### GIGAMIND

# 1. The Time Value of Money and Interest Rates

## a. interpret interest rates as required rates of return, discount rates, or opportunity costs;

## b. explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk;

What does the Time Value of Money (TVM) mean?

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.

What is a "discount rate"?

The discount rate is the interest rate used to discount cash flows to allow for the time value of money (to bring the future value to present day value)

What is "opportunity cost"?

Opportunity cost is the most valuable alternative that an investor is giving up pursuing a different opportunity.

In a "certain world" what is the interest rate called?

In a certain world, the interest rate is called the risk-free rate.

What is the "risk free rate"?

The real risk-free interest rate is the single-period interest rate for a completely risk-free security if no inflation were expected. (90 day US T-bill)

What two factors complicate the risk-free rate in an uncertain world?

1. Inflation - lenders charge the opportunity cost (for postponing consumption) and an inflation premium (taking into account the expected upcoming increase in prices) - called the Nominal Cost

2. Risk - called Default Risk, lenders charge an amount

What is the short-hand for "real risk free interest rate"?

Real rate

What two factors make up the Nominal Risk-free rate?

1. The risk-free interest rate (real rate)

2. Inflation premium

What is the "inflation premium"?

The Inflation Premium is an additional amount added to the risk-free rate which reflects the expected inflation over the maturity of the debt.

How can you know what the current risk-free interest rate is?

Get the interest rate for a 90 day US T-bill.

What is default risk premium?

Default risk premium compensates investors for the possibility that the borrower won't make a promised payment on time or in the right amount.

What is the liquidity premium?

The liquidity premium is compensation for the amount an investor expects to lose if they have to convert an investment to cash quickly. US T-bills have no liquidity premium because they are very liquid, but small issuer bonds may not be liquid and have a high cost (price impact) of selling quickly.

What is the maturity premium?

The maturity premium compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended.

What is compounding? What is continuous compounding?

Compounding is the process of accumulating interest over time. Continuous compounding is when the number of compounding periods becomes infinite - interest is added continuously.

What is the compounding period?

Compounding period is the number of times that interest is paid per year.

What is discounting?

Discounting is the calculation of the present value of some known future value.

What is the discount rate?

The discount rate is the rate used to calculate the present value of some future cash flow.

What is discounted cash flow?

Discounted cash flow is the present value of some future cash flow.

##### Source:

- CFA