Question

1. Suppose you are going to purchase a new heater for your home. You have a choice of an electric heater or a natural gas heater. The cost of the electric heater is $4,000 and the natural gas heater is $6,000. The cost of electricity is $0.10/kwh and the cost of natural gas is $0.50/therm. Assume you use 10,000 kwh of electricity or 1,000 therms each year to heat your home. Each heater is expected to last 25 years. To simplify the problem, do not account for the time value of money.

A. If you did not account for the time value of money and you expected the prices of natural gas and electricity to remain the same, which heater would be the lowest total cost? How much would the other one cost?

B. If you assumed that the cost electricity would increase at 5% a year and natural gas would increase at 10% a year, which heater would be the lowest total cost? How much would the other one cost?

I already have A figured out I need help with B though!

Answer 1

Since you have already figured out the Answer to (A) , proving the answer to (B) only :

Answer (B): Total cost of electricity in one year = 10,000 * 0.10 = $ 1000

If the cost of electricity increases by 5%, then the total cost of electricity = $1000 + (5% of 1000) = $1050

In this case, the cost of electric heater = $4000 + consumption of electricity in 25 years

                                                                     = $4000 + (1050 x 25)

                                                                     = $4000 +   $26,250

                                                                     = $ 30,250

& The Total cost of Natural Gas in one year = 1,000 * 0.50 = $ 500

If the cost of Natural Gas increases by 10%, then the total cost of Natural Gas = $500 + (10% of 500) = $550

In this case, the cost of Natural Gas heater = $6000 + consumption of Natural Gas in 25 years

                                                                     = $6000 + (550 x 25)

                                                                     = $6000 +   $13,750

                                                                     = $ 19,750

We can see that even if the price of electricity increases by 5% and that of Natural Gas increases by 10%, even then, at the end of 2 years, the total cost of Electric heater is $30,250 and that of the Natural Gas heater is $19,750.

The Natural Gas heater would be of lower cost.