Question

Your landlord has read up on the benefits of electric heat pumps, and has decided to replace your ancient 45,000 BTU/hr gas furnace with a 1500W electric heat pump space heater (which has both space heating and cooling capacity) in your Berkeley house.

1. a) Given the following information, what is the net present value of replacing the appliance? Will the cost of the initial investment be recovered?

   • The heat pump appliance costs $1,200.

   • Installation costs are $3,000.

   • The heat pump can be expected to last 15 years with an average of $115/year of

     maintenance costs. Its resale value in 15 years will be -$300; you will have to hire

     a contractor to dispose of the heat pump safely.

   • Continued operation of the furnace would have cost an average of $350/year in

     maintenance for the next 15 years.

   • The resale value of the furnace is -$300; you will have to hire a contractor to

     dispose of the furnace safely.

   • In the winter months (Nov-Feb) your house will use the heat pump for 6 hours per

     day; In all other months, your house will use the heat pump for an average of 1.5

     hours per day.

   • In the winter months (Nov-Feb) your house used your gas furnace for 14 hours

     per day; In all other months, your house never used the furnace.

   • The cost of gas is $1.15/therm and the cost of electricity is $0.13/kWh.

   • The inflation rate is 1.5%.

b) Assuming that you plan to live in your house forever, and pay your ​utility bills,​ but your landlord pays for the appliances, installation, and maintenance, what fraction of the net present value is captured by you and your housemates through utility bill savings?

In 2019, you bought a hybrid car to replace your old gas guzzler. Your hybrid (used) cost you $13,000, and gets 48 mpg city/45 mpg highway. Your old car’s mileage was 25 mpg city/30 mpg highway. Gas costs $3.15/gallon, and you drive 12,000 miles per year. You sold your car for $1,900. You typically drive 74 percent of your miles on the highway and 26 percent in the city.

c) Use the simple payback equation to calculate the number of years it will take to recover the cost of your investment.

d) Now assume that California levies a carbon tax. Carbon dioxide emissions are priced at $50/ton, and paid at annual inspections. Every gallon of gas burned creates 8,887 grams of CO2. What is the new payback period for the new car?

what kind of new information do you need?

Answer 1

( A )

Heat Pump
Total Days	365	Hours	Electricity Cost
Nov-Feb	120	6	93.6
Other	245	1.5	47.775
	Per Annum Electricity Cost		141.375
Year	Particulars	Cash Flow	PVF @1.5%	PV
0	Heat Pump Cost and Installation	-4,200.00	1	-4,200.00
0	Resale value of Gas furnance	300	1	300.00
1 - 15	Maintenance & Electricity Cost	-256.38	13.3432	-3,420.86
15	Resale Value	300.00	0.799852	239.96
	Net Present Value			-7,080.91

Gas Furnance.
Total Days	365	Hours	Gas Cost
Nov-Feb	120	14	1932
Other	245	0	0
	Per Annum Gas Cost		1932
Year	Particulars	Cash Flow	PVF @1.5%	PV
1 - 15	Maintenance & Gas cost	-2282	13.3432	-30,449.18
	Net Present Value			-30,449.18

From the above Caculation, it is advisable to replace the gas furnance with Heat Pump, since Net Present VAlue of Heat pump is more.

(B) 26.64 percent fraction of the net present value is captured by me and my housemates through utility bill savings.

(C)

Sr. No.	Paticulars	Data	City	Highway	Total Cost
1	New Car	MPG	48	45
2	Old Car	MPG	25	30
3	Total Miles	12000	26%	74%
4	Miles Per Year		3,120	8,880
5	New Car	Gallon Required (4 / 1)	65	197
6		Cost of Gallon (Gallon Req.* 3.15)	204.75	621.60	826.35
7	Old Car	Gallon Required (4 / 2)	124.80	296.00
8		Cost of Gallon (Gallon Req.* 3.15)	393.12	932.40	1,325.52
9	Saving Each Year by New Car	499.17
10	Investment	13,000
11	Sale of Old Car	1,900
12	Net Investment to be recover ( 11-10)	11,100
13	No. of Year required to recover balance investment ( 12 /9)	22.236913
				Approx.	22.5 years

(D) For Calculating the payback period in case when CAlifornia levies Carbon Tax, There would require additional information such as how the tax is being levied, whether it to be paid every year or only in the year when inspection conducted? etc.