Question

7. The bridge 9340 on I-35 in Minnesota collapsed in August 2007 and the state is now considering installing a better structure that will cos $250 Million now and additional cost of S75 million for additional reinforcement 10-years from now. After this, there will a perpetual resurfacing cost of $15 Milliohm every 10 years. Assuming an interest rate of 6% year compounded quarterly, determine the capitalized cost the state must have to fund this project. Show work

Answer 1

i = 6% compounded quarterly = 6%/4 = 1.5% per quarter

Effective rate = (1+0.015)^4 - 1 = 0.06136355 = 6.136355%

CC = 250m + 75m *(P/F,6.136355%,10) + 15m *(A/F,6.136355%,10)*(P/F,6.136355%,10) / 0.06136355

(A/F,6.136355%,10) = i/((1 + i)^n-1) = 0.06136355 / (( 1 +0.06136355)^10 -1) = 0.07538349

(P/F,6.136355%,10) = (1 + i)^-n = (1 + 0.06136355)^-10 = 0.55126232

CC = 250000000 + 75000000 * 0.55126232 + 15000000 * [0.07538349*0.55126232 / 0.06136355]

CC = 250000000 + 41344674 + 10158166.60

CC = 301502840.60

CC = 301.50 m