Question

Consider the relative costs of a timber pedestrian bridge and a steel one; their initial capital costs, annual OMR costs and useful lives are given below:

Timber Bridge             Steel Bridge

Initial capital cost      $500,000                     $700,000

Annual OMR cost       $30,000                       $5000

Life span                     15 years                      30 years

Find the alternative of the least overall costs (use i = 8%). Use both present worth and annual worth methods.

Answer 1

For present worth analysis, LCM method will be used to equate the lives of the different alternatives. So, the LCM based evaluation period will be 30 years.

PW of Timber Bridge alternative = -500000 - 500000*(P/F, 8%, 15) - 30000*(P/A, 8%, 30)

PW of Timber Bridge alternative = -500000 - 500000*.3152 - 30000*11.2578

PW of Timber Bridge alternative = -$995334

PW of steel Bridge alternative = -700000 - 5000*(P/A, 8%, 30)

PW of steel Bridge alternative = -700000 - 5000*11.2578

PW of steel Bridge alternative = -$756289

Since steel bridge is more cost effective ( $756289) than the timber bridge alternative (995334), so steel bridge alternative should be selected.

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Annual worth analysis:

AW of Timber Bridge alternative = -995334*(A/P, 8%, 30) = -995334*.0888

AW of Timber Bridge alternative = -$88385.66 or - $88386

AW of steel Bridge alternative = -756289*(A/P, 8%, 30) = -756289*.0888

AW of steel Bridge alternative = -$67158

Since steel bridge is more cost effective in terms of AW than the timber bridge alternative, so steel bridge alternative should be selected.