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The **time value of money** (TVM) refers to the fact that $1 today is worth more than $1 in the future. This is because the $1 today can be invested to earn interest immediately. The TVM reflects the relationship between present value, future value, time, and interest rate. The time value of money underlies rates of return, interest rates, required rates of return, discount rates, opportunity costs, inflation, and risk. It reflects the relationship between time, cash flow, and interest rate.
*certain world*, the interest rate is called the risk-free rate. For investors preferring current to future consumption, the risk-free interest rate is the rate of compensation required to postpone current consumption. For example, the interest rate paid by T-bills is a risk-free rate of interest.
**Compounding** is the process of accumulating interest over a period of time. A compounding period is the number of times per year that interest is paid. **Continuous compounding** occurs when the number of compounding periods becomes infinite; interest is added continuously.

There are three ways to interpret interest rates:

**Required rate of return**is the return required by investors or lenders to postpone their current consumption.**Discount rate**is the rate used to discount future cash flows to allow for the time value of money (that is, to bring a future value equivalent to present value).**Opportunity cost**is the most valuable alternative investors give up when they choose what to do with money.

In an *uncertain world*, there are two factors that complicate interest rates:

**Inflation**: When prices are expected to increase, lenders charge not only an opportunity cost for postponing consumption but also an inflation premium that takes into account the expected increase in prices. The**nominal cost of money**consists of the**real rate**(a pure rate of interest) and an**inflation premium**.**Risk**: Companies exhibit varying degrees of uncertainty concerning their ability to repay lenders. Lenders therefore charge interest rates that incorporate**default risk**. The return that borrowers pay thus comprises the nominal risk-free rate (real rate + an inflation premium) and a default risk premium.

**Discounting** is the calculation of the present value of some known future value. Discount rate is the rate used to calculate the present value of some future cash flow. Discounted cash flow is the present value of some future cash flow.

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