Question

An engineer wants to estimate the annual inflation-free cost of owning an aerobic digester system with a capacity of 195 million gallons per day (MGD) for the first 8 years of operation. Company records show that the cost of a similar system with a capacity of 75 MGD was $8 million five years ago. The equipment cost index has increased 26% per year since then, and the future general inflation rate is forecast to be 2% per year. He estimates that the annual operating expenses of the new system would be $440,000 per year for the first two years and increase to $441,500 per year thereafter, due to the increase in maintenance costs. Calculate the annual inflation-free cost of owning the 295-MGD system for the first 8 years. Use a cost-capacity exponent of 0.14 for the system and a market-based MARR of 8% per year.

Answer 1

Step 1: Calculate Initial Cost of New System (Power Sizing Technique)

The initial cost of the new system with the use of power sizing technique is determined as below:

Initial Cost of the New System = Cost of System 5 Years Ago*(Capacity of New System/Capacity of Old System)^Cost-Capacity Index*(1+Percentage Increase in Equipment Cost Index)^8

Using the values provided in the question in the above formula, we get,

Initial Cost of the New System = 8,000,000*(195/75)^.14*(1+26%)^5 = $29,042,833.25

_____

Step 2: Calculate Present Worth of Costs Associated with New System

The present worth of the costs can be calculated with the use of following formula:

Present Worth of Costs = -Initial Costs of New Equipment - Operating Expenses Year 1/(1+MARR)^1 - Operating Expenses Year 2/(1+MARR)^2 - Operating Expenses Year 3/(1+MARR)^3 - Operating Expenses Year 4/(1+MARR)^4 - Operating Expenses Year 5/(1+MARR)^5 - Operating Expenses Year 6/(1+MARR)^6 - Operating Expenses Year 7/(1+MARR)^7 - Operating Expenses Year 8/(1+MARR)^8

Using the value calculated in Step 1 and information provided in the question in the above formula, we get,

Present Worth of Costs = -29,042,833.25 - 440,000/(1+8%)^1 - 440,000/(1+8%)^2 - 441,500/(1+8%)^3 - 441,500/(1+8%)^4 - 441,500/(1+8%)^5 - 441,500/(1+8%)^6 - 441,500/(1+8%)^7 - 441,500/(1+8%)^8 = $31,577,243.45

_____

Step 3: Calculate Real Rate of Interest

The real rate of interest is arrived with the use of following equation

MARR = Real Rate of Interest + Inflation + Inflation*(Real Rate of Interest)

Substituting values in the above formula, we get,

8% =  Real Rate of Interest + 2% + 2%* Real Rate of Interest

Rearranging values, we get,

Real Rate of Interest = (8% - 2%)/(1+2%) = 5.88%

_____

Step 4: Calculate Annual Worth

The annual worth can be calculated with the use of following formula:

Annual Worth = Present Worth of New System/PVIFA(Real Interest Rate, Period) = 31,577,243.45/6.2394 = -$5,061,832.12 per year (answer)

_____

Notes:

1) There can be a difference in final answer on account of rounding off values.

2) I have used actual figures in the calculation of answer. However, I have posted rounded off values in the answer.