Question

Une entreprise de construction envisage de mettre en place un center de calculs techniques. Ce center comprendra trois postes de travail, coûtant chacun 25 000$ pour une durée de service de 5 ans. La valeur de récupération escomptée pour chaque poste de travail est de 2 000$. Les coûts annuels d’exploitation et d’entretien sont estimés à 15 000$ par poste de travail. Si le taux d’intérêt nominal est de 15%, déterminez le coût d’exploitation annuel équivalent de ce centre.

Answer 1

ANSWER:

First we will find out at the present worth and then the equivalent annual cost.

initial cost = $25,000 ( for 1 station) and for 3 stations it will be $25,000 * 3 = $75,000

salvage value = $2,000 (for 1 station) and for 3 stations it will be $2,000 * 3 = $6,000

annual operating and maintenance cost = $15,000 (for 1 station) and for 3 stations it will be $15,000 * 3 = $45,000.

i = 15% , n = 5 years

pw = initial cost + annual operating and maintenance cost(p/a,i,n) + salvage value(p/f,i,n)

pw = -75,000 + 45,000(p/a,15%,5) + 6,000(p/f,15%,5)

pw = -75,000 + 45,000 * 3.352 + 6,000 * 0.4972

pw = -75,000 + 150,840 + 2983.2 = $78,823.2

equiavalent annual operating cost = r * pw / ( 1- ( 1+r)^ -n)

equiavalent annual operating cost = 15% * 78,823.2 / ( 1 - ( 1+15%) ^ -5)

equiavalent annual operating cost = 11,823.48 / ( 1 - (1.15) ^ -5

equiavalent annual operating cost = 11,823.48 / ( 1 - 0.4971)

equiavalent annual operating cost = 11,823.48 / 0.5028

equiavalent annual operating cost = $23,514.19

Therefore the equivalent annual operating cost is $23,514.19