A local telephone company is considering installing a new phone line for a new row of apartment complexes. Two types of cables are being examined: conventional copper wire and fiber optics. Transmission by copper-wire cables, although cumbersome, involves much less complicated and less expensive support hardware than does fiber optics. The local company may use five different types of copper wire cables: 100 pairs, 200 pairs, 300 pairs, 600 pairs, and 900 pairs per cable. In calculating the cost of cable, the following equation is used:
Cost = [cost per foot
+ cost per pair (number of pairs)](length)
where
22-gauge copper wire = $1,692 per foot
and
Cost per pair = $0,013 per pair
The annual cost of the cable as a percentage of the initial cost is 18.4%. The life of the system is 30 years.
In fiber optics, a cable is referred to as a ribbon. One ribbon contains 12 fibers, grouped in fours; therefore, one ribbon contains three groups of 4 fibers. Each group can produce 672 lines (equivalent to 672 pairs of wires), and since each ribbon contains three groups, the total capacity of the ribbon is 2,016 lines. To transmit signals via fiber optics, many modulators, wave guides, and terminators are needed to convert the signals from electric currents to modulated light waves. Fiber-optic ribbon costs $ 15,000 per mile. At each end of the ribbon, three terminators are needed, one for each group of 4 fibers, at a cost of $30,000 per terminator. Twenty-one modulating systems are needed at each end of the ribbon, at a cost of $12,092 for a unit in the central office and $21,217 for a unit in the field. Every 22,000 feet, a repeater is required to keep the modulated light waves in the ribbon at an intensity that is intelligible for detection. The unit cost of this repeater is $15,000. The annual cost, including income taxes for the 21 modulating systems, is 12.5% of the initial cost of the units. The annual cost of the ribbon itself is 17.8% of the initial cost. The life of the whole system is 30 years. (All figures represent after-tax costs.)
(a) Suppose that the apartments are located 5 miles from the phone company's central switching system and that about 2,000 telephones will be required. This would require either 2,000 pairs of copper wire or one fiber-optic ribbon and related hardware. If the telephone company's interest rate is 15%, which option is more economical?
(b) In part (a), suppose that the apartments are located 10 miles or 25 miles from the phone company's central switching system. Which option is more economically attractive under each scenario?