Question

A Newly-acquired Equipment Requires An Annual Maintenance Costs Of P10,000. If The Annual Maintenance Cost Us Increased By 20% Each Year Every Year For 10 Years, What Is The Estimated Present Worth Of The Maintenance Costs If Money Is Worth 15%?

Answer 1

Money worth $15\%$ implies $15\%$ is the opportunity cost of incurring maintenance cost. This is taken as the discount rate.

$PV=$$10000\over 1.15$$+$ $10000\times 1.20\over 1.53^2$ $+$ $10000\times 1.20^2\over 1.15^3$$+$ $10000\times 1.20^3\over 1.15^4$ $+$ $....$ $+$ $10000\times 1.20^9\over 1.15^{10}$

$PV=$ $10000\over 1.15$ $(1+$ $1.20\over 1.15$ $+$ $1.20^2\over 1.15^2$ $+$ $1.20^3\over1.15^3$ $+$ $.....$ $1.20^9\over 1.15^9$ $)$

$PV=$ $10000\over 1.15$ ${(1-{{(1.20\over1.15)}}^{10}}\over{{1-{(1.20\over1.15)}}}$ $=P106,100.509$