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A section of roadway pavement costs $50,000 a year to maintain. What immediate expenditure for a replacement for the existing pavement is justifiable if the new pavement requires no maintenance in the first five years, $20,000 per year for the next 10 years , and $ 50,000 per year thereafter ( assume money to cost 10 % per annum)?

A section of roadway pavement costs $50,000 a year to maintain. What immediate expenditure for a replacement for the existing pavement is justifiable if the new pavement requires no maintenance in the first five years, $20,000 per year for the next 10 years, and $50,000 per year thereafter (assume money to cost 10% per annum)? Old pAvement: 3. New p ovemene: (all figures X 2 3 5 7 2345 656 52G250 so52 20 po
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Answer #1

Year Annual costs PV Factor @ 10% (2) Present Value (1)x (2) $18,181.818 $16,528.926 $15,026.296 $13,660.269 $12,418.426 $11,289.479 $10,263.162 $9,330.148 $8,481.952 $7,710.866 Year-6 Year-7 Year-8 Year-9 Year-10 Year-11 Year-12 Year-13 Year-14 Year-15 20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000$20,000 $20,000 $20,000 0.90909 0.82645 0.751310.68301 0.62092 0.564470.51316 0.46651 0.42410 0.38554 Ref: NOTE PV at year-5 of annual costs from year-6 thru 15 PV Factor @ 10% for 5 years PV of annual costs from year-6 thru 15 Add: PV of horizon value PV of replacement proposal Less: PV of existing roadway pavement costs Justifiable immediate expenditure for replacement $122,891.34 [Sum of PV of annual dividends from year-6 thru 15] 0.62092 [1/(1+1096 $76,305.85 [$122,891.34 x 0.62092] $119,696.02 Ref: Workings $196,001.88 S425,678.19 [Ref: Workings] $229,676.31 [Difference between PV of replacement and PV of existing annual costs ($425,678.19-$196,001.88) NOTE: PV Factor @ 10% ปุ่(1+10%,-; 1/(1+10%), 1/(1+10%,-; and so on 1/(1+10%) ; 1/(1+10%)10. Workings: Present Value of Annuity Regular: PV in year-15 of Perpetual Costs (Horizon value) Perpetual annual costs/Required return Perpetual annual costs Required return Horizon value at year-15 (1) PV Factor @ 10% for 15 years PV of horizon value (1)x(2) $50,000 [Given] 7 $50,000 10% 20 1096 500,000 [$50,000/10%] 0.23939 [1/(1+10%)15] P-Periodic Payment rrate per period nmumber of periods Present Value of future annual costs $425,678.19 [S50.000 x [1-(1 + 10%)(1/20) ] $119,696.02 [$500,000 x 0.23939)

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