Internal rate of return (IRR) and yield to maturity are calculations used by companies to assess investments, but they refer to different things. Here's what each term means, and an example of when it might be used.

Internal rate of return (IRR)
This is a metric used when evaluating the profitability of potential investments. Without getting too mathematical, IRR is the interest rate at which the net present value of all cash flows from an investment is equal to zero.

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In a nutshell, companies have a "required rate of return" -- that is, the return they want in order for a project or investment to be worthwhile. If the calculated IRR is greater than or equal to this rate, the investment looks like a good idea (at least on paper). If not, the investment is probably not worth pursuing.

The actual formula to calculate IRR is rather complex, but fortunately there are several good IRR calculators available online, like this one.

For example, let's say that a company is deciding whether to invest in an expansion of its factory, which will cost \$5,000,000. It knows it can earn an additional \$1,000,000 per year from this investment for the next 10 years, the useful lifespan of the equipment, or it could choose to use that capital elsewhere and obtain a 10% return. Using a calculator, we see that the IRR of this investment would by approximately 15.1%, which is greater than the 10% required rate of return. Therefore, building the factory would be a good idea.

Yield to maturity
The biggest difference between IRR and yield to maturity is that the latter is talking about investments that have already been made.

Yield to maturity, or YTM, is used to calculate an investment's (usually a bond or other fixed income security) yield based on its current market price. A precise calculation of YTM is rather complex, as it assumes that all coupon payments are reinvested at the same rate as the current yield, and takes into account the present value of the bond.

However, YTM for an investment can be approximated rather easily by combining the coupon yield with the difference between the market price and the face value of the bond using the following formula.

Where C is the coupon interest payment, F is the face value of the bond, P is the market price of the bond, and "n" is the number of years to maturity.

For example, let's say that we buy a bond for \$980 with five years until maturity. The bond's face value is \$1,000 and its coupon rate is 6%, so we get a \$60 annual interest payment. We can calculate the YTM as follows:

In other words, because we bought the bond for a discount, our effective YTM is slightly higher than the bond's coupon interest rate. If we had paid a premium, we would expect the opposite to be true.

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