Question

A company buys a machine for 10,000 € and sells it for 2,000 € at Year 3. Running costs of the machine are: Year 1 = 3,000 €; Year 2 = 5,000 €; Year 3 = 5,000 €.

If a series of machines are bought, run and sold on an infinite cycle of replacements, what is equivalent annual cost of the machine if the discount rate is 10%? (to calculate you need to use PV interest factors and PV interest factor of an ordinary annuity)

Select one:

a. 22,114 €

b. 8,892 €

c. 8,288 €

d. 7,371 €

Answer 1

The correct answer is option d

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Present value of costs = 10000 + 3000 (P/F, 10%, 1 year) + 5000 (P/F, 10%, 2 year) + 5000 (P/F, 10%, 3 year) - 2000 (P/F, 10%, 3 year)

Present value of costs = 10000 + 3000 0.909091 + 5000 0.826446 + 5000 0.751315 - 2000   0.751315

Present value of costs = 19113.448 €

Annuity factor for 3 years at 10% = 2.486852