# Chapter 17

INVESTORS AND MARKETS : The internal rate of return

In this chapter we learned about the theoretical foundations of interest rates, which force financial managers to discount cash flows, i.e. to depreciate the flows in order to factor in the passage of time.

This led us to a definition of present value, the basic tool for valuing a financial investment, which must be compared to its market value. The difference between present value and the market value of an investment is net present value.

In a market in equilibrium, the net present value of a financial investment is nil because it is equal to its present value.

As the value of an investment and the discount rate are fundamentally linked, we also looked at the concept of yield to maturity (which cancels out NPV). Making an investment is only worth it when the yield to maturity is equal to or greater than the investor's required return. At fair value, internal rate of return is identical to the required return rate. In other words, net present value is nil.

The internal rate of return should be handled with care, as it is based on the implicit assumption that cash flows will be reinvested at the same rate. It should only be relied on for an investment decision concerning a single asset and not for choosing from among several assets, whether they are financial (e.g. an investment) or industrial (e.g. a mine, a machine). NPV should be used for such decisions.

Finally, some financial mathematics helped us look at the link between the nominal interest rate and the yield to maturity of an operation. The nominal (annual) rate of a loan is the rate used to calculate interest in proportion to the period of the loan and the capital borrowed. However, one must use the yield to maturity, which may differ from the apparent nominal rate, when interest is not paid on an annual basis.

Two rates referring to two different time periods are equivalent if the future value of the same sum is the same at a same date. Finally, two rates are proportional if they are in the same proportion as the maturity to which they refer to. Proportional rates are just a means to compute the interest that is actually to be paid. They have no other use.