Answer:
The capitalized cost for an asset, in this case, an asphalt road, can be calculated using the present worth formula for a project with recurring annual costs. The formula is:
\[ C = P + \frac{A \cdot (P/A, i, n-1)}{i} \]
where:
- \( C \) is the capitalized cost,
- \( P \) is the initial construction cost,
- \( A \) is the annual cost (in this case, maintenance cost),
- \( i \) is the effective interest rate, and
- \( n \) is the number of years.
Given:
- \( P = $10,000 + $5,000 + $2,000 \) (Construction cost + Installation cost + Freight expenses),
- \( A = $1,000 \),
- \( i = 5\% \) (0.05),
- \( n = \infty \) (since the maintenance cost is recurring every year).
\[ C = (10,000 + 5,000 + 2,000) + \frac{1,000 \cdot (P/A, 0.05, \infty-1)}{0.05} \]
\[ C = 17,000 + \frac{1,000 \cdot (1 - 1/(1.05)^{\infty-1})}{0.05} \]
This is a perpetuity, and the present worth of a perpetuity is given by \( \frac{A}{i} \).
\[ C = 17,000 + \frac{1,000}{0.05} \]
Calculate \( C \) to find the capitalized cost.
