yield rate and internal rate of return

Suppose you put money into an investment, get some cash back over the years, and want to summarise the whole thing in one number: how good was it, as a percentage per year? That single summary rate is the yield rate, or internal rate of return (IRR). It is the constant interest rate at which the investment exactly breaks even — the rate that makes everything you put in worth exactly as much as everything you take out.

Formally, the IRR is the interest rate that sets the net present value of all cash flows to zero — that is, the rate that solves the equation of value where the present value of inflows equals the present value of outflows. Because that equation is a polynomial in the discount factor v, there is generally no formula for the answer; you find it by trial and improvement or numerical root-finding. For simple cases — money in, money out later — there is one clean positive yield. For more complex patterns with money flowing both directions repeatedly, there can be multiple roots or none, which is a genuine limitation, not a footnote.

Yield rate is how actuaries and investors judge and compare projects, bond purchases, and insurance products: the bond's yield to maturity is its IRR, and a product's profitability is often expressed as the IRR to the company. But IRR has well-known traps. It implicitly assumes interim cash flows are reinvested at the IRR itself, which may be unrealistic; it can be undefined or ambiguous for non-standard cash-flow patterns; and a high IRR on a tiny project can look more attractive than a modest IRR on a large, more valuable one. Professionals therefore pair IRR with net present value rather than trusting it alone.