Two pavement maintenance plans have been proposed for a county road. Select the most cost-effective alternative based on equivalent annual cost. Assume an interest rate of 8% per year and a design life of 25 years. Show cash flow diagrams for each alternative. Alternative A entails expenses of $500 per year for the entire lifespan plus an additional $1000 in year 6, $1500 in year 11, $2000 in year 16, and $2500 in year 21. Alternative B entails expenses of $600 per year for the entire lifespan plus an additional $100 per year starting in year 14 and continuing through year 25 ($700 per year during this period).

Question

What will be an ideal response?

Answer 1

The cash flow diagram for alternative A is shown as follows:



EUACA = AA + 1000(P/F, 8%, 6)(A/P, 8%, 25) + 1500(P/F, 8%, 11)(A/P, 8%, 25)

+ 2000(P/F, 8%, 16)(A/P, 8%, 25) + 2500(P/F, 8%, 21)(A/P, 8%, 25)

= 500 + (1000 × 0.6302 × 0.0937) + (1500 × 0.4289 × 0.0937) + (2000 ×

0.2919 × 0.0937) + (2500 × 0.1987 × 0.0937)

= 720.58

The cash flow diagram for alternative A is shown as follows:



EUACB = AB + 100(P/A, 8%, 12)(P/F, 8%, 13)(A/P, 8%, 25)

EUACB = 600 + 100(7.536)(0.3677)(0.0937)

EUACB = 625.96

Since Alternative B cost less, this maintenance plan is preferred.