458. A farmer wants to install a tube-well but is unsure about its feasibility. The water table in his area is at 60 meters, and the cost of pumping water increases by \textdollar 100 for every meter below 15 meters. The total initial installation cost is \textdollar 8,000. If the farmer expects to recover the cost in 5 years through increased farm production, what is the minimum annual profit required from the tube-well to justify its installation, assuming the operational cost is \textdollar 1,000 per year?
Key Concept: Tube-Well Feasibility, Economic Factors
b) \textdollar 3,500
[Solution Description]
First, calculate the additional pumping cost due to the water table depth:
Depth beyond 15 meters = 60 - 15 = 45 meters.
Additional cost = 45 * 100 = \textdollar 4,500.
Total installation cost = Initial cost + Additional cost = 8,000 + 4,500 = \textdollar 12,500.
Total operational cost for 5 years = 1,000 * 5 = \textdollar 5,000.
Total cost over 5 years = 12,500 + 5,000 = \textdollar 17,500.
To break even, the farmer needs to recover \textdollar 17,500 in 5 years.
Minimum annual profit required = 17,500 / 5 = \textdollar 3,500.
Your Answer is correct.
b) \textdollar 3,500
[Solution Description]
First, calculate the additional pumping cost due to the water table depth:
Depth beyond 15 meters = 60 - 15 = 45 meters.
Additional cost = 45 * 100 = \textdollar 4,500.
Total installation cost = Initial cost + Additional cost = 8,000 + 4,500 = \textdollar 12,500.
Total operational cost for 5 years = 1,000 * 5 = \textdollar 5,000.
Total cost over 5 years = 12,500 + 5,000 = \textdollar 17,500.
To break even, the farmer needs to recover \textdollar 17,500 in 5 years.
Minimum annual profit required = 17,500 / 5 = \textdollar 3,500.