Yields: Internal Rate of Return (IRR)

Computing the Yield (Internal Rate of Return)

The yield, also known as the internal rate of return (IRR), is a key measure used in bond and investment analysis. It represents the rate of return that equates the present value of a bond's cash flows to its market price. Computing the yield helps investors assess the profitability and attractiveness of an investment opportunity. This section will provide a detailed explanation of how to compute the yield using the internal rate of return method.

Let's Actually Compute the Yield (Internal Rate of Return)

The yield of a bond can be calculated by solving for the discount rate that sets the present value of the bond's cash flows equal to its market price. The general steps involved in computing the yield are as follows:

Step 1: Set up the cash flow equation:
Write down the cash flows associated with the bond, including coupon payments and the principal payment at maturity. Assign the appropriate signs (+ or -) to denote inflows and outflows of cash.

Step 2: Determine the market price:
Obtain the market price of the bond. This represents the present value of the bond's cash flows based on prevailing market conditions.

Step 3: Define the IRR equation:
Formulate an equation that equates the present value of the cash flows to the market price. This equation represents the internal rate of return (IRR) calculation.

Step 4: Solve for the yield (IRR):
Using mathematical techniques, solve the IRR equation to find the yield that makes the present value of cash flows equal to the market price.

Example:
Let's consider a bond with the following characteristics:
Face value (F) = $1,000
Coupon rate = 6% (annual coupon payment rate)
Coupon payment (C) = $60 (6% of $1,000)
Maturity = 5 years
Market price = $950

To compute the yield (IRR) for this bond, we set up the cash flow equation as follows:

-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 equation, we find that the yield (IRR) for this bond is approximately 7.72%.

Therefore, the yield (IRR) for this bond is 7.72%, representing the rate of return that makes the present value of its cash flows equal to the market price of $950.

Conclusion

Computing the yield, or internal rate of return (IRR), is a valuable tool for bond and investment analysis. By determining the discount rate that equates the present value of a bond's cash flows to its market price, investors can assess the profitability and attractiveness of an investment opportunity. The IRR calculation involves setting up the cash flow equation, defining the IRR equation, and solving for the yield using mathematical techniques. Computing the yield provides investors with a measure to evaluate bond returns and make informed investment decisions in debt and money markets.

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