A small company heats its building and will spend $ in year 1 on natural gas for this purpose. Cost increases of natural gas are expected to be % per year starting year 2. Their maintenance on the gas furnace is going to be $ in the first year and this expense is expected to increase by % per year starting year 2. If the planning horizon is years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is % per year.

(a) The total present worth of operating and maintaining the furnace is $72.18 thousands.

(b) Total annual equivalent expense for operating and maintaining the furnace is $14.41 thousands.

Explanation:

Note: This question is not complete as almost all the data in it and the requirement are omitted. The complete question is therefore provided before answering the question as follows:

A small company heats its building and will spend $9,156 in year 1 on natural gas for this purpose. Cost increases of natural gas are expected to be 9% per year starting year 2. Their maintenance on the gas furnace is going to be $391.00 in the first year and this expense is expected to increase by 15% per year starting year 2. If the planning horizon is 14 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 18% per year.

(a) The total present worth of operating and maintaining the furnace is $ thousands. (Round to two decimal places.)

(b) The total annual equivalent expense for operating and maintaining the furnace is $ thousands (Round to two decimal places.)

The explanation to the answers are now provided as follows:

(a) The total present worth of operating and maintaining the furnace is $ thousands. (Round to two decimal places.)

Note: See the attached excel file for the calculation of the total present worth of operating and maintaining the furnace.

Discounting factor = 1/(1 + r)^n

Where;

r = interest rate per year = 18%

n = relevant year

In the attached excel file, the total present worth of operating and maintaining the furnace is $72,175.29.

Presenting the answer as required by the question, the total present worth of operating and maintaining the furnace is $72.18 thousands.

(b) The total annual equivalent expense for operating and maintaining the furnace is $ thousands (Round to two decimal places.)

To calculate this, the formula for calculating the present value of an ordinary annuity is used as follows:

PW = P * ((1 – (1 / (1 + r))^n / r) …………………………………. (1)

Where;

PW = Total present worth of operating and maintaining the furnace as already obtained in part a above = $72,175.29.

P = total annual equivalent expense for operating and maintaining the furnace = ?

r = interest rate = 18% = 0.18

n = number of years = 14

Substitute the values into equation (1) and solve for P, we have:

$72,175.29 = P * ((1 - (1 / (1+18%))^14) / 18%)

$72,175.29 = P * 5.00806151960626

P = $72,175.29 / 5.00806151960626

P = $14,411.82

Presenting the answer as required by the question, total annual equivalent expense for operating and maintaining the furnace is $14.41 thousands.

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