A residential building is heated with a 78 percent efficient gas-fired furnace (

Question

A residential building is heated with a 78 percent efficient gas-fired furnace (costing
$1,600). The annual heating load is estimated at 160 MMBtu. The cost of gas is $6.00/
MMBtu. For the discount rate of 5 percent and a 10-year cycle, determine:
(a) The life cycle of the existing heating system
(b) If it is worth considering a 90 percent efficient gas-fired furnace that costs $2,800
(c) The variation of the life-cycle cost savings between the two systems [the existing system
and that proposed in (b)] versus the life of the system for life cycles ranging from
3 to 20 years
Conclude.

Explanation / Answer

Question a. Cost of Furnace 1600 Life 10 year Annual Depreciation 160 Cost of gass per unit 6 Working at 78% level, hence cost per unit = 6/78% = 7.6923 per MMBtu So annual operating cost = 160 x 7.6923 = 1230.77 PV factor Present Year Cash inflows at 5% Value 0 1600 1 1600 1 1230.77 0.952381 1172.161 2 1230.77 0.9070295 1116.344 3 1230.77 0.8638376 1063.185 4 1230.77 0.8227025 1012.557 5 1230.77 0.7835262 964.3399 6 1230.77 0.7462154 918.419 7 1230.77 0.7106813 874.6847 8 1230.77 0.6768394 833.0331 9 1230.77 0.6446089 793.3649 10 1230.77 0.6139133 755.5856 Total 13907.69 11103.67 Question b. Working at 90% level, hence cost per unit = 6/90% = 6.66667 per MMBtu So annual operating cost = 160 x 6.66667 = 1066.667 PV factor Present Year Cash inflows at 5% Value 0 1600 1 1600 1 1066.67 0.952381 1015.873 2 1066.67 0.9070295 967.4984 3 1066.67 0.8638376 921.4271 4 1066.67 0.8227025 877.5496 5 1066.67 0.7835262 835.7615 6 1066.67 0.7462154 795.9633 7 1066.67 0.7106813 758.0603 8 1066.67 0.6768394 721.9622 9 1066.67 0.6446089 687.5831 10 1066.67 0.6139133 654.841 Total 12266.67 9836.52 Question c. Cost Savings if 90%efficient furnace accepted over the existing system = 11,103.67-9836.52 = 1267.15

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