Derive the equation to compute the equivalent annual cost given the capital cost of a highway, such that A = (A/P) x P, where A/P is the capital recovery factor. Compute the equivalent annual cost if the capital cost of a transportation project is $100,000, annual interest = 10%, and n = 15 years.

Question

What will be an ideal response?

Answer 1

Knowing that:
F = A(1 + i)n–1 + A(1 + i)n–2 + … + A(1 + i) + A
Multiplying by (1 + i),
(1 + i)F = A(1 + i)n + A(1 + i)n–1 + … + A(1 + i)
Subtracting the first equation from the second,
i F = A(1 + i)n – A
F = A [(1 + i)n – 1] / i
Knowing that:
F = P (1 + i)n
A [(1 + i)n – 1 ] / i = P (1 + i)n
A/P = i (1 + i)n / [(1 + i)n – 1 ]
From Table 13.3, or using the equation derived above, determine the appropriate
(A/P) term.
EUAC = P(A/P, 10%, 15)
EUAC = 100,000 × (0.1315)
EUAC = $13,150.00
Therefore, the EUAC for this project will be $13,150.00.