Question

One year​ ago, your company purchased a machine used in manufacturing for $105,000.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 $55,000 per year for the next ten years. The current machine is expected to produce EBITDA of $23,000per 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 $9,545 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 40%​, and the opportunity cost of capital for this type of equipment is 10%. Is it profitable to replace the​ year-old machine?

The NPV of the replacement is $_(Round to the nearest​ dollar.)

Answer 1

NPV is difference between initial outlay and present value of cash flows.

We will consider incremental cash flows between old and new machine

we will first gather the given information:

• cost of old machine is sunk cost as ithas already been incured so it is not relevant
• new machine cost= $150,000
• sale value of old machine = $50,000
• EBITDA new = $55,000 (1)
• EBITDA old = $23,000 (2)
• Depreciation Old= $9,545 (3)
• Depreciation New = $15,000 per year($150,000/0) (4)
• Book value of old machine = purchase cost-depreciation for year 1

=$105,000-$9,545

=$95,455

Loss on sal= sale value-book value

=$50,000-95,455

=$45,455

Tax saved on loss = $45,455*40%

=$18,182

Net cash flow from sale of old machine = $50,000+$18,182

=$68,182

	Year 0	Year 1-10
Incremental EBIDTA		$32,000[(1)-(2)]55000-23000
Less: Depreciation		$5,455[(4)-(3)]$15,000-9,545
EBT		$26,545 [$32,000-5,455]
Tax @ 40%		$10,618 [26,545*40%]
EAT		$15,927 [$26,545-10,618]
Add: Non cash expense (Depreciation)		$5,455
Incremental Cash flow		$21,382[15,927+5,455]
Capital expenditure	-$81,818[-$150,000+$68,182]
PV factor at 10%	1	6.144567
		[(1/1.10)^1+(1/1.10)^2+(1/1.10)^3........+(1/1.10)^10
Present value of cash flows	-$81,818	$131,383[21,382*6.144567]

NPV of replacement = -$81,818+$131,383

=$49,565

As NPV is positive yes machine should be replaced

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