Respuesta :
Answer:
(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.
