Suppose you have just bought a new house and are considering the installation of
ID: 2644084 • Letter: S
Question
Suppose you have just bought a new house and are considering the installation of 10 compact fluorescent bulb (CFB) fixtures instead of the 10 conventional incandescent lighting fixtures (The incandescent lighting fixtures without the bulbs cost a total of $450). According to the builder, CFBs use 75% less electricity than incandescent bulbs, and they last 10 times longer before the bulb needs replacement. Bob calculates that 1,100 watts of incandescent lighting will be required in the house for 2,750 hours of usage per year. The cost of electricity is $0.10 per kWh. Also, each CFB will save 124 pounds of CO2 per year. Each pound of CO2 has a penalty of $0.02. If incandescent bulbs cost $0.75 each and last for one year, use a 10 year study period to determine the maximum cost of CFB fixtures and bulbs that can be justified in this house.
MARR = 8%
The maximum cost of the CFB fixtures and bulbs is $______ per CFB.
Please show work so I can analyze
Suppose you have just bought a new house and are considering the installation of 10 compact fluorescent bulb (CFB) fixtures instead of the 10 conventional incandescent lighting fixtures (The incandescent lighting fixtures without the bulbs cost a total of $450). According to the builder, CFBs use 75% less electricity than incandescent bulbs, and they last 10 times longer before the bulb needs replacement. Bob calculates that 1,100 watts of incandescent lighting will be required in the house for 2,750 hours of usage per year. The cost of electricity is $0.10 per kWh. Also, each CFB will save 124 pounds of CO2 per year. Each pound of CO2 has a penalty of $0.02. If incandescent bulbs cost $0.75 each and last for one year, use a 10 year study period to determine the maximum cost of CFB fixtures and bulbs that can be justified in this house. MARR = 8% The maximum cost of the CFB fixtures and bulbs is $_ per CFB.Explanation / Answer
CFBs last 10 times longer than incandescent bulbs. Since useful life of each incandescent bulb is 1 year, useful life of each CFB is 10 years.
For annual usage of 2,750 hours,
Electricity consumed by 10 incandescent bulbs = 1,100 W
Electricity consumed by 10 CFB bulbs = 1,100 W x 25% = 275 W
Total annual saving of electricity if CFB are used = (1,100 - 275) W x $0.10 / 100 = $0.01 x 825 W = $82.5 per year
Total saving from CO2 penalty = 10 x 124 pounds x $0.02 per pound = $24.8 per year
Total annual saving from using CFB = $(82.5 + 24.8) = $107.3 per year
Total cost of incandescent bulbs per year = $0.75 x 10 = $7.50
Net annual benefit from using CFB = $(107.3 - 7.5) = $99.8 per year
Maximum justified cost is the NPV of initial costs of CFB fixtures and net annual benefit for 10 years.
NPV ($) = - 450 + 99.8 x P/A (8%, 10 years)
= - 450 + 99.8 x 6.7101
= - 450 + 669.67
= 219.67
So, maximum justified cost is $219.67.
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