Question

A project has a life of 10 years and no salvage value. Your firm uses an MARR of 8% to evaluate projects. The project has uncertain costs and revenue as shown in the table below:

Determine the risk for the project expressed as the standard deviation of the expected value of the EUAW. Express your answer in $ to the nearest $100.

Answer 1

EUAW or EUAC = Equivalent Uniform Annual Worth or Cost

The equivalent uniform annual cost (EUAC) formula converts upfront costs into an equivalent annual expense to enable accurate comparisons between similar expense terms. The annual worth is the net of all the benefits and costs incurred over a one-year period. we present the net of all the different benefits and costs incurred at different points of time in a one-year period with one number, and we call it the annual worth. For a system whose life is longer than one year, this number will be different for different years. For systems having more than one year of life, we can calculate a single virtual number that represents an equivalent annual net benefit or cost for the duration of the system life. This virtual number is called the equivalent uniform annual worth (EUAW) and is equal to the total benefit and cost of the system as if it was spread evenly throughout the years of its life. We can express this in a different way. The net present worth ofthe system, calculated as if its net benefit or cost for each year was the calculated EUAW, is the same as the net present worth of the same system using the real values of costs and benefits at their real time of occurrence.

(A/P, i, n) is the capital recovery factor, and its value for any i and n can be found in compound interest tables. This is the same as spreading the NPW of a project over the life of the project. When the EUAW of a system or project is a positive number, it indicates that the project is economically viable or profitable. The advantage of this method is that we need not worry about the unequal lives or the unequal initial investment of the two systems being compared. They are taken into account automatically through the mathematics of the analysis method

1. EUAW of Worth = (37500)(A/F,8%,10) + 4800

= 10387.26

2. EUAW of Worth = (132000)(A/F,8%,10) + 22000

= 41667.15

3. EUAW of Worth = (51000)(A/F,8%,10) +16200

= 23798.67