Question

1. Assume a firm is considering replacing a machine that will increase EBITDA from $20,000 to $51,000 per year. The new machine will cost $100,000 and has a life of 8 years. The firm’s tax rate is 40%, and the cost of capital is 12%. The straight-line depreciation method will be used for tax purposes.
2. 1. Calculate the NPV of the project if neither machine has a salvage value and are fully depreciated. Should the replacement be made?
   2. Assume that the old machine has a book value of $40,000 and still has a useful life of 8 years, but can be sold today for a salvage value of $15,000. Further assume that the new machine will have a salvage value of $12,000. Should the replacement be made?

Answer 1

Solution (a)

Calculation of Yearly Cash Inflows
Particulars	Amount
Incremental EBITDA	$    31,000.00
Less: Depreciation	$    12,500.00
EBT	$    18,500.00
Less: Tax @ 40%	$      7,400.00
EAT	$    11,100.00
Add: Depreciation	$    12,500.00
Cash Inflows	$    23,600.00
Present Value Factor of Annuity @ 12% for 8 years	4.9676
Present Value of Cash Inflows	$ 117,235.00
Less: Cash Outflow	$ 100,000.00
Net Present Value	$    17,235.00

Since NPV is a Positive Value, Replacement should be made

Solution (b) Depreciation = (Book Value - Salvage Value) / Number of useful life

Calculation of Incremental Depreciation

Incremental Depreciation
Year	New Machine	Old Machine	Increase in Depreciation
1	$   12,500.00	$ 3,500.00	$   9,000.00
2	$   12,500.00	$ 3,500.00	$   9,000.00
3	$   12,500.00	$ 3,500.00	$   9,000.00
4	$   12,500.00	$ 3,500.00	$   9,000.00
5	$   12,500.00	$ 3,500.00	$   9,000.00
6	$   12,500.00	$ 3,500.00	$   9,000.00
7	$   12,500.00	$ 3,500.00	$   9,000.00
8	$   12,500.00	$ 3,500.00	$   9,000.00

Calculation of Present Value of Cash Inflows

Particulars	1	2	3	4	5	6	7	8
Incremental EBITDA	$ 31,000.00	$ 31,000.00	$ 31,000.00	$ 31,000.00	$ 31,000.00	$ 31,000.00	$ 31,000.00	$ 31,000.00
Less: Loss on Sale of Old machine	$ 25,000.00
Less: Incremental Depreciation	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00
EBT	$ (3,000.00)	$ 22,000.00	$ 22,000.00	$ 22,000.00	$ 22,000.00	$ 22,000.00	$ 22,000.00	$ 22,000.00
Less: Tax @ 40%	$ (1,200.00)	$     8,800.00	$     8,800.00	$     8,800.00	$     8,800.00	$     8,800.00	$     8,800.00	$     8,800.00
EAT	$ (1,800.00)	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00
Add: Loss on Sale of Old Machine	$ 25,000.00	-	-	-	-	-	-	-
Add: Incremental Depreciation	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00	$ 9,000.00
Add: Sale Value of Old machine	$ 15,000.00	-	-	-	-	-	-	-
Less: Opportunity lost (Salvage Value of Old Machine at the end of 8 Years)	-	-	-	-	-	-	-	$ 12,000.00
Cash Inflow	$ 53,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$ 13,200.00	$     1,200.00
Present Value Factor @ 12%	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066	0.4523	0.4039
Present Value of Cash Inflow	47,502.00	10,523.00	9,396.00	8,389.00	7,490.00	6,687.00	5,970.00	485.00

Total Present Value of Cash Inflows = $ 96,442

Less: Cost of New Machine = $1,00,000

Net Present Value = - $ 3,558

Since NPV is Negative, Replacement decision will not be beneficial