a 50 meter tunnel must be constructed for a new city aqeduct. one alternative is

Question

a 50 meter tunnel must be constructed for a new city aqeduct. one alternative is to builf a full-capacity tunnel now for $500,000. The other alternativ is to build a half-capacity tunnel now for $300,000 and then to build a second parallel half-capacity tunnel 20 years hence for $300,000. The cost to repair the tunnel lining every 10 years is $20,000 for the full-capacity tunnel and $16,000 for each half-capacity tunnel. Determine whether the full-capacity tunnel or the half-capacity tunnel should be constructed now. Solve the problem by the conventional benefit-cost ratio analysis, using 4% interest rate and a 50-year analysis period. There will be no tunnel lining repar at the end pf the 50 years.

Explanation / Answer

A. Building a full capacity tunnel:

PV of total cash outflow over the tunnel's lifetime= $532,960

B. Building a half capacity tunnel:

PV of total cash outflow over the tunnel's lifetime= $463,168

Benefit cost ratio is calculated by dividing cash inflows by cash outflows. Cash inflow is not present in this problem. However we can calculate how many times higher is the cost of constructing full capacity tunnel.

532,960/463,168= 1.15 times

It is better to construct the half capacity tunnel now because of its lower cost than the full capacity tunnel.

Particulars Year 0 1st Ten years Next 10 Next 10 Next 10 Initial cost ($) (500,000) Tunnel repair cost ($) 20,000 20,000 20,000 20,000 PVF@4% 1 0.676 0.456 0.308 0.208 PVAF (500,000) 13,520 9,120 6,160 4,160

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