Question

A company's management is considering to buying a new machine. A new machine will cost $25,000. Annual operating and maintenance costs will be $8,000 in the first year, increasing by $400 each year. Assume the machine depreciates by $4,000 per year according to straight-line depreciation. Assume the machine can be re-sold at its book value at any time.

a) Owning the proposed new machine for how many years will result in the minimum EAC if the interest rate is 8%? (show steps)

b) If the old machine reached its minimum EAC several years ago and its operating and maintenance cost this year are expected to be $9,000, should the arena’s management buy the new machine? Assume the operating and maintenance costs of the old machine will increase, and assume it has a salvage value of zero.

Answer 1

New machine cost	25,000
Opex (1st year)	8,000
Growth in Opex per year	400

Schedule of machine	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Beginning balance of machine	25,000	21,000	17,000	13,000	9,000	5,000
Less: Depreciation	4,000	4,000	4,000	4,000	4,000	4,000
Closing balance of machine	21,000	17,000	13,000	9,000	5,000	1,000

Suppose it is sold in year	1
Cash flows will be as follows
Year 0	Year 1
(25,000)	13,000
NPV	(12,963)
EAC (equivalent annual cost)	(14,000)

Suppose it is sold in year	2
Cash flows will be as follows
Year 0	Year 1	Year 2
(25,000)	(8,000)	8,600
NPV	(25,034)
EAC (equivalent annual cost)	(14,038)

Suppose it is sold in year	3
Cash flows will be as follows
Year 0	Year 1	Year 2	Year 3
(25,000)	(8,000)	(8,400)	4,200
NPV	(36,275)
EAC (equivalent annual cost)	(14,076)

Suppose it is sold in year	4
Cash flows will be as follows
Year 0	Year 1	Year 2	Year 3	Year 4
(25,000)	(8,000)	(8,400)	(8,800)	(200)
NPV	(46,742)
EAC (equivalent annual cost)	(14,112)

Suppose it is sold in year	5
Cash flows will be as follows
Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
(25,000)	(8,000)	(8,400)	(8,800)	(9,200)	(4,600)
NPV	(56,488)
EAC (equivalent annual cost)	(14,148)

Suppose it is sold in year	6
Cash flows will be as follows
Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
(25,000)	(8,000)	(8,400)	(8,800)	(9,200)	(9,600)	(9,000)
NPV	(65,562)
EAC (equivalent annual cost)	(14,182)

Least EAC is when the machine is used for 1 year. i.e. 14000.

If old machine reaches minimum EAC several years ago, then the operating and maintenance expense will be high. Thus, EAC will increase if that old machine is used for more number of years. So, it is better to replace the old machine by using the new machine.

NPV xr Equivalent Annual Cost = = 1 - (1 + r)-n