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Maintenance costs on a bridge are $5,000 every five years starting at the end of year 5. For analysis purposes, the bridge is assumed to have an infinite life. What is the Capitalized Equivalent (CE) cost of these infinite payments, assuming an annual interest rate of 10% compounded annually?

Respuesta :

Answer:

$8,189.87

Explanation:

The Capitalized Equivalent (CE) cost will be computed using the PV value of a perpetuity formula. Thus, for an amount (A) paid every 5 years, an annual interest rate of 10%, the CE cost will be

[tex]CE Cost = \frac{A}{r_{5} }[/tex]

where [tex]r_{5}[/tex] is the rate over a 5-year period.

The rate over a 5-year period is computed as follows:

[tex](1+r)^{5} -1[/tex]

[tex]=1.10^{5} -1[/tex]

= 1.61051 - 1 = 0.61051 = 61.051%

Therefore, the CE Cost = [tex]\frac{5,000}{0.61051}[/tex] = $8,189.87