Question

QUESTION 4 10 A company purchased a quality control system for $43,799 which requires $9,154 per year mainten ance fees for the first 5 years, after which the maintenance fees will increase by 12% per year for the upcoming 7 years. Determine the equivalent total present worth value of preached system during the 12 years operation at i = 15% per year.

Answer 1

The equivalent total present worth value of the quality control system during its 12 years operation at a 15% annual interest rate involves calculating the present value of the initial purchase cost, the present value of the maintenance fees for the first 5 years using the annuity formula, and the present value of escalating maintenance fees for the remaining 7 years individually.

Step-by-step explanation:

To determine the equivalent total present worth value of the quality control system during its 12 years of operation at a 15% annual interest rate, we'll first calculate the present value of the initial purchase cost of $43,799. This is a one-time expense, so its present value is simply the purchase price itself, as it occurs at the beginning of the period. Next, the maintenance fees for the first 5 years are constant at $9,154 per year. We can find the present value of these fees using the present value of an annuity formula.

After the first 5 years, the maintenance fees increase by 12% yearly. We need to calculate the present value of each of these increasing fees individually using the present value of a future amount formula for years 6 through 12. Once all the present values are found, we sum them up to get the total present worth value.