5-20 Luis is responsible for buying some specialized manufacturing equipment tha

Question

5-20 Luis is responsible for buying some specialized manufacturing equipment that has a purchase price of $10,000 and annual operating costs of $1000. The vendor is offering a special buyer incen- tive that provides free maintenance for the first four years. After that time, the maintenance is $500 per year over the 10-year life, and there is an overhaul expense in year 5 of $2000. The equipment has a salvage value of $1000. If the interest rate is 8%, what is the present value? Contributed by Gillian Nicholls, Southeast Missouri State University

Explanation / Answer

Present value of costs is computed as follows. Note that

(i) Annual cost, years 1-4 = $1,000

(ii) Annual cost, year 5 = $(1,000 + 500 + 2,000) = $3,500

(iii) Annual cost, years 6-9 = $(1,000 + 500) = $1,500

(iv) Net Annual cost, year 10 = $(1,500 - 1,000 salvage value) = $500

(v) PV Factor in year N = (1.08)-N

Year Cost ($) PV factor @8% Discounted Cost ($) (A) (B) (A) x (B) 0 10,000 1.0000 10,000.00 1 1,000 0.9259 925.93 2 1,000 0.8573 857.34 3 1,000 0.7938 793.83 4 1,000 0.7350 735.03 5 1,500 0.6806 1,020.87 6 3,500 0.6302 2,205.59 7 1,500 0.5835 875.24 8 1,500 0.5403 810.40 9 1,500 0.5002 750.37 10 500 0.4632 231.60 Present Value ($) = 19,206.20

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