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Calculating the Yield of an Annuity
The yield of an annuity is commonly found using either the percent change in the value from PV to FV, or the internal rate of return.
Learning Objective

Calculate the yield of an annuity using the internal rate of return method
Key Points
 The yield of an annuity may be found by discounting to find the PV, and then finding the percentage change from the PV to the FV.
 The Internal Rate of Return (IRR) is the discount rate at which the NPV of an investment equals 0.
 The IRR calculates an annualized yield of an annuity.
Terms

Net Present Value (NPV)
The present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision.

Internal Rate of Return (IRR)
The discount rate that will cause the NPV of an investment to equal 0.

yield
In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return. Yield applies to various stated rates of return on stocks (common and preferred, and convertible), fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance products
Full Text
The yield of annuity can be calculated in similar ways to the yield for a single payment, but two methods are most common.
The first is the standard percentagechange method. Just as for a single payment, this method calculated the percentage difference between the FV and the PV. Since annuities include multiple payments over the lifetime of the investment, the PV (or V_{1} in is the present value of the entire investment, not just the first payment.
The second popular method is called the internal rate of return (IRR). The IRR is the interest rate (or discount rate) that causes the Net Present Value (NPV) of the annuity to equal 0. That means that the PV of the cash outflows equals the PV of the cash inflows. The higher the IRR, the more desirable is the investment. In theory, you should make investment with an IRR greater than the cost of capital.
Let's take an example investment: It is not technically an annuity because the payments vary, but still is a good example for how to find IRR:
Suppose you have a potential investment that would require you to make a $4,000 investment today, but would return cash flows of $1,200, $1,410, $1,875, and $1,050 in the four successive years. This investment has an implicit rate of return, but you don't know what it is. You plug the numbers into the NPV formula and set NPV equal to 0. You then solve for r, which is your IRR (it's not easy to solve this problem by hand. You will likely need to use a business calculator or Excel). When r = 14.3%, NPV = 0, so therefore the IRR of the investment is 14.3%.
IRR Example
The setup to find the IRR of the investment with cash flows of 4000, 1200, 1410, 1875, and 1050. By setting NPV = 0 and solving for r, you can find the IRR of this investment.
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Key Term Reference
 Interest
 Appears in these related concepts: Interest Compounded Continuously, Accounting for Interest Earned and Principal at Maturity, and Tax Considerations
 annuity
 Appears in these related concepts: Future Value, Multiple Flows, Impact of Payment Frequency on Bond Prices, and Applications of Geometric Series
 capital
 Appears in these related concepts: Temple Architecture in the Greek Orientalizing Period, Minoan Architecture, and The Acropolis
 cash flow
 Appears in these related concepts: Calculating the NPV, Interpreting the NPV, and Defining the Cash Flow Cycle
 cash inflow
 Appears in these related concepts: Reporting Financing Activities, Defining NPV, and The Financial Statements
 cash outflow
 Appears in these related concepts: Managing Disbursements, Advantages of the NPV method, and Selected Financial Ratios and Analyses
 cost of capital
 Appears in these related concepts: Advantages of the Payback Method, Calculating the IRR, and Cost of Capital Considerations
 discount
 Appears in these related concepts: The Discount Rate, Par Value at Maturity, and Present Value, Multiple Flows
 discount rate
 Appears in these related concepts: Discounted Cash Flow Approach, The Discount Rate, and The Federal Reserve and the Financial Crisis of 2008
 discounting
 Appears in these related concepts: The Relationship Between Present and Future Value, ShortTerm Approach, and Importance of the Time Value of Money
 interest rate
 Appears in these related concepts: Greenspan Era, The Financial Account, and Determinants of investment
 investment
 Appears in these related concepts: Functions of Corporate Finance, The Role of the Financial System, and GDP Equation in Depth (C+I+G+X)
 net present value
 Appears in these related concepts: Other Considerations in Capital Budgeting, The Role of Financial Managers, and CostBenefit Analysis
 present value
 Appears in these related concepts: Capital Leases vs. Operating Leases, Calculating Values for Different Durations of Compounding Periods, and Present Value and the Time Value of Money
 return
 Appears in these related concepts: Dollar Returns, Comparing the Fields of Finance, Economics, and Accounting, and Disadvantages of the Payback Method
Sources
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Cite This Source
Source: Boundless. “Calculating the Yield of an Annuity.” Boundless Finance. Boundless, 26 May. 2016. Retrieved 25 Oct. 2016 from https://www.boundless.com/finance/textbooks/boundlessfinancetextbook/thetimevalueofmoney5/yield60/calculatingtheyieldofanannuity2787559/