Question

The Texas Department of Transportation (TxDOT) is considering two designs for crash barriers along a reconstructed portion of I-10. Design 2B will cost $3 million to install and $125,500 per year to maintain. Design 4R will cost $3.7 million to install and $55,000 per year to maintain. Determine which design should be selected based on a rate of return analysis if TxDOT uses a MARR of 6% per year and a 20-year project period. The rate of return is Not attempted ______%.

Answer 1

incremental initial cost (4R - 2B) = 3.7m - 3m = 0.7m = 700000

incremental annual cost (4R - 2B) = 55000 - 125000 = -70000 (Annual savings)

Let incremental ROR be i%, then

70000*(P/A,i%,20) = 700000

(P/A,i%,20) = 700000 / 70000 = 10

using trail and error method

When i = 7%, value of (P/A,i%,20) = 10.594014

When i = 8%, value of (P/A,i%,20) = 9.818147

using interpolation

i = 7% + (10.594014-10)/(10.594014-9.818147)*(8%-7%)

i = 7% + 0.76% = 7.76% (Approx)

As incremental IRR is greater than 6% (MARR), Design 4R should be selected