Question

A small company heats its building and spends ​$8000 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 9​% per year starting one year from now​ (i.e., the first cash flow is ​$8,720 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.

What is the total annual equivalent expense for operating and maintaining the furnace?

Please show all work.

Answer 1

i=20% = 0.2

Planning horizon = 15 years

Expense on natural gas in EOY1 = 8720 increasing at 9% per year uptil EOY 15, it is a geometric cash flow series

Present value at EOY 0 of this series is given by = C * [(1+g)^n/(1+i)^n - 1] / (g-i)

here c= 8720 ,g= 0.09, n = 15, i = 0.2

Putting values in the formula

P1 = 8720 * [(1+0.09)^15/(1+0.2)^15 - 1] / (0.09-0.2)

= 8720 * [(1.09)^15/(1.2)^15 - 1] / (-0.11)

= 8720 * 6.94166

= 60531.30

Expense on maintenace in EOY1 = 402.50 increasing at 15% per year uptil EOY 15, it is a geometric cash flow series

Present value at EOY 0 of this series is given by = C * [(1+g)^n/(1+i)^n - 1] / (g-i)

here c= 402.50 ,g= 0.15, n = 15, i = 0.2

Putting values in the formula

P2 = 402.50 * [(1+0.15)^15/(1+0.2)^15 - 1] / (0.15-0.2)

= 402.50 * [(1.15)^15/(1.2)^15 - 1] / (-0.05)

= 402.50 * 9.4372

= 3798.4744

Total present value = P1+P2

= 3798.4744 +60531.30 = 64329.77

total annual equivalent expense = 64329.77 * (A/P,20%,15)

= 64329.77 * 0.2138821

= 13758.98

= 13759 (rounding off)