chuong gioi thieu Time Value of Money Ke toan quan tri

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Appendix A- 1

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Time Value of Money

Managerial Accounting

Fifth Edition

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Appendix

A- 3

study objectives

problems.

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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 Concepts

Time Value of Money

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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 Interest

SO 1 Distinguish between simple and compound interest.

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Interest computed on the principal only

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Appendix

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Computes interest on

 the principal and

 any interest earned that has not been paid or

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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 Interest

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

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Appendix

The future value is the value at a future date of a

given amount invested assuming compound interest.

Future value computation

Future Value of a Single Amount

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Illustration: If you earn a 9% rate of return, compute

the future value of $1,000 at the end of three years:

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Appendix

A- 11 SO 2 Solve