Equivalent Annual Annuity Approach

Equivalent Annual Annuity Approach (EAA) What Is the Equivalent Annual Annuity Approach? 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. When used to compare projects with unequal lives, an investor should choose the one with the higher EAA. Understanding the Equivalent Annual Annuity Approach (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, assume a company with a weighted average cost of capital of 10% is comparing two projects, A and B. Project A has an NPV of $3 million and an estimated life of five years, while Project B has an NPV of $2 million and an estimated life of three years. Using a financial calculator, Project A has an EAA of $791,392.44, and Project B has an EAA of $804,229.61. Under the EAA approach, the company would choose Project B since it has the higher equivalent annual annuity value. Formula for Equivalent Annual Annuity Approach Often, an analyst uses 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. C = (r x NPV) / (1 - (1 + r)-n ) Where: C = equivalent annuity cash flow NPV = net present value r = interest rate per period n = number of periods For example, consider two projects. One has a seven-year term and an NPV of $100,000. The other has a nine-year term and an NPV of $120,000. Both projects are discounted at a 6 percent rate. The EAA of each project is: EAA Project one = (0.06 x $100,000) / (1 - (1 + 0.06)-7 ) = $17,914 EAA Project two = (0.06 x $120,000) / (1 - (1 + 0.06)-9 ) = $17,643 Project one is the better option. In capital budgeting, NPV and IRR conflict refers to a situation in which the NPV method ranks projects differently from the IRR method. In event of such a difference, a company should accept project(s) with higher NPV. Net present value (NPV) and internal rate of return (IRR) are two of the most widely used investment analysis and capital budgeting techniques. They are similar in the sense that both are discounted cash flow models i.e. they incorporate the time value of money. But they also differ in their main approach and their strengths and weaknesses. NPV is an absolute measure i.e. it is the dollar amount of value added or lost by undertaking a project. IRR, on the other hand, is a relative measure i.e. it is the rate of return that a project offers over its lifespan. Cause of NPV and IRR Conflict The underlying cause of the NPV and IRR conflict is the nature of cash flows (normal vs non-normal), nature of project (independent vs mutuallyexclusive) and size of the project. Independent Projects Independent projects are projects in which decision about acceptance of one project does not affect decision regarding others. Since we can accept all independent projects if they add value, NPV and IRR conflict does not arise. The company can accept all projects with positive NPV. Mutually Exclusive Projects However, in case of mutually-exclusive projects, an NPV and IRR conflict may arise in which one project has a higher NPV but the other has higher IRR. Mutually exclusive projects are projects in which acceptance of one project excludes the others from consideration. The conflict either arises due to relative size of the project or due to the different cash flow distribution of the projects. Since NPV is an absolute measure, it will rank a project adding more dollar value higher regardless of the initial investment required. IRR is a relative measure, and it will rank projects offering best investment return higher regardless of the total value added. NPV is the Preferred Technique Whenever an NPV and IRR conflict arises, always accept the project with higher NPV. It is because IRR inherently assumes that any cash flows can be reinvested at the internal rate of return. This assumption is problematic because there is no guarantee that equally profitable opportunities will be available as soon as cash flows occur. The risk of receiving cash flows and not having good enough opportunities for reinvestment is called reinvestment risk. NPV, on the other hand, does not suffer from such a problematic assumption because it assumes that reinvestment occurs at the cost of capital, which is conservative and realistic. Examples Example 1: Conflict Due to Size of Project Project A needs $10 million investment and generates $10 million each in year 1 and year 2. It has NPV of $7.4 million @ 10% discount rate and IRR of 61.8%. Project B needs $1 million investment and generates $2 million in Year 1 and $1 million in Year 2. Its NPV @ 10% and IRR turn out to be $1.6 million and 141.4% respectively. Based on NPV one would conclude that Project A is better, but IRR offers a contradictory view. This conflict arose due to the size of the project. Example 2: Conflict Due to Unconventional Cash Flows Let us consider two projects: A and B, both need $10 million investment each. Project A generates $15 million in Year 1 and $10 million in Year 2. Project B generates 0 in Year 1 and $30 million in Year 2. You can verify that Project A has NPV of $11.9 million at 10% discount rate and IRR of 100%. Project has NPV of $14.8 million and IRR of 73.2%. Despite both having the same initial investment, NPV is higher for Project B while IRR is higher for Project B. This is because in case of Project A more cash flows are in Year 1 resulting in longer reinvestment periods at higher reinvestment assumption and hence higher IRR. Reinvestment assumption does not affect NPV. Similarities and Differences between NPV and IRR NPV is theoretically sound because it has realistic reinvestment assumption. It considers the cost of capital and provides a dollar value estimate of value added, which is easier to understand. Another particularly important feature of NPV analysis is its ability to notch the discount rate up and down to allow for different risk level of projects. However, NPV is dependent on the size of the project. Without careful analysis, an investor might select a high NPV project ignoring the fact that many smaller NPV projects could be completed with the same investment resulting in higher aggregate NPV. It requires careful analysis in capital rationing. The size of project is irrelevant for IRR. It will rank a project requiring initial investment of $1 million and generating $1 million each in Year 1 and Year 2 equal to a project generating $1 in Year 1 and Year 2 each with initial investment of $1. This feature makes it a good complement to NPV. IRR is also easier to calculate because it does not need estimation of cost of capital or hurdle rate. It just requires the initial investment and cash flows. However, this same convenience can become a disadvantage if we accept projects without comparison to cost of capital. However, IRR’s assumption of reinvestment at IRR is unrealistic and could result in inaccurate ranking of projects. Another, quite serious weakness is the multiple IRR problem. In case of non-normal cash flows, i.e. where a project has positive cash flows followed by negative cash flows, IRR has multiple values.