appendix a- 1. appendix a- 2 time value of money managerial accounting fifth edition weygandt kimmel...

Appendix A- 1

Appendix A- 2

Time Value of MoneyTime Value of MoneyTime Value of MoneyTime Value of Money

Managerial AccountingFifth Edition

Weygandt Kimmel Kieso

Appendix A- 3

study objectives

1. Distinguish between simple and compound interest.

2. Solve for future value of a single amount.

3. Solve for future value of an annuity.

4. Identify the variables fundamental to solving present

value problems.

5. Solve for present value of a single amount.

6. Solve for present value of an annuity.

7. Compute the present values in capital budgeting

situations.

8. Use a financial calculator to solve time value of money

problems.

Appendix A- 4

In accounting (and finance), the term indicates that a dollar received today is worth more than a dollar promised at some time in the future.

Basic Time Value ConceptsBasic Time Value ConceptsBasic Time Value ConceptsBasic Time Value Concepts

Time Value of Money

Appendix A- 5

Payment for the use of money.

Excess cash received or repaid over the amount invested or borrowed (principal).

Variables involved in financing transaction:

1. Principal (p) - Amount borrowed or invested.

2. Interest Rate (i) – An annual percentage.

3. Time (n) - The number of years or portion of a year that the principal is borrowed or invested.

Nature of InterestNature of InterestNature of InterestNature of Interest

SO 1 Distinguish between simple and compound interest.

Appendix A- 6

Interest computed on the principal only.



Illustration:

On January 2, 2010, assume you borrow $5,000 for 2 years at a simple interest of 12% annually. Calculate the annual interest cost.

Interest = p x i x n

= $5,000 x .12 x 2

= $1,200

FULL YEARFULL YEAR

Illustration A-1

Simple Interest

Appendix A- 7

Computes interest on

the principal and

any interest earned that has not been paid or withdrawn.

Most business situations use compound interest.



Compound Interest

Appendix A- 8

Illustration: Assume that you deposit $1,000 in BankOne,

where it will earn simple interest of 9% per year, and you

deposit another $1,000 in CityCorp, where it will earn

compound interest of 9% per year compounded annually.

Also assume that in both cases you will not withdraw any

cash until three years from the date of deposit.

Nature of Interest - Compound Nature of Interest - Compound InterestInterestNature of Interest - Compound Nature of Interest - Compound InterestInterest


Year 1 $1,000.00 x 9% $ 90.00 $ 1,090.00

Year 2 $1,090.00 x 9% $ 98.10 $ 1,188.10

Year 3 $1,188.10 x 9%$106.93 $ 1,295.03

Illustration A-2

Appendix A- 9 SO 2 Solve for future value of a single

amount.

The future value is the value at a future date of a given amount invested assuming compound interest. Illustration A-3

Future value computation

Future Value of a Single AmountFuture Value of a Single AmountFuture Value of a Single AmountFuture Value of a Single Amount


amount.

Illustration: If you earn a 9% rate of return, compute the future value of $1,000 at the end of three years:

Illustration A-4



amount.

Illustration: If you earn a 9% rate of return, compute the future value of $1,000 at the end of three years:

Illustration A-4


What table do we use?

Appendix A- 12

What factor do we use?

Present Value

Factor Future Value

SO 2 Solve for future value of a single amount.


$1,000 x 1.29503 = $1,295.03

Appendix A- 13

Illustration: John and Mary Rich invested $20,000 in a savings account paying 6% interest at the time their son, Mike, was born. The money is to be used by Mike for his college education. On his 18th birthday, Mike withdraws the money from his savings account. How much did Mike withdraw from his account?

Illustration A-5



Appendix A- 14

Present Value

Factor Future Value



$20,000 x 2.85434 = $57,086.80

Appendix A- 15

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

1. the interest rate,

2. the number of compounding periods, and

3. the amount of the periodic payments or

receipts.

SO 3 Solve for future value of an annuity.

Future Value of a AnnuityFuture Value of a AnnuityFuture Value of a AnnuityFuture Value of a Annuity

Appendix A- 16

Illustration: Assume that you invest $2,000 at the end

of each year for three years at 5% interest compounded

annually. Compute the future value.Illustration A-6

SO 3 Solve for future value of an annuity.


Appendix A- 17 SO 3 Solve for future value of an

annuity.


Illustration A-7

Solution on notes page

Appendix A- 18 SO 3 Solve for future value of an

annuity.


Annual Investment

Factor Future Value

$2,000 x 3.15250 = $6,305


Appendix A- 19 SO 4 Identify the variables fundamental to solving present value

problems.

The present value is the value now of a given amount to be paid or received in the future, assuming compound interest.

Present value variables:

1. Dollar amount to be paid or received in the future,

2. Length of time until amount is paid or received, and

3. Interest rate (the discount rate).

Present Value VariablesPresent Value VariablesPresent Value VariablesPresent Value Variables

Appendix A- 20

Present Value = Future Value / (1 + i )n

Illustration A-9Formula for present value

i = interest rate for one period n = number of periods

Present Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single Amount

SO 5 Solve for present value of a single amount.

