Chapter 5

Discounting

Discounting is the process of calculating the present value of a cash flow to be received or paid in the future. Compounding, which is the process of determining the future, or terminal, value of a current cash flow, is the opposite of discounting.

Opportunity cost of funds

The interest rate that represents the return on an investor's best available alternative investment of comparable (equal) risk is the investor's opportunity cost of funds.

Future value

A future value represents the amount to which a current (present) value will grow over a given period of time when compounded at a given rate of interest. Mathematically, a future value is calculated as FV = PV x (1 + r)nn.

Perpetuity

A perpetuity is a series of equal cash flows that are expected to continue forever. A perpetuity can be considered to be a special type of annuity. While both a perpetuity and an annuity exhibit constant periodic cash flows, the annuity has a definite end date, and the perpetuity does not. Instead, a perpetuity's cash flows are expected to continue indefinitely.

Ordinary annuity

A series of equal cash flows that are paid or received at regular intervals, such as a day or a month, is called an annuity. When the cash flows occur at the end of each of the regular intervals, the series is called an ordinary annuity. An example of an ordinary annuity is the 60 monthly payments of $676.65 made at the end of each month to repay a $35,000 loan that charges 6% interest and is to be repaid over five years. If the cash flow were to occur at the beginning of each of the regular intervals, then the annuity would be called an annuity due.

Amortization schedule

An amortization schedule or table reports the amount of principal and the amount of interest that make up each payment made to repay a loan by the end of its regular term. Remember, the term amortization has two meanings. One meaning refers to the process of decreasing the principal outstanding on a loan via payments containing both interest and principal. The second meaning refers to the depreciation of the intangible assets owned by a firm.

Amortized loan

An amortized loan is one that is repaid with payments that are composed of both the interest owed on the loan and a portion of the loan's principal. In contrast, a zero-interest loan is one on which interest is not charged and the payments made to repay the loan will consist only of principal.

Annuity due

An annuity due is the name given to a series of equal cash flows that occur at the beginning of each of the equally spaced intervals (such as daily, monthly, annually, and so on).

Annual percentage rate

The annual percentage rate (APR) is the cost of borrowed funds as quoted by lenders and paid by borrowers, in which the interest required is expressed as a percentage of the principal borrowed. This rate does not reflect the effects of compounding if interest is earned more than once per year.

Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. Which of the following equations can be used to solve for the present value of an ordinary annuity?

The correct formula for the calculation of the present value of an ordinary annuity is PMT x {1 - [1/(1 + r)nn]}/r, where PMT is the amount of the constant cash flow received or paid each period, r is the opportunity cost or the interest rate (return) paid or received each period, and n represents the number of periods for which interest is earned. PMT/r is the equation used to calculate the present value of a perpetuity. PMT x {[(1 + r)nn - 1]/r} x (1 + r) is the formula used to calculate the future value of an annuity due. PMT x {[(1 + r)nn - 1]/r} is the equation used to calculate the future value of an ordinary annuity.

Time value of money

The financial concept that maintains that the timing of a receipt or payment of a cash flow will affect its value is called the time value of money (TVM). The time value of money illustrates that, due to its capacity to earn interest, a cash flow received today is worth more than an identical cash flow to be received on a future date. The exact current value of a future cash flow is a function of the magnitude of the future cash flow, the return required by the owner (recipient) of the cash flow, and when in the future the cash flow will occur.