Question

Infrastructure Economics

Do it in steps (FULL SOLUTION)

NOT IN EXCEL PLEASE

1) (10pts) Given the following cost and benefit data for two potential roadway project alternatives, find the rate of return (ROR) for each alternative and determine which project should be chosen. Alt. A 10 Basic Data Service Life (yrs) Construction cost Annual O&M cost Annual safety and operational Benefits Alt. B 10 $700,000 $30,000 $600,000 $25,000 $115,000 $150,000

Answer 1

Net annual benefit (NAB) = Annual benefits - Annual O&M cost

NAB, Alt A ($) = 115,000 - 25,000 = 90,000

NAB, Alt B ($) = 150,000 - 30,000 = 120,000

Without Excel, we find ROR using Approximation method, using which

ROR = RL + [NPVL / (NPVL - NPVH)] x (RH - RL) where

RL: Lower discount rate = 5% (assumed)

RH: Higher discount rate = 10% (assumed)

NPVL: NPV at 5%

NPVH: NPV at 10%

(I) Alt A

NPVL = - 600,000 + 90,000 x P/A(5%, 10) = - 600,000 + 90,000 x 7.7217** = - 600,000 + 694,953 = 94,953

NPVH = - 600,000 + 90,000 x P/A(10%, 10) = - 600,000 + 90,000 x 6.1446** = - 600,000 + 553,014 = - 46,986

Therefore,

ROR (%) = 5 + [94,953 / (94,953 + 46,986)] x (10 - 5)

= 5 + (94,953 / 141,939) x 5

= 5 + 0.6690 x 5

= 5 + 3.34

= 8.34%

(II) Alt B

NPVL = - 700,000 + 120,000 x P/A(5%, 10) = - 700,000 + 120,000 x 7.7217** = - 700,000 + 926,604 = 226,604

NPVH = - 700,000 + 120,000 x P/A(10%, 10) = - 700,000 + 120,000 x 6.1446** = - 700,000 + 737,352 = 37,352

Therefore,

ROR (%) = 5 + [226,604 / (226,604 - 37,352)] x (10 - 5)

= 5 + (226,604 / 189,252) x 5

= 5 + 1.1974 x 5

= 5 + 5.99

= 10.99%

(III) Since Alt B has higher ROR, Alt B should be selected.

**From P/A Factor table