Question

x=04

Q3. [20 marks] For this question, X is the first two digits (from the right) of your student ID. A Chinese official is considering construction of a lift system that transports visitors from the tops of the mountain peaks to the valley at the National Forest Parks in China. The lift system is expected to last for 30 years. Annual maintenance costs are expected to be $260,000. Moreover, inspection and repair costs of $40,000 every five years (including year 30) are expected. Annual benefits are estimated to be $425,000. If an interest rate of 15% per year is used and a conventional B-C ratio of at least 1.X (using the PW method) is targeted, what is the maximum investment cost allowed for the lift system?

Answer 1

The conventional B-C ratio is obtained using the following equation

ratio = Present worth of benefits Initial investment + Present worth of annual maintenance + Present worth of inspection every 5 years

Present worth of benefits = $ 425,000 $\times$ (P/A, 15%, 30 years)

(P/A, 15%, 30 years) = Uniform series present worth factor

Present worth of benefits = $ 425,000 $\times$   6.566 = $ 2,790,550

Present worth of annual maintenance = $ 260,000 $\times$ (P/A, 15%, 30 years) =   $ 260,000 $\times$   6.566

Present worth of annual maintenance = $ 1,707,160

Present worth of inspection and repair costs = $ 40,000 $\times$ (P/F, 15%, 5 years) + $ 40,000 $\times$ (P/F, 15%, 10 years) + $ 40,000 $\times$ ​​​​​​​ (P/F, 15%, 15 years) + $ 40,000 $\times$ ​​​​​​​ (P/F, 15%, 20 years) + $ 40,000 $\times$ ​​​​​​​ (P/F, 15%, 25 years) + $ 40,000 $\times$ ​​​​​​​ (P/F, 15%, 30 years)

(P/F, 15%, 5 years) = Single payment present worth factor

Present worth of inspection and repair costs = $ 40,000 $\times$ 0.4972 + $ 40,000 $\times$ ​​​​​​​ 0.2472 +  $ 40,000 $\times$ ​​​​​​​​​​​​​​ 0.1229 +  $ 40,000 $\times$ ​​​​​​​​​​​​​​ 0.0611 + $ 40,000 $\times$ ​​​​​​​​​​​​​​ 0.0304 + $ 40,000 $\times$ 0.0151

Present worth of inspection and repair costs = $ 38956

1.04 $ 2,790,550 Initial investment + $ 1,707,160 + $ 38956

Solving for the initial investment, we get

Maximum investment cost allowed for the lift system = $ 937105.2 $\approx$ $ 937,105