Question

5) (17 points) Maintenance costs for a bridge are cyclic with the following costs occurring over a 5-year period. MARR is 10% per year compounded annually. EOY 2 3 5 Maintenance S50 million $75 million $75 million $75 million $150 million Cost 1 4 a) (14 points) Compute an equivalent uniform annual cost over a single 5-year maintenance cycle. b) (3 points) It is anticipated that the sequence of costs will repeat every 5 years forever. If so, determine the capitalized cost (worth) of the maintenance costs.

Answer 1

Solution :-

(a)

Present Worth of Costs =

= [ $50 / ( 1 + 0.10 ) ] + [ $75 / ( 1 + 0.10 )² ] + [ $75 / ( 1 + 0.10 )³ ] + [ $75 / ( 1 + 0.10 )⁴ ] + [ $150 / ( 1 + 0.10 )⁵ ]

= ( $50 * 0.909 ) + ( $75 * 0.826 ) + ( $75 * 0.751 ) + ( $75 * 0.683 ) + ( $150 * 0.621 )

= $308.15

Now Annual Worth = Present Worth / PVAF ( r , n )

= $308.15 / PVAF ( 10% , 5 )

= $308.15 / 3.791

= $81.29

(b)

Capitalized Cost = Annual Worth / Discount Rate

= $81.29 / 10% = $812.89

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