Question

Calligraphy Pens is deciding when to replace its old machine. The machine's current salvage value is $3,050,000. Its current book value is $1,800,000. If not sold, the old machine will require maintenance costs of $710,000 at the end of the year for the next five years. Depreciation on the old machine is $360,000 per year. At the end of five years, it will have a salvage value of $155,000 and a book value of $0. A replacement machine costs $4,650,000 now and requires maintenance costs of $380,000 at the end of each year during its economic life of five years. At the end of the five years, the new machine will have a salvage value of $745,000. It will be fully depreciated by the straight-line method. In five years, a replacement machine will cost $3,650,000. The company will need to purchase this machine regardless of what choice it makes today. The corporate tax rate is 25 percent and the appropriate discount rate is 7 percent. The company is assumed to earn sufficient revenues to generate tax shields from depreciation.

  

Calculate the NPV for the new and old machines.

Answer 1

NPV is the difference between present value of net cash inflows and present value of net cash outflows for an investment.

We are considering whether to replace an old machine by replacing it with a new machine or to continue its usage. After 5 years, in both the cases, the company will need to purchase a replacement machine costing $3,650,000 regardless of the choice made by it. As this cash flow will be the same in both decisions, it will be ignored in our calculations as it does not effect the cash flows for the decision to be made.

First we shall calculate NPV for the new machine (i.e old machine is replaced by new machine)

Applicable Cash flows if the asset is replaced :

at Year 0:

Purchase of new machine (outflow)

Net Sale proceeds after tax of old machine (inflow)

Years 1-5

Maintenance Costs (outflow)

Depreciation tax shield (inflow)

at the end of Year 5

Net Sale proceeds after tax of new machine (inflow)

So, the Cash flows are as follows :

Old machine is replaced by new machine
Particulars	0	1	2	3	4	5
Cost of new machine	$ (4,650,000)
Salvage of new machine						$   745,000
Tax on gain of sale of new machine => [Sale Value - WDV] * tax rate i.e [745,000 - 0] * 0.25 => $186,250						$ (186,250)
Sale value of old machine	$   3,050,000
Tax on sale of old machine => [Sale Value - WDV] * tax rate i.e [3,050,000 - 1,800,000] * 0.25 => $312,500	$     (312,500)
Annual Cash Flows
Depr. tax shield on new machine => [(Cost - salvage value) / remaining useful life] * tax rate i.e [(4,650,000 - 745,000)/5]* .25 => $195,250 per year		$   195,250	$   195,250	$   195,250	$   195,250	$   195,250
Maintenance Costs		$ (380,000)	$ (380,000)	$ (380,000)	$ (380,000)	$ (380,000)
Annual Net Cash Flows	$ (1,912,500)	$ (184,750)	$ (184,750)	$ (184,750)	$ (184,750)	$   374,000
Discount Factor @ 7%	1.000	0.935	0.873	0.816	0.763	0.713
Discounted Cash flows	$ (1,912,500)	$ (172,664)	$ (161,368)	$ (150,811)	$ (140,945)	$   266,657
NPV [Sum of Discounted Cash flows from Year 0-5]	$(2,271,630)

Now, we shall calculate NPV for the old machine (i.e old machine is continued to be used for next 5 years)

Applicable Cash flows if the asset is replaced :

at Year 0:

No cash flow as there is no sale of machine or no additional cost has been incurred on old machine.

Years 1-5

Maintenance Costs (outflow)

Depreciation tax shield (inflow)

at the end of Year 5

Net Sale proceeds after tax of old machine (inflow)

So, the Cash flows are as follows :

Old machine is continued to be used
Particulars	0	1	2	3	4	5
Salvage of old machine						$   155,000
Tax on gain of sale of old machine						$   (38,750)
Annual Cash Flows
Depr. tax shield on old machine => [(WDV - salvage value) / remaining useful life] * tax rate i.e [(1,800,000 - 155,000)/5]* .25 => $82,250 per year		$      82,250	$      82,250	$      82,250	$      82,250	$      82,250
Maintenance Costs		$ (710,000)	$ (710,000)	$ (710,000)	$ (710,000)	$ (710,000)
Annual Net Cash Flows	$                   -	$ (627,750)	$ (627,750)	$ (627,750)	$ (627,750)	$ (511,500)
Discount Factor @ 7%	1.000	0.935	0.873	0.816	0.763	0.713
Discounted Cash flows	$                   -	$ (586,682)	$ (548,301)	$ (512,431)	$ (478,907)	$ (364,692)
NPV [Sum of Discounted Cash flows from Year 0-5]	$(2,491,014)

So, the NPV for new machine is ($2,271,630) and NPV for the old machine is ($2,491,014).