Appendix A- 21

Illustration: If you want a 10% rate of return, you would compute the present value of $1,000 for one year as follows:

Illustration A-10



Appendix A- 22

Illustration: If you want a 10% rate of return, you can also compute the present value of $1,000 for one year by using a present value table.

Illustration A-10




Appendix A- 23


Future Value Factor Present Value

$1,000 x .90909 = $909.09



Appendix A- 24

Illustration: If you receive the single amount of $1,000 in two years, discounted at 10% [PV = $1,000 / 1.102], the present value of your $1,000 is $826.45.

Illustration A-11




Appendix A- 25




$1,000 x .82645 = $826.45


Appendix A- 26


Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from now or taking the present value of $10,000 now. The state uses an 8% rate in discounting. How much will you receive if you accept your winnings now?


$10,000 x .79383 = $7,938.30


Appendix A- 27

Illustration: Determine the amount you must deposit now in a savings account, paying 9% interest, in order to accumulate $5,000,000 four years from today.


$5,000,000 x .70843 = $3,542,150



Appendix A- 28

The value now of a series of future receipts or payments, discounted assuming compound interest.

0 1

Present Value

2 3 4 19 20

$100,000

100,000

100,000

100,000

100,000. . . . .

100,000

SO 6 Solve for present value of an annuity.

Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity

Appendix A- 29

Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount rate is 10%.


Illustration A-14



Appendix A- 30

Illustration A-15

Solution on notes page SO 6 Solve for present value of an

annuity.


Appendix A- 31

Annual Receipts

Factor Present Value

$1,000 x 2.48685 = $2,486.85




Appendix A- 32

Illustration: Christel Company has just signed an agreement to purchase equipment for installment payments of $6,000 each, to be paid at the end of each of the next 5 years. The appropriate discount rate is 12%. What is the present value of the installment payments?

Payments Factor Present Value

$6,000 x 3.60478 = $21,628.68



Appendix A- 33

Illustration: When the time frame is less than one year, you need to convert the annual interest rate to the applicable time frame. Assume that the investor received $500 semiannually for three years instead of $1,000 annually when the discount rate was 10%.

$500 x 5.07569 = $2,537.85

Time Periods and DiscountingTime Periods and DiscountingTime Periods and DiscountingTime Periods and Discounting


Appendix A- 34

The decision to make long-term capital investments

is best evaluated using discounting techniques

that recognize the time value of money.

To do this, many companies calculate the present

value of the cash flows involved in a capital

investment.

Present Value in a Capital Budgeting Present Value in a Capital Budgeting DecisionDecisionPresent Value in a Capital Budgeting Present Value in a Capital Budgeting DecisionDecision

SO 7 Compute the present values in capital budgeting situations.

Appendix A- 35

Illustration: Nagel-Siebert Trucking Company, a cross-country freight carrier in Montgomery, Illinois, is considering adding another truck to its fleet because of a purchasing opportunity. Navistar Inc., Nagel-Siebert’s primary supplier of overland rigs, is overstocked and offers to sell its biggest rig for $154,000 cash payable upon delivery. Nagel-Siebert knows that the rig will produce a net cash flow per year of $40,000 for five years (received at the end of each year), at which time it will be sold for an estimated salvage value of $35,000. Nagel-Siebert’s discount rate in evaluating capital expenditures is 10%. Should Nagel-Siebert commit to the purchase of this rig?

Present Value in a Capital Budgeting Present Value in a Capital Budgeting DecisionDecisionPresent Value in a Capital Budgeting Present Value in a Capital Budgeting DecisionDecision


Appendix A- 36

Present Value in a Capital Budgeting Present Value in a Capital Budgeting DecisionDecision


The cash flows that must be discounted to present value are:

Cash payable on delivery (today): $154,000.

Net cash flow from operating the rig: $40,000 for 5 years.

Cash received from sale of rig at the end of 5 years: $35,000.

Illustration A-17


Appendix A- 37


Present Value in a Capital Budgeting Present Value in a Capital Budgeting DecisionDecisionNotice the present value of the net operating cash flows is discounting an annuity, while computing the present value of the $35,000 salvage value is discounting a single sum.

Illustration A-18

Accepted


Appendix A- 38 SO 8 Use a financial calculator to solve time value of money

problems.

Using Financial CalculatorsUsing Financial Calculators

Illustration C-20Financial calculator keys

N = number of periods

I = interest rate per period

PV = present value

PMT = payment

FV = future value

Appendix A- 39


Illustration A-21

Present Value of a Single Sum

Assume that you want to know the present value of $84,253 to be received in five years, discountedat 11% compounded annually.

SO 8 Use a financial calculator to solve time value of money problems.

Appendix A- 40


Illustration A-22

Present Value of an Annuity

Assume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12%.


Appendix A- 41

The loan has a 9.5% nominal annual interest rate, compounded monthly. The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase.


Illustration A-23

Useful Applications – Auto Loan


Appendix A- 42


Useful Applications – Mortgage LoanYou decide that the maximum mortgage

payment you can afford is $700 per month. The annual interest rate is 8.4%. If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum purchase price you can afford? Illustration A-24


Appendix A- 43

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