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Yields: Internal Rate of Return (IRR)

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Simplified Explanation of Computing the Yield (Internal Rate of Return)

Understanding the yield, also known as the internal rate of return (IRR), is important for analyzing bonds and investments. It tells us how much profit we can expect from an investment. Let's break down how to compute the yield using a simpler language.

What is Yield (Internal Rate of Return)? The yield is like a measuring tool. It helps investors figure out how good an investment is by comparing the money they get over time with how much they paid for it.

How to Compute the Yield (Internal Rate of Return):

Step 1: Set up the Money Flow Equation:

  • Write down all the money you expect to get from the investment, like regular payments and the final payment. Also, decide if each part is adding money (+) or taking it away (-).

Step 2: Find out the Market Price:

  • Know how much the investment is worth now. This is based on what others in the market think.

Step 3: Create the Internal Rate of Return (IRR) Equation:

  • Make an equation that says the value of the money you expect to get equals the market price. This equation helps find the internal rate of return (IRR).

Step 4: Solve for the Yield (IRR):

  • Use math skills to solve the IRR equation. This gives the yield, which makes the value of expected money equal to the market price.

Example: Imagine a bond with these details:

  • Face value (F) = $1,000
  • Coupon rate = 6% (annual payment rate)
  • Coupon payment (C) = $60 (6% of $1,000)
  • Maturity = 5 years
  • Market price = $950

To find the yield (IRR), set up the money flow equation like this:

-950 + 60 / (1 + IRR) + 60 / (1 + IRR)^2 + 60 / (1 + IRR)^3 + 60 / (1 + IRR)^4 + 1,060 / (1 + IRR)^5 = 0

By solving this, we find the yield (IRR) is about 7.72%. This means the investment gives a profit of 7.72%, making the expected money equal to the market price of $950.

Calculating the yield, or internal rate of return (IRR), is a useful tool for investors. It helps them decide if an investment is worth it by comparing the expected money with the market price. The process involves setting up the money flow equation, creating the IRR equation, and using math to find the yield. This helps investors evaluate bond returns and make smart decisions in the world of investments.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.