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 $12,600 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 $1,400. A new power line will cost $11,000 to install, with power costs expected to be $800 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 10% per year, which alternative should be selected on the basis of a future worth analysis?

Answer 1

Answer:

Since the total future worth of running an electric line of $19,353.42 is less than the total future worth of solar cells is $24,132.22, it implies that it will be cheaper to run an electric line than to use solar cells. Therefore, running an electric line should be selected.

Explanation:

The future worth analysis refers to an act of determining what the the worth of present amount of money or stream of money invested at an interest rate will after in some period or years to come.

To determine which one to select between solar cells and running an electric line, the we need to calculate the future worth of both and compared as follows:

a. Calculation of future value of solar cells

Calculation of future worth of $12,600 installation cost

FW of $12,600 = PW of $12,600 * (1 + r)^n ................ (1)

Where;

FW of $12,600 = Future worth of $12,600 installation cost = ?

PW of $12,600 = Present worth of $12,600 installation cost = $12,600

r = interest rate = 10%, or 0.10

n = number of years = 4

Substitute the values into equation (1), we have:

FW of $12,600 = $12,600 * (1 + 0.10)^4

FW of $12,600 = $12,600 * 1.4641

FW of $12,600 = $18,447.66

Calculation of future worth of annual costs for inspection, cleaning, etc. of $1,400

The future worth of annual costs for inspection, cleaning, etc. of $1,400 can also be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FW of $1,400 = M * (((1 + r)^n - 1) / r) ................................. (2)

Where,

FW of $1,400 = Future value of Annual costs for inspection, cleaning, etc. of $1,400 =?

M = Annual costs for inspection, cleaning, etc. = $1,400

r = interest rate = 10%, or 0.10

n = number of years = 4

Substitute the values into equation (2), we have:

FW of $1,400 = $1,400 * (((1 + 0.01)^4 - 1) / 0.01)

FW of $1,400 = $1,400 * 4.060401

FW of $1,400 = $5,684.56

Calculation of total future worth of solar cells

This is calculated by simply adding the FW of $12,600 and FW of $1,400 as follows:

Total future worth of solar cells = FW of $12,600 + FW of $1,400 = $18,447.66 + $5,684.56 = $24,132.22

Therefore, the total future worth of solar cells is $24,132.22.

b. Calculation of future value of running an electric line

Calculation of future worth of $11,000 installation cost

FW of $11,000 = PW of $11,000 * (1 + r)^n ................ (3)

Where;

FW of $11,000 = Future worth of $11,000 installation cost = ?

PW of $11,000 = Present worth of $11,000 installation cost = $11,000

r = interest rate = 10%, or 0.10

n = number of years = 4

Substitute the values into equation (3), we have:

FW of $11,000 = $11,000 * (1 + 0.10)^4

FW of $11,000 = $11,000 * 1.4641

FW of $11,000 = $16,105.10

Calculation of future worth of expected annual power costs of $800

The future worth of expected annual power costs of $800 can also be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FW of $800 = M * (((1 + r)^n - 1) / r) ................................. (4)

Where,

FW of $800 = Future value of expected annual power costs of $800 =?

M = Expected annual power costs = $800

r = interest rate = 10%, or 0.10

n = number of years = 4

Substitute the values into equation (4), we have:

FW of $800 = $800 * (((1 + 0.01)^4 - 1) / 0.01)

FW of $800 = $800 * 4.060401

FW of $800 = $3,248.32

Calculation of total future worth of running an electric line

This is calculated by simply adding the FW of $11,000 and FW of $800 as follows:

Total future worth of running an electric line = FW of $11,000 + FW of $800 = $16,105.10 + $3,248.32 = $19,353.42

Therefore, the total future worth of running an electric line is $19,353.42.

c. Conclusion

Since the total future worth of running an electric line of $19,353.42 is less than the total future worth of solar cells is $24,132.22, it implies that it will be cheaper to run an electric line than to use solar cells. Therefore, running an electric line should be selected.