# Equivalent Annual Annuity, Eaa

When used to compare projects with unequal lives, an investor should choose the one with the higher EAA. Equivalent annual annuity is an approach used in capital budgeting to choose between mutually exclusive projects with unequal useful lives. The equivalent annual annuity approach is used for evaluation of projects that have unequal life spans.

Process, as it is an effective way to compare the cost-effectiveness of different assets. The main disadvantage of the EAA method is assuming that a project can be replicated an infinite number of times. Moreover, its cash flows and cost of capital remain stable, but such a scenario is unlikely in practice.

Despite the disadvantages, the EAA is quite a useful tool when it comes to comparing mutually exclusive projects with different life spans. You just have to consider the limitations before using the calculator. The most important thing to note is that the project with highest EAA should be accepted. The Internal Rate of Return is the discount rate that makes the net present value of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment. The annuity method of depreciation, also known as the compound interest method, looks at an asset’s depreciation be determining its rate of return.

## Formula

Alternatively, EAC can be obtained by multiplying the NPV of the project by the “loan repayment factor”. The prime advantage of EAA ratio is that it considers ‘time value of money’. The time spent waiting for the money to be collected is the money wasted. This means that if you receive a payment today, you can reinvest it today, and start making profits immediately, rather than receiving the same amount on a later date. Learn more about how you can improve payment processing at your business today. Applying a sinking fund amortization factor to the after-tax amount of any salvage value. Calculating how much should be invested in an asset in order to achieve a desired result (i.e., purchasing a storage tank with a 20-year life, as opposed to one with a 5-year life, in order to achieve a similar EAC).

• Lastly, the analyst compares each project’s EAA and selects the one with the highest EAA.
• When comparing two different investments using the net present value method, the length of the investment is not taken into consideration.
• In other words, it is the expected compound annual rate of return that will be earned on a project or investment.
• During this time, the machine will enable Sally to realize significant cost savings and represents an NPV of \$4 million.
• Deciding whether to make an investment in one asset or another can be challenging.

Company C is considering two mutually exclusive projects with the same initial investment of \$20,000,000. The life span of Project L is 5 years, and the life span of Project S is 4 years. When several mutually exclusive projects with unequal life spans are compared, the one with the highest EAA value should be accepted.

## Tax Calculators

Learn financial modeling and valuation in Excel the easy way, with step-by-step training. WACC is a firm’s Weighted Average Cost of Capital and represents its blended cost of capital including equity and debt. Suppose that Sally’s Doughnut Shop is considering purchasing one of two machines.

• Cost of debt is used in WACC calculations for valuation analysis.
• This evaluates the constant average cash flow of a project during its entire life cycle as if it were an annuity.
• Moreover, its cash flows and cost of capital remain stable, but such a scenario is unlikely in practice.
• The company might change or opt for new, more profitable projects after the completion of one project.

That is, the calculation translates return into an equivalent annual rate. In this way, all investments can be compared and assessed on equal terms. The equivalent annual annuity formula is used in capital budgeting to show the net present value of an investment as a series of equal cash flows for the length of the investment. The net present value formula shows the present value of an investment that has uneven cash flows. When comparing two different investments using the net present value method, the length of the investment is not taken into consideration. An investment with a 15 year term may show a higher NPV than an investment with a 4 year term. By showing the NPV as a series of cash flows, the equivalent annual annuity formula provides a way to factor in the length of an investment.

## Equivalent Annual Annuity Eaa

The EAA approach uses a three-step process to compare projects. The present value of the constant annual cash flows is exactly equal to the project’s net present value. The first thing an analyst does is calculate each project’s NPV over its lifetime. After that, they compute each project’s EAA so that the present value of the annuities is exactly equal to the project’s NPV. Lastly, the analyst compares each project’s EAA and selects the one with the highest EAA. For example, if the company is facing difficulties making interest payments on its debt, choosing a project with a lower NPV but higher average cash flows may be a better decision. In contrast, if the business is financially healthy, going with the highest NPV-project may be the way to go since this will provide the greatest financial benefit.

The main disadvantage of equivalent annual cost analysis is the fact that you’ll need to estimate the discount rate. These types of forecasts tend to be inaccurate, which can throw the entire equivalent annual cost formula off. As such, it’s always important to remember to combine equivalent annual cost analysis with other capital budgeting tools to make sure that you’re getting the most accurate data regarding the investments that you’re comparing. The main advantage of the equivalent annual annuity approach lies in that it considers the impact of time value of money and it is easier to apply in practice than the replacement chain method. It is because we do not need to lay out the complete cash flow time line till the common life of the mutually-exclusive projects. All we need is to find NPV of each project and then use the EAA formula. An example of how the equivalent annual annuity formula may be useful is comparing two new projects where one project has a 15 year term and the other has a 4 year term.

• The equivalent annual annuity formula uses the annuity payment formula for when present value is given.
• The internal rate of return is a metric used in capital budgeting to estimate the return of potential investments.
• David has helped thousands of clients improve their accounting and financial systems, create budgets, and minimize their taxes.

