Question

12- A small company pays $ 8,000 per year on electricity for the air conditioning purpose. Cost increases of electricity are expected to be 10%. per year starting one year from know (.e. the first cash flow is $8,800 at the end of year one). Their maintenance on the air conditioners is $ 345 per year and this expense is expected to increase by 15% per year starting one year from new. If the planning-horizon-is-15 year, what is the total annual equivalent expense for operating and nu intaining the air conditioning system? The interest rate is 18% per year,

Answer 1

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

Present value of air conditioning cost = 8800 * [1 - (1+0.1)^15 / (1+0.18)^15] / (0.18 - 0.1)

= 8800 * [1 - (1.1)^15 / (1.18)^15] / 0.08

= 8800 * 8.139159

= 71624.61

Present value of maint. cost = 345 * 1.15 * [1 - (1+0.15)^15 / (1+0.18)^15] / (0.18 - 0.15)

= 396.75 * [1 - (1.15)^15 / (1.18)^15] / 0.03

= 396.75 * 10.980828

= 4237.62

Total Present value = 71624.61 + 4237.62 = 75862.23

Equivalent annual cost = 75862.23 * (A/P, 18%,15)

= 75862.23 * 0.196403

= 14899.55 ~ 14900