The Time Value of Money

A loan that is paid off in equal amounts that include principal as well as interest is called

An amortized loan (Page 212)

A series of equal cash flows spaced evenly over time is called

An annuity (Page 198)

Find the future and present values of an annuity.

Annuities are a series of equal cash flows. An annuity that has payments that occur at the end of each period is an ordinary annuity. An annuity that has payments that occur at the beginning of each period is an annuity due. A perpetuity is a perpetual annuity. To find the future and present values of an ordinary annuity, we may use the algebraic, table, or financial calculator method. To find the future and present values of an annuity due, multiply the applicable formula by (1 + k) to reflect the earlier payment.

Explain the relationship between the present value of a sum of money and the discount rate.

As we increase the discount rate, we need less today to receive a certain future value. We are earning a higher return, and interest on interest will be higher. (Page 194)

The smallest compounding period is used when we do what type of compounding?

Continuous (Page 216)

If the number of periods increases, the present value will (increase/decrease)

Decrease (Page 196)

________ is the inverse of compounding.

Discounting

The real rate of interest does not include interest charged for:

Expected Inflation, and other factors from ch.2

Felix, Inc., purchased machinery and gave a five-year note with a maturity value of $10,000. The discount rate for the note was 12% compounded annually. Calculate how much they borrowed.

FV=10,000;i=12;n=5;PV=$5,674 (Page195)

_________ is the value of a starting amount at a future point in time, given the rate of growth per period and the number of periods until that future time.

Future value (Page 190)

If the interest rate increases, the future value will

Increase (Page 193)

If we increase the compounding periods, the future value will (increase/decrease)

Increase (Page 193)

If the discount rate is lowered, what will happen to the present value?

Increases it (Page 194)

If the discount rate is lowered, what will happen to the present value? _______________________________________________________________

Increases it (Page 194)

Compound interest is

Interest earned on interest and on the original principal (Page 193)

Discounting is the _________of compounding.

Inverse (Page 194)

Explain the time value of money and its importance in the business world.

Money grows over time when it earns interest. Money expected or promised in the future is worth less than the same amount of money in hand today. This is because we lose the opportunity to earn interest when we have to wait to receive money. Similarly, money we owe is less burdensome if it is to be paid in the future rather than now. These concepts are at the heart of investment and valuation decisions of a firm.

Present value moves in what direction from n?

Opposite (Page 196)

An annuity that goes on forever is called a?

Perpetual annuity or a Perpetuity.

Give an example of a perpetuity.

Preferred stock or perpetual bond (Page 204)

Give an example of a perpetuity. _____________________________________

Preferred stock or perpetual bond (Page 204)

______ value is today's dollar value of a specific future amount.

Present

Today's dollar value of a specific future amount is called the

Present value (Page 194)

Explain which would have a higher future value: quarterly or semi-annually compounded amounts, all else equal.

Quarterly compounding would provide a higher future value: you are compounding more frequently and thus earning interest on your interest more frequently. (Page 193)

The pure time value of money uses the ________ rate of interest.

Real (Page 196)

The money you hold in your hand today is worth more than money you expect to receive in the future. This is called

The time value of money (Page 189)

Calculate the future value and present value of a single amount.

To calculate the future value and the present value of a single dollar amount, we may use the algebraic, table, or calculator methods. Future value and present value are mirror images of each other. They are compounding and discounting, respectively. With future value, increases in k and n result in an exponential increase in future value. Increases in k and n result in an exponential decrease in present valu

Solve special time value of money problems, such as finding the interest rate, number or amount of payments, or number of periods in a future or present value problem.

To solve special time value of money problems, we use the present value and future value equations and solve for the missing variable, such as the loan payment, k, or n. We may also solve for the present and future values of single amounts or annuities in which the interest rate, payments, and number of time periods are expressed in terms other than a year. The more often interest is compounded, the larger the future value.

Solve time value of money problems with uneven cash flows.

To solve time value of money problems with uneven cash flows, we find the value of each payment (each single amount) in the cash flow series and total each single amount. Sometimes the series has several cash flows of the same amount. If so, calculate the present value of those cash flows as an annuity and add the total to the sum of the present values of the single amounts to find the total present value of the uneven cash flow series.

If Annuity due just multiply by (1 +k) T/F

True

Future Value has a positive relationship with the number of periods (N) and interest rate (K) --> T/F

True, as the interest rate increases, future value increases. Similarly, as the number of periods increases, so does future value.

Present value is inversely related to k and n values. T/F

True, present value moves in the opposite direction of k and n. If k increases, present value decreases; if k decreases, present value increases. If n increases, present value decreases; if n decreases, present value increases.

Annuities in which the cash flows occur at the beginning of each of the specified time periods are known as?

annuities due

A series of equal cash flows, spaced evenly over time.

annuity

What is the name of interest earned on interest and on the original principal?

compounding interest

The ____ ____ is the required rate of return on an investment. It reflects the lost opportunity to spend or invest now (the opportunity cost) and the various risks assumed because we must wait for the funds.

discount rate

The time value of money means that money you hold in your hand today is worth more than the same amount of money you expect to receive in the ______.

future

The cost paid by the borrower to the lender for reducing consumption, known as an ______ ________, is the real rate of interest.

opportunity cost

Annuities in which the cash flows occur at the end of each of the specified time periods are known as?

ordinary annuities.

The real rate of interest reflects compensation for the ____ _____ ____ ______.

pure time value of money

The ___ ___ ____ on an investment reflects the pure time value of money, an adjustment for expected inflation, and any risk premiums present.

required rate of return

What is the name of interest earned only on the original principal.

simple interest