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.
Step-by-step 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.