The equivalent annual annuity method is used in capital budgeting to rank mutually exclusive projects with unequal life spans. The concept is based on assuming that a project is an ordinary annuity with the same life span, its net present value is equal to the present value of this annuity, and the cost of capital is equal to the required annual rate. The next assumption is that such an ordinary annuity is an ordinary perpetuity and its present value is equal to the NPV of a project.

## How To Calculate Equivalent Annual Cost

The equivalent annual annuity approach is one of two methods used in capital budgeting to compare mutually exclusive projects with unequal lives. The EAA approach calculates the constant annual cash flow generated by a project over its lifespan if it was an annuity.

Comparison can also be made by other companies, given they belong to the same industry. Comparing these two projects, the 4 year project will return a higher amount relative to the time of the investment. Although the 15 year project has a higher NPV, the 4 year project can be reinvested and have additional earnings for the 11 years that remain on the 15 year project.

## The Advantages Of Using The Eaa Ratio

Also the EAA method is easier to apply than other available methods. You do not need to lay out the complete cash flow timeline for the entire life span of mutually exclusive projects. In this equivalent annual cost formula, “discount rate” is the return that’s necessary to make the project viable . It ignores inflation and assumes that that the cash flows, costs and initial investment will remain the same for each iteration of the projects.

It is not likely that an alternate and equally-profitable opportunity will be available exactly at the end of the project; and even if any such opportunity exists, whether the company would want to reinvest. Are you confused about choosing a project that will help you expand your business? The Equivalent Annual Annuity calculator can help you choose a project that will be most beneficial for your business.

The present value of an annuity is the current value of future payments from that annuity, given a specified rate of return or discount rate. As you can see, our equivalent annual cost analysis indicates that – purely from a financial point of view – Asset 2 is a better option as its EAC is considerably less than Asset 1. Here, CFt is the cash flow at the end of the relevant year t, r is the cost of capital, and N is the life of a project in years. The EAA disregards inflation and assumes that all the costs and cash flows related to the project will remain the same every time it’s repeated. The equivalent annual annuity formula uses the annuity payment formula for when present value is given. Net present value replaces present value to give relevance to the use of the equivalent annual annuity formula. The internal rate of return is a metric used in capital budgeting to estimate the return of potential investments.

### What are the three conditions must be met in order to use equivalent annual annuity EAA when you compare multiple projects quizlet?

You use EAA when you are comparing projects that are mutually exclusive, have different lives, and can be repeated at the same cash flows.

The equivalent annual annuity formula provides a comparison relative to time which eliminates the need for considering reinvestment with the same earnings as the current investment. When used to compare projects with unequal lives, an investor should choose the one with the higher equivalent annual annuity.

## Math Calculators

The company might change or opt for new, more profitable projects after the completion of one project. Number of periods – Enter the expected life span of the project. An EAA calculator can support your business in many ways as it is online and very easy to use. The Equivalent Annual Annuity Calculator requires just a few inputs and clicks to show you the important numbers. It can also help you make comparisons between various projects of your company.

Equivalent annual cost is a tool similar to equivalent annual annuity with is used to calculate annualized cost of different alternatives. Often, an analyst will use a financial calculator, using the typical present value and future value functions to find the EAA. An analyst can use the following formula in a spreadsheet or with a normal non-financial calculator with exactly the same results. The weighted average cost is available as wacc, and the net present values for projects 1 and 2 are available as npv_project1 and npv_project2.

## How Is The Equivalent Annual Annuity Formula Derived?

The 4 year project will receive the return sooner so it will show a higher cash flow when using the equivalent annual annuity formula. In real life, comparing two investments will not always be so obvious and the formula should be applied. Deciding whether to make an investment in one asset or another can be challenging. Fortunately, there are numerous financial metrics that can assist you in the decision-making process. One of the most effective tools is the equivalent annual cost formula, which can help you understand the annual cost of an asset throughout its life. Find out everything you need to know about how to calculate equivalent annual cost with our definitive guide.

Machine A is a dough mixing machine that has a useful life of 6 years. During this time, the machine will enable Sally to realize significant cost savings and represents an NPV of \$4 million. Since the net present values of each project are not directly comparable given the different lifespans of each project, you will have to consider a different approach. Where an asset undergoes a major overhaul, and the cost is not fully reflected in salvage values, to calculate the optimum life (i.e., lowest EAC) of holding on to the asset. Assessing whether increased maintenance costs will economically change the useful life of an asset. It assumes that the projects can and will be repeated indefinitely.

## Canadian Context With Capital Cost Allowance

Here, the NPV is the net present value of a project, r is the cost of capital, and N is the life of a project in years. Rate per period – Enter the expected rate of return of the project. Discounted cash flow is a valuation method used to estimate the attractiveness of an investment opportunity. It assumes that the projects can and will be repeated for an unlimited number of times, which does not seem practical.