Q1 A new highway is being evaluated at an interest rate of i

Q1) A new highway is being evaluated at an interest rate of i cost to determine which plan is most suitable. 5.5%. Use capitalized $28M 342,000 238,000 Initial Cost Annual maintenance periodic major maintenance periodic major maintenance done every 1.6 M 1.2M 12 18 in years

Solution

FOr A

Initial cost = 18000 k

Annual maintenance = 342k

i = 5.5%

Periodic maintenance = 1600k

n = 12

Capitalized cost = -18000k - 1600 k (P/F,i%,n) - 342k/i

Capitalized cost = -18000k - 1600 k (P/F,5.5%,n) - 342k/5.5%

(P/F,i,n) = 1 / (1+i)ⁿ

(P/F,5.5%,12) = 1 / (1 + 0.055)¹² = 0.526

Capitalized cost = -18000k - 1600 k x0.526 - (342k/0.055)

Capitalized cost = -25059k

For B

Initial cost = 28000 k

Annual maintenance = 238k

i = 5.5%

Periodic maintenance = 1200k

n = 18

Capitalized cost = -28000k - 1200 k (P/F,i%,n) - 238k/i

Capitalized cost = -28000k - 1200 k (P/F,5.5%,n) - 238k/5.5%

(P/F,i,n) = 1 / (1+i)ⁿ

(P/F,5.5%,18) = 1 / (1 + 0.055)¹⁸ = 0.382

Capitalized cost = -28000k - 1200 k x0.382 - (238k/0.055)

Capitalized cost = -32785.67

As the value for A is greater than B we select A