Question

A remotely located air sampling station can be powered by solar cells or by running an electric line to the site and using conventional power. Solar cells will cost $14,600 to install and will have a useful life of 4 years with no salvage value. Annual costs for inspection, cleaning, etc., are expected to be $1700. A new power line will cost $12,000 to install, with power costs expected to be $700 per year. Since the air sampling project will end in 4 years, the salvage value of the line is considered to be zero. At an interest rate of 6% per year, which alternative should be selected on the basis of a present worth analysis? Show your equations and solve problem using factors: solve it in Excel,

Answer 1

Solution :

Facts Given

Particulars	Solar Cells	Electric Line
First Cost	$14,600	$12,000
Annual Maintenance	$1,700	$700
Salvage Value	0	0
Useful Life	4	4
Interest rate	0.06 (6/100)	0.06 (6/100)

Present Worth Analysis based on The Net Present Value.

The Net Present Value = -C₀  + C₁ / (1+r) + C₂ / (1+r)^2 + C₃ / (1+r)^3 + C₄/ (1+r)^4

C_{0 =} Initial Investment

C = Cash Flow,  _{1,2,3 ,4 = time}

r = Interest Rate

The Net Present Value For Solar Cells

Net Present Value (Present Worth) = -14600+(-1700)/1.06+(-1700)/1.06^2+(-1700)/1.06^3+(-1700)/1.06^4

NPV = - $ 20,490.68

The Net Present Value For Electric Line

Net Present Value (Present Worth) = -12000+(-700)/1.06+(-700)/1.06^2+(-700)/1.06^3+(-700)/1.06^4

NPV = - $ 14,425.58

Although both are negative but in comparison of both the lower negative cost is NPV = - $ 14,425.58. The best alternative is to go for Electric Line

Calculation in Excel

A G H I J K L M N Present Worth Analysis Year Year 0 Solar Cell Initial Cost Expenses SV 0 - $14,600 -$1,700 $1,700 -$1,700 $1,700 Total -$14,600 -$1,700 $1,700 -$1,700 $0 $1,700 Electric Line Initial Cos Expenses SV $12,000 -$700 $700 -$700 $700 Total $12,000 -$700 -$700 -$700 $700 ŞO Present Worth -$20,490.68 Present Worth $14,425.57 Present Worth Formula =G9+NPV(0.06, G10:G13) Present Worth Formula =M9+NPV(0.06, M10:M13)