Question

Laser cutting machine is to be purchased at a cost of SR 160,000. The cash flow which is denoted as (Year, O & M Costs, Market value) is provided as follows: (1, 25000, 145000), (2, 33000, 100000), (3, 42000, 75000), (4, 56000, 25000). It is also given that the AEC is an increasing function with N. If the interest rate is 12%, which one of the following statements is correct:

		a) The economic service life is undetermined in this case.
		b) The maximum cost is attained at year 2
		c) The economic service life is 4 years
		d) The minimum cost is attained at year 3
		e) The economic service life is one year

Answer 1

e) The economic service life is one year

This is found by

First find the PV of annual cost and market value

Then use NPV = 160000 + PV of annual cost – PV of market value

Finally use AEC = (A/P, 12%, n)*NPV for n = 1 to 4

Note that AEC is minimum in year 1

Year	Annual cost	Salvage value	PV of the annual cost	PV of the market value	Net present value	AEC
1	25000	145000	22321.43	129464.29	52857.14	59200.00
2	33000	100000	48628.83	79719.39	128909.44	76275.47
3	42000	75000	78523.60	53383.52	185140.08	77082.88
4	56000	25000	114112.61	15887.95	258224.66	85016.45