Question

A remotely located air sampling station can be pow- ered by solar cells or by running an above ground electric line to the site and using conventional power. Solar cells will cost $16,600 to install and will have a useful life of 5 years with no salvage value. Annual costs for inspection, cleaning, etc., are expected to be $2400. A new power line will cost $31,000 to install, with power costs expected to be $1000 per year. Since the air sampling project will end in 5 years, the salvage value of the line is considered to be zero. At an interest rate of 10% per year, (a) which alternative should be selected on the basis of an annual worth analysis and (b) what must be the first cost of the above ground line to make the two alternatives equally attractive economically? both excel and hand solutions , please capture the excel solution.

Answer 1

MARR = 10%

t = 5 yrs

a. EUAC of solar option = 16600*(A/P,10%,5) + 2400 = 16600*0.263797 + 2400 = 6779.04

EUAC of convention power = 31000*(A/P,10%,5) + 1000 = 31000*0.263797 + 1000 = 9177.72

Solar option should be selected as EUAC of solar is less

b. Let first cost be P, then as per condition givrn in question

EUAC of convention power = EUAC of solar option

P*(A/P,10%,5) + 1000 = 6779.04

P*0.263797 = 5779.04

P = 5779.04 / 0.263797 = 21907.11

Using Excel

a.

Year	Cash Flow of Solar	Cash Flow of Conventional
0	-16,600.00	-31000
1	-2,400.00	-1000
2	-2,400.00	-1000
3	-2,400.00	-1000
4	-2,400.00	-1000
5	-2,400.00	-1000
NPV	-25,697.89	-34,790.79
EUAC	6,779.04	9,177.72

As EUAC of Solar option is less it should be selected

b.

O&M conventional	1,000.00
EUAC of solar	6,779.04
Price	21,907.11

Showing formula in excel

Year	Cash Flow of Solar	Cash Flow of Conventional
0	-16600	-31000
1	-2400	-1000
2	-2400	-1000
3	-2400	-1000
4	-2400	-1000
5	-2400	-1000
NPV	=NPV(10%,N9:N13)+N8	=NPV(10%,O9:O13)+O8
EUAC	=PMT(10%,5,N14)	=PMT(10%,5,O14)
O&M conventional	1000
EUAC of solar	6779.04
Price	=-PV(10%,5,N17-N16)