Chapter 5: The Time Value of Money

Question 1

Explain the mechanics of compounding and bringing the value of money back to the present (1)

Answer 1

Compound interest occurs when interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on this new sum.

Question 2

Explain the mechanics of compounding and bringing the value of money back to the present (2)

Answer 2

Although there are several ways to move money through time, they all give you the same result. In the business world, the primary method is through the use of a financial spreadsheet, with Excel being the most popular. If you can use a financial calculator, you can easily apply your skills to a spreadsheet.

Question 3

Explain the mechanics of compounding and bringing the value of money back to the present (3)

Answer 3

Actually, we have only one formula with which to calculate both present value and future value - we simply solve for different variables - FV and PV. This single compounding formula is FV=PV(1 + r/m)^(n x m).

Question 4

Compound Interest

Answer 4

The situation in which interest paid on an investment during the first period is added to the principal. During the second period, interest is earned on the original principal plus the interest earned during the first period.

Question 5

Future Value

Answer 5

The amount to which your investment will grow, or a future dollar amount.

Question 6

Future Value Factor

Answer 6

The value of (1 + r/m)^(n x m) used as a multiple to calculate an amount’s future value.

Question 7

Simple Interest

Answer 7

If you only earned interest on your initial investment, it would be referred to as simple interest.

Question 8

Present Value

Answer 8

The value in today’s dollars of a future payment discounted back to present at the required rate of return.

Question 9

Present Value Factor

Answer 9

The value of 1/(1 + r/m)^(n x m) used as a multiplier to calculate an amount’s present value.

Question 10

Future Value at the End of Year n Equation

Answer 10

Present Value x (1 + r/m)^(n x m).

Question 11

Present Value Equation

Answer 11

Future Value at the End of Year n x [1/(1 + r/m)^(n x m).

Question 12

Understand annuities (1)

Answer 12

An annuity is a series of equal payments made for a specified number of years. In effect, it is calculated as the sum of the present or future value of the individual cash flows over the life of the annuity.

Question 13

Understand annuities (2)

Answer 13

If the cash flows from an annuity occur at the end of each period, the annuity is referred to as an ordinary annuity. If the cash flows occur at the beginning of each period, the annuity is referred to as an annuity due. We will assume that cash flows occur at the end of each period unless otherwise stated.

Question 14

Understand annuities (3)

Answer 14

The procedure for solving for PMT, the annuity payment value when i, n, and PV are known, is also used to determine what payments are associated with paying off a loan in equal installments over time. Loans that are paid off this way, in equal periodic payments, are called amortized loans. Although the payments are fixed, different amounts of each payment are applied toward the principal and the interest. With each payment you make, you owe a bit less on the principal. As a result, the amount that goes toward the interest payment declines with each payment made, whereas the portion of each payment that goes toward the principal increases.

Question 15

Annuity

Answer 15

A series of equal dollar payments made for a specified number of years.

Question 16

Ordinary Annuity

Answer 16

An annuity where the cash flows occur at the end of each period.

Question 17

Compound Annuity

Answer 17

Depositing an equal sum of money at the end of each year for a certain number of years and allowing it to grow.

Question 18

Annuity Future Value Factor

Answer 18

The value of [(1 + r/m)^(n x m) - 1]/(r/m) used as a multiplier to calculate the future value of an annuity.

Question 19

Annuity Present Value Factor

Answer 19

The value of [1 - (1 + r/m)^(-n x m)]/(r/m) used as a multiplier to calculate the present value of an annuity.

Question 20

Annuity Due

Answer 20

An annuity in which the payments occur at the beginning of each period.

Question 21

Amortized Loan

Answer 21

A loan that is paid off in equal periodic payments.

Question 22

Future Value of an Annuity Equation

Answer 22

PMT{[(1 + r/m)^(n x m) - 1]/(r/m)}

Question 23

Present Value of an Annuity Equation

Answer 23

PMT{[1 - 1/[1 + r/m]^(n x m)}/(r/m)

Question 24

Future Value of an Annuity Due Equation

Answer 24

PMT{[(1 + r/m)^(n x m) - 1]/(r/m)} x (1 + r/m)

Question 25

Present Value of an Annuity Due Equation

Answer 25

PMT{[1 - 1/[1 + r/m]^(n x m)}/(r/m) x (1 + r/m)

Question 26

Determine the future or present value of a sum when there are nonannual compounding periods.

Answer 26

With nonannual compounding, interest is earned on interest more frequently because the length of the compounding period is shorter. As a result, there is an inverse relationship between the length of the compounding period and the effective annual interest rate.

Question 27

Effective Annual Rate (EAR)

Answer 27

The annual compound rate that produces the same return as the nominal, or quoted, rate when something is compounded on a nonannual basis. In effect, the EAR provides the true rate of return.

Question 28

Effective Annual Rate (EAR) Equation

Answer 28

[1 +(Quoted Rate)/m]^m - 1

Question 29

FV for n years Equation

Answer 29

PV{[1 + (r/m)]^(m x n)}

Question 30

Determine the present value of an uneven stream of payments and understand perpetuities (1).

Answer 30

Although some projects will involve a single cash flow and some will involve annuities, many projects will involve uneven cash flows over several years. However, finding the present or future value of these flows is not difficult because the present value of any cash flow measured in today’s dollars can be compared, by adding the inflows and subtracting the outflows, to the present value of any other cash flow also measured in today’s dollars.

Question 31

Determine the present value of an uneven stream of payments and understand perpetuities (2).

Answer 31

A perpetuity is an annuity that continues forever; that is, every year following its establishment the investment pays the same dollar amount. An example of a perpetuity is preferred stock, which pays a constant dollars dividend infinitely. Determining the present value of a perpetuity is delightfully simple. We merely need to divide the constant flow by the discount rate.

Question 32

Perpetuity

Answer 32

An annuity with an infinite life.

Question 33

Present Value of a Perpetuity Equation

Answer 33

(Constant Dollar Amount Provided by the Perpetuity)/r