# Chapter 16

INVESTORS AND MARKETS : The time value of money and net present value

Capitalisation involves foregoing immediate spending of a given sum of money. By using the interest rate at which the money will be invested, the future amounts can be calculated. Thus, the future value of a sum of money can be determined by way of capitalisation.

Discounting involves calculating today's value of a future cash flow, what is known as the *present value*, on the basis of rates of return required by investors. By calculating the present value of a future sum, discounting can be used for comparing future cash flows that will not be received on the same date.

Discounting and capitalisation are two ways of expressing the same phenomenon: the time value of money.

Capitalisation is based on compound interest. *V _{n}* =

*V*

_{0}× (1 +

*r*)

^{n}

where *V*_{0} is the initial value of the investment, *r* is the rate of return, *n* is the duration of the investment in years, (1+*r*)^{n} is the capitalisation factor and *V _{n}* is the terminal value.

Discounting is the inverse of capitalisation. It is important to note that any precise financial calculation must account for cash flows at the moment when they are received or paid, and not when they are due.

Net present value (NPV) is the difference between present value and the value at which the security or share can be bought. Net present value measures the creation or destruction of value that could result from the purchase of a security or making an investment. When markets are in equilibrium, net present values are usually nil.

Changes in present value and net present value move in the opposite direction from changes in discount rates. The higher the discount rate, the lower the present value and net present value, and vice versa.

In many cases, calculating present value and net present value can be made a lot simpler through ad hoc formulas.