Question

One year​ ago, your company purchased a machine used in manufacturing for $90,000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $150,000 today. It will be depreciated on a​ straight-line basis over ten​ years, after which it has no salvage value. You expect that the new machine will contribute EBITDA​ (earnings before​ interest, taxes,​ depreciation, and​ amortization) of $40,000 per year for the next ten years. The current machine is expected to produce EBITDA of $25,000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, after which it will have no salvage​ value, so depreciation expense for the current machine is $8,182 per year. All other expenses of the two machines are identical. The market value today of the current machine is $50,000. Your​ company's tax rate is 38%, and the opportunity cost of capital for this type of equipment is 12%.

1. What is the NPV of replacing the year-old machine is?

Answer 1

Step 1:

Calculation of Cash Outflows (Period: 0)

Particulars	Amount
Cost of Machine	$(150,000.00)
Cash inflow on sale of old machine(Note 1)	$62,090.84
Cash Outflows	$(87,909.16)

Note

1: Cash Inflow on Sale of Old Machine

Value in Machinery in (Yr 1)	$81,818.00
Less: Sale value (A)	$50,000.00
Loss on sale	$31,818.00
Tax savings on Loss (B)	$12,090.84
Cash inflow on sale of old Machine (A)+(B)	$62,090.84

Step 2:

Calculation of Cash inflows: (Period:1- 10)

Particulars	Amount
Incremental EBIDTA (note 1)	$15,000.00
Less: Incremental Depreciation (note 2)	$(6,818.00)
EBT	$8,182.00
Less: Tax @38%	$(3,109.16)
EAT	$5,072.84
Add: Incremental Depreciation	$6,818.00
Cash Inflows	$11,890.84

Notes:

1. Incremental EBIDTA = $40,000 - $25,000 = $15000

2. Calculation of depreciation

Particulars	Old Machine	New Machine
Purchase cost	$90,000.00	$150,000.00
Life	11 years	10 years
Depreciation p.a.	$8,182.00	$15,000.00
Incremental Depreciation		$6,818.00

Step 3:

Calculation of NPV

NPV= Present value of cash inflows - Present value of cash outflows

Particulars	Amount	Period	PVF@12%	Present Value
Cash Outflows	(87,909.16)	0	1	$(87,909.16)
Cash Inflows	11,890.84	1-10	5.6502230	$67,185.90
NPV				$(20,723.26)

NPV of Project = $(20,723.26)

Decision : Since, NPV of replacing the old machine with new is negative, we should not accept the proposal of replacement.