Question

Problem 4-88 (algorithmic) 3 Question Help A small company heats its building and spends $8,500 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 10% per year starting one year from now (i.e., the first cash flow is $9,350 at EOY one). Their maintenance on the gas furnace is $345 per year, and this expense is expected to increase by 12% per year starting one year from now (i.e., the first cash flow for this expense is $386.40 at the EOY one). If the planning horizon is 14 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 15% per year. 5 Click the icon to view the interest and annuity table for discrete compounding when i = 10% per year. Click the icon to view the interest and annuity table for discrete compounding when i = 12% per year. Click the icon to view the interest and annuity table for discrete compounding when i = 15% per year. The total annual equivalent expense for operating and maintaining the furnace is $ thousands. (Round to two decimal places.)

Answer 1

Present value of geometric series = A *[1 - (1+g)^n / (1+i)^n] / (i - g)

MARR = 15%

t = 14 years

natural gas cost = 9350 at EOY1 and increasing at rate of 10%

A = 9350, N = 14, i = 15%, g = 10%,

Present value using the equation given = 9350 *[1 - (1+0.1)^14 / (1+0.15)^14] / (0.15 - 0.1)

= 9350 *[1 - (1.1)^14 / (1.15)^14] / (0.05)

= 9350 * 9.26609313

= 86637.97

Maintanence cost = 386.40 at EOY1 and increasing at rate of 12%

A = 386.40, N = 14, i = 15%, g = 12%

A = 9350, N = 14, i = 15%, g = 10%,

Present value using the equation given = 386.40 *[1 - (1+0.12)^14 / (1+0.15)^14] / (0.15 - 0.12)

= 386.40 *[1 - (1.12)^14 / (1.15)^14] / (0.03)

= 386.40 * 10.31036598

= 3983.93

Total present value = 86637.97 + 3983.93 = 90621.90

Total annual equivlent cost = 90621.90 * (A/P, 15%,14)

= 90621.90 * 0.174688

= 15830.60

= 15.83 thousands (Round to two decimal places)