Question

A small company heats its building and spends $8,400 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 8% per year starting one year from now (i.e., the first cash flow is $9,072 at EOY one). Their maintenance on the gas furnace is $350 per year, and this expense is expected to increase by 15% per year starting one year from now i.e., the first cash flow for this expense is $402.50 at the EOY one if the planning horizon is 15 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 20% per year.

The total annual equivalent expense for operating and maintaining the furnace is_____thousands.​ (Round to two decimal​ places.)

Answer 1

Cost of gas in EOY 1 = $9072

Cost of maintenance in EOY1 = $402.5

Time = 15 years

R = 20%

g1 = 8%

g2 = 15%

Present value of the cost of gas = (9072/(.2-.08))*(1- (1.08/1.20)^15)

Present value of the cost of gas = $60034.63

Present value of the maintenance cost = (402.5/(.2-.15))*(1- (1.15/1.20)^15)

Present value of the maintenance cost = $3798.47

So,

Present value of total cost = 60034.63 + 3798.47

Present value of total cost = $63833.1

Let, uniform annual O&M expenses = P

Then,

P = 63833.1/((1-1/1.2^15)/.15)

P = $10239.57

So, total uniform annual O&M expenses is $10239.57.