Question

A new storage tank can be purchased and installed for $10,000. The estimated service life of this tank is 10 years. It has been proposed that an available tank with the capacity equivalent to the new tank be used instead of buying the new tank. If the latter tank were required, it would have a service life of 3 years before similar repairs would be needed again. Neither tank has any scrap value. Money is worth 6 percent compounded annually. On the basis of equal capitalized costs for the two tanks. How much can be spent for repairing the existing tank?

Answer 1

capitalized cost of equipment is used to determine the cost spread of equipment over the long period.

purchased and installed cost of a new storage tank

Total cost Cv = $10,000

Replacement cost C_R = $10000

Years n = 10

Annually compound interest rate i = 6 % = 0.06

Capitalized cost of new tank

= ($10000) + ($10,000)/[(1+0.06)¹⁰ - 1]

= $22644.66

For existing tank

Total cost of repairing = Cv

Replacement cost C_R = Cv

Years n = 3

Annually compound interest rate i = 6 % = 0.06

Capitalized cost of existing tank

= (Cv) + (Cv)/[(1+0.06)³ - 1]

On the basis of equal capitalized costs for the two tanks

$22644.66 = (Cv) + 5.235(Cv)

Cv = $3631.86