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Internal Rate of Return and Yield to Maturity

We now assume that the discount rate is endogenous, in which case we solve for the rate that equates two sets of cash flows. Suppose you make an investment in a business equal to dollars. This investment is expected to yield a stream of cash flows for n periods equal to . The internal rate of return (IRR) is the discount rate, which makes the two streams, the outflow and the present value of the inflows , equivalent. That is, the IRR is the value of r that discounts the following set of cash flows to the initial outlay P₀:

Since is an outlay, hence, a negative cash flow, then the preceding equation is the same as:

Notice that this is a net present value, too, but with the important exception that the discount rate is exogenous in NPV problems. ...