cost of machine - salvage value) / life of machine

                                   = (520,000 - 22,600) / 6

                                  = $82,900

Incremental Income (Pre depreciation) = $175,000 + $82,900 = $257,900

Discount rate = required rate of return = 12%

Discount factor = 1/(1+r)^n

Discount factor for year 6 = 1/ (1+0.12)^6

                                          = 1 / (1.12)^6

                                         = 1 / 1.9738

                                         = 0.5066

Cumulative discount factor formula = (1 - (1+r)^-t) / r

Cumulative discount factor formula (years 1-6) = (1 - (1.12)^-6) / 0.12 = 4.1114

Net present value calculation:

                                                                                   Inflow / (outflow)                       discount factor                Present value

Initial Investment (outflow) at year 0                        (520,000)                                             1                               (520,000)

Incremental Income (Pre depreciation) year 1-6 =   257,900                                             4.1114                        1,060,330

Salvage value at year 6                                             22,600                                              0.5066                          11,449

Total                                                                                                                                                                      551,779

Second Investment

Cost of Investment = 430,000

Life = 8 years

Incremental Income = $66,000 (post depreciation)

Salvage value = $33,200

Depreciation charged = (Cost of machine - salvage value) / life of machine

                                   = (430,000 - 33,200) / 8

                                  = $49,600

Incremental Income (Pre depreciation) = $66,000 + $49,600 = $115,600

Discount factor = 1/(1+r)^n

Discount factor for year 8 = 1/ (1+0.12)^8

                                          = 1 / (1.12)^8

                                         = 1 / 2.4760

                                         = 0.4039

Cumulative discount factor formula = (1 - (1+r)^-t) / r

Cumulative discount factor formula (years 1-8) = (1 - (1.12)^-8) / 0.12 = 4.9676

Net present value calculation:

                                                                                   Inflow / (outflow)                       discount factor                Present value

Initial Investment (outflow) at year 0                        (430,000)                                             1                               (430,000)

Incremental Income (Pre depreciation) year 1-8 =   115,600                                             4.9676                         574,255

Salvage value at year 8                                             33,200                                              0.4039                           13,409

Total                                                                                                                                                                       157,664