Question

A steam generation system at a biomassfueled power plant uses an electrostatic precipitator​ (ESP) to clean its gaseous effluents. The power plant has consistently made use of the same type of ESP over the past several years. The installed cost of a new ESP has been relatively constant at ​$75 comma 00075,000. Records of operation and maintenance expenses indicate the following average expenses per year as a function of the age of the ESP. The MVs of the ESP are also reasonably well known as a function of age. Determine the best time to replace the ESP if the MARR is 99​% per year.

Answer 1

To determine the best time to replace the ESP, calculate the present value of expenses and benefits at different ages. Compare the two to find the age where benefits exceed expenses.

Step-by-step explanation:

To determine the best time to replace the electrostatic precipitator (ESP), we need to consider the present value of the expenses and compare it to the present value of the benefits. The present value of the expenses is the sum of the installation cost and the average annual operation and maintenance expenses, multiplied by the discount factor. The present value of the benefits is the sum of the market values (MVs) of the ESP at different ages, multiplied by the discount factor.

We can calculate the present value of the expenses and benefits for different ages of the ESP, and find the age at which the present value of the benefits exceeds the present value of the expenses. This will be the best time to replace the ESP.

Let's assume the discount factor for the MARR of 99% per year is d=1/(1+MARR) = 1/(1+0.99) = 1/1.99 ≈ 0.5025.

1. Calculate the present value of the expenses:
   • For each age of the ESP, multiply the average annual expense by the discount factor and sum them up.
   • Add the installation cost of $75,000 to the sum.
2. Calculate the present value of the benefits:
   • For each age of the ESP, multiply the market value by the discount factor and sum them up.
3. Compare the present value of the expenses and benefits for each age of the ESP to identify the age where the benefits exceed the expenses. This will be the best time to replace the ESP.