Accounting Appendix A Homework Appendix Time Value Money Learning Objectives Compute

APPENDIX A

TIME VALUE OF MONEY

LEARNING OBJECTIVES

1. COMPUTE INTEREST AND FUTURE VALUES.

2. COMPUTE PRESENT VALUE.

3. SOLVE FOR FUTURE VALUE OF AN ANNUITY.

4. IDENTIFY THE VARIABLES FUNDAMENTAL

TO SOLVING PRESENT VALUE PROBLEMS.

APPENDIX A REVIEW

Value of Interest

1. (L.O. 1) Interest is payment for the use of another person’s money. The amount of interest involved

in any financing transaction is based on three elements:

a. Principal: The original amount borrowed or invested.

b. Interest Rate: An annual percentage of the principal.

c. Time: The number of years that the principal is borrowed or invested.

2. Simple interest is computed on the principal amount only. Simple interest is usually expressed as:

Interest = Principal X Rate X Time

Future Value of a Single Amount

4. The future value of a single amount is the value at a future date of a given amount invested

assuming compound interest. Future value is usually expressed as:

FV = P X (1 + i)n

FV = future value of a single amount

P = principal

i = interest rate for one period

n = number of periods

5. The Future Value of 1 table is used for obtaining a 5-digit decimal number which is multiplied by the

principal to calculate the future value.

Future Value of an Annuity

6. The future value of an annuity is the sum of all the payments (receipts) plus the accumulated

compound interest on them. In computing the future value of an annuity, it is necessary to know the

(1) interest rate, (2) the number of compounding periods, and (3) the amount of the periodic payments

or receipts. When the periodic payments or receipts are the same in each period, the future value can

be computed by using a future value of an annuity of 1 table.

Present Value Variables

7. (L.O. 2) The present value is based on three variables: (1) the dollar amount to be received (future

amount), (2) the length of time until the amount is received (number of periods), and (3) the interest

rate (the discount rate).

PV = FV/(1 + i)

PV = present value

Present Value of an Annuity

9. In computing the present value of an annuity, it is necessary to know (1) the discount rate, (2) the

number of discount periods, and (3) the amount of the periodic receipts or payments. When the future

Time Periods and Discounting

10. Discounting may also be done over shorter periods of time such as monthly, quarterly, or

semiannually. When the time frame is less than one year, it is necessary, to convert the annual

interest rate to the applicable time frame.

Computing the Present Value of a Long-Term Note or Bond

11. The present value (or market price) of a long-term note or bond is a function of three variables: (1) the

payment amounts, (2) the length of time until the amounts are paid, and (3) the discount rate. When

the investor’s discount rate is equal to the bond’s contractual interest rate, the present value of the

bonds will equal the face value of the bonds.

Computing the Present Values in Capital Budgeting Situations

12. (L.O. 3) The decision to make long-term capital investments is best evaluated using discounting

techniques that calculate the present value of the cash flows involved in a capital investment.

Using a Financial Calculator

14. (L.O. 4) Financial calculators can be used to solve the same and additional problems as those solved

with time value of money tables. The amounts for all of the known elements of a time value of money

problem are entered into a financial calculator and it solves for the unknown element. Financial

calculators are particularly useful in situations involving interest rates and compounding periods not

presented in the compound interest tables.

LECTURE OUTLINE

A. Nature of Interest

1. Interest is payment for the use of another person’s money. It is the

difference between the amount borrowed or invested (called the principal)

and the amount repaid or collected.

2. The amount of interest involved in any financing transaction is based on:

a. Principal (p): The original amount borrowed or invested,

3. Simple interest is computed on the principal amount only.

4. Compound interest is computed on principal and on any interest earned

that has not been paid or withdrawn. It is the return on the principal for two

or more time periods.

B. Future Value of a Single Amount

1. The future value of a single amount is the value at a future date of a given

amount invested assuming compound interest.

2. The future value of a single amount can be computed using the following

formula:

FV = p X (1 + i )n

C. Future Value of an Annuity

1. An annuity is an equal dollar amount of payments or receipts.

2. The future value of an annuity is the sum of all the payments (receipts) plus

the accumulated compound interest on them.

3. In computing the future value of an annuity, it is necessary to know the:

a. interest rate,

b. number of compounding periods,

D. Present Value Variables

1. The present value is based on the:

a. dollar amount to be received (future amount),

b. length of time until the amount is received (number of periods),

E. Present Value of a Single Amount

1. The present value of a single amount is the value today of a future amount

to be received (or paid), assuming compound interest.

2. The present value of a single amount can be computed using the following

formula:

PV = FV ÷ (1 + i )n

FV = future amount; i = interest rate; n = number of periods.

F. Present Value of an Annuity

1. The present value of an annuity is the value today of a series of future

receipts or payments, discounted assuming compound interest.

2. In computing the present value of an annuity, one needs to know the:

a. discount rate.

b. number of discount periods.

c. amount of the periodic receipts or payments.

G. Computing the Present Value of a Long-Term Note or Bond

1. The present value (or market price) of a long-term note or bond is a

function of the:

a. payment amounts.

b. length of time until the amounts are paid.

c. discount rate.

2. The payment amounts are made up of two elements:

3. To compute the present value of the bond, one must discount both the

interest payments and the principal amount.

a. Multiply the principal amount by the appropriate present value factor

from Table 3.

b. Multiply the amount of the interest payments by the appropriate

present value factor from Table 4.

H. Computing the Present Values in a Capital Budgeting Decision

1. The decision to make long-term capital investments is best evaluated using

discounting techniques that recognize the time value of money. This is

done by calculating the present value of the cash flows involved in a capital

investment.

2. When the present value of the cash receipts (inflows) from a capital

I. Using Financial Calculators.

1. Financial calculators can be used to solve present and future value

problems using the following keys.

a. N = Number of periods

b. I = interest rate per period

c. PV = present value (occurs at the beginning of the first period)

10 MINUTE QUIZ

Circle the correct answer.

True/False

1. Simple interest is computed on the principal and any interest earned that has not been paid

or received.

True False

2. The future value of an annuity is the sum of all the payments plus the accumulated

compound interest on them.

True False

3. The process of determining the present value is referred to as discounting the present

amount.

True False

4. In computing the present value of an annuity, it is necessary to know the discount rate, the

number of discount periods, and the amount of the periodic payments.

True False

5. To compute the present value of a bond, both the interest payments and the principal

amount must be discounted.

True False

Multiple Choice

1. Interest that is computed on the principal and any interest earned is called

a. simple interest.

b. present interest.

c. future interest.

d. compound interest.

2. The value at a future date of a given amount invested assuming compound interest is the

a. compounded value of a single amount.

b. compounded value of an annuity.

c. future value of a single amount.

d. future value of an annuity.

3. The process of determining the present value is referred to as discounting the

a. compound amount.

b. future amount.

c. present amount.

d. simple amount.

4. In computing the present value of an annuity, it is not necessary to know the

a. discount rate.

b. number of discount periods.

c. amount of the periodic payments.

d. year the payments will begin.

5. Cogswell Company issued 6%, 10-year bonds that pay interest semiannually. The discount

rate of interest for such bonds is 8%. In computing the present value of these bonds, the

appropriate discount rate is

a. 8%.

b. 6%.

c. 4%.

d. 3%.

ANSWERS TO QUIZ

True/False

1. False

Multiple Choice

1. d.