Question

vii) A road needs to be repaired. It can be paved with either asphalt or concrete. Concrete costs $150,000 per km and lasts 20 years (but maintenance costs are extra). What is the breakeven cost for asphalt (which only lasts 10 years and then has to be replaced)? Annual costs of maintenance for both types of road are $5000/km; and MARR is 12%. a) $75,000. b) $83,000. c) $113,500. d) $114,700. e) None of the above.

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Answer 1

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ANSWER IS OPTION C) $ 113,500 Cost of concrete A B C Initial cost maintenance cost Annuity 20YEARS @ 12% Present vanlue of maintence cost BXC TOTAL COST A +D 150000 5000 8.36578 41,829 191,829 D $ $ E A B cost Asphalt maintenance cost present value of initial cost 1st + 10th year 10th yearPV FACTOR 1st year PV factor Total C+D = Break even cost B/E= ROUNDED TO $ 41,829 150,000 0.32197 1.00000 1.32197 113,467 113,500 PV factor @ 12% 1.00000 0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197 0.28748 0.25668 0.22917 0.20462 0.18270 0.16312 0.14564 0.13004 0.11611 8.36578 yearo year1 year2 year3 year4 year5 year6 year7 years year9 year10 year11 year12 year13 year14 year15 year16 year17 year18 year19 Annuity E $