## Annual Worth and Equivalent Uniform Annual Worth

Vertex42 The Excel Nexus

Get Instant Access

The annual worth is the net of all the benefits and costs incurred over a one-year period. Therefore, 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.

The simplest process for calculating this number takes two steps.

Step 1:

All the costs and benefits are transferred to the present year using equation 2.2a to calculate the NPW.

Step 2:

Multiplying the NPW by a factor called capital recovery factor converts it to EUAW. This multiplier is

### Or as in previous cases

(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.

If the EUAW method is used for choosing among more than two alternatives, we simply have to calculate the EUAW of all of them and choose the one with the highest EUAW.

When a bank gives you a loan to buy a house, it spreads the loan over the next 15 or 30 years. In effect, your mortgage payments are the EUAW of the loan.

Example 4.1

Find the EUAW for the project of example 1.3. Step 1:

Draw the cash flow diagram and calculate the NPW:

5000

24h00Q

We have already done this and we know that NPW = 326.61

We can either use equation 4.1a or expression 4.1b. Using the latter, EUAW = 8 26.61 (A/P, 10,4) = 826.51 (.3155) = 260%

This means that the NPW of 826.61 is the same as an annual value of 260.8 for four years. The use of spreadsheet will give us the same result.

 jl p b o r mat 4 H ■ J M m Ei amp I* +.1 i EK up ths- sp'eadshep! ji shown bp-low: I_ hUnHI 10« > iff Ye,ar 0 1 2 3 4 r '1+050 + 600 +600 +600 HUH t First wt oiloul it* th" NPW u w* M In tMimp[f 2 1 L .1 11 J I 11 Fof Excel: Us* *D7.NP¥(tXE7..H73

Example 4.2

A \$120,000 house is bought by making a \$20,000 down payment and obtaining a loan from the local bank at an interest of10% for 30 years. What is the annual payment?

We can use equation 4.1a or expression 4.1b to solve this problem. Using expression 4.1b EUAW = A=P{A/P.I0,30)

Using the compound interest rate tables EUAW = 1M,0OO (0.1061) = 10.610

 ™ rt ! 8 " D '" t | . . F [: .¡ft H ..La-. ... .1.. 1 : BampLH.I 2 1 5 kioei 10% + Vatic-Dawn Payment - Loan itipunt Lean Amount= 33X00-20000 - L000DD —! ? Ttitt usiog the ken annual si Hie {rad vi'ui * i ForFJicel Use ^MT CCliiJS.D.O) alKK BJAW- 10 ForQiHBiflPioUtefflPTTrCJM^KIQ EUAW- ■I0.6D7.9Q fll

+2 -3

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

Get My Free Ebook

### Responses

• ambrosia pisano
How to calculate Equivalent Uniform Annual Worth?
2 years ago
• demetria
How to interpolate equivalent uniform annual worths?
1 year ago
• Anssi
How to find equivalent uniform anual worth of a house?
1 year ago
• almaz
What is the equivalent uniform quarterly worth of this project?
7 months ago
• russom haile
How to calculate euaw?
7 months ago
• joel bassett
How to find the equivalent uniform cost?
24 days ago
• bell
What is the difference between equivalent uniform annual cost and equivalent annual cost?
21 days ago