16-27 A 50-meter tunnel must be constructed for a new city aqueduct. One alterna

Question

16-27 A 50-meter tunnel must be constructed for a new city aqueduct. One alternative is to build a full-capacity tunnel now for $500,000. The other alternative 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 a 4% interest rate and a 50-year analysis period. There will be no tunnel lining repair at the end of the 50 years.

Explanation / Answer

Statement showing present value of cash flow if we select to build full capacity now

Thus one should go for half capacity now

Year Total Particulars 0 10 20 30 40 Additional Initial expense 200000 Additional Repair expense 4000 4000 4000 4000 Savings in cost of further expansion -300000 Total cash outflow 200000 4000 -296000 4000 4000 PVIF @ 4 % 1 0.6246 0.4564 0.3083 0.2083 PV 200000 2498 -135091 1233 833 69474

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