Question

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 $150,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.

Required A Required B
Cash Flow Select Chart Amount * PV Factor = Present Value
Annual Cash Flow Present Value of an Annuity of 1
Residual value Present Value of 1
Present value of cash inflows
Immediate Cash Flow
Net Present Value
A machine costs $380,000, has a $20,000 salvage value, is expected to last eight years, and will generate an after-tax income of $60,000 per year after straight-line depreciation.
Required A Required BCash Flow Select Chart Amount * PV Factor = Present Value Annual Cash Flow Present Value of an Annuity of 1Residual value Present Value of 1 Present value of cash inflows Immediate Cash Flow Net Present Value
Assume the company requires a 10% rateo return on its vestments. Compute the net present value of each potential investment.

Answer 1

a. $509,141

b. $189,495

Step-by-step explanation:

The computation of the net present value for each case is shown below:

a.

Net present value = Present value after considering the discount rate and salvage value - initial investment

where,

Present value is

= Incremental after tax income + depreciation expense

= $150,000 + ($520,000 - $10,000) ÷ 6 years

= $150,000 + $85,000

= $235,000

Now PVIFA factor at 6 years for 10% is 4.3553

So, present value is

= $235,000 × 4.3553

= $1,023,496

For salvage value, the present value is

= $10,000 × 0.5645 (Discounting factor)

= $5,645

So, total present values is

= $1,023,496 + $5,645

= $1,029,141

And, the initial investment is $520,000

So, the net present value is

= $1,029,141 - $520,000

= $509,141

b.

Net present value = Present value after considering the discount rate and salvage value - initial investment

where,

Present value is

= Incremental after tax income + depreciation expense

= $60,000 + ($380,000 - $20,000) ÷ 8 years

= $60,000 + $45,000

= $105,000

Now PVIFA factor at 6 years for 10% is 5.3349

So, present value is

= $105,000 × 5.3349

= $560,164.50

For salvage value, the present value is

= $20,000 × 0.4665 (Discounting factor)

= $9,330

So, total present values is

= $560,164.50 + $9,330

= $569,494.50

And, the initial investment is $380,000

So, the net present value is

= $564,494.50 - $380,000

= $189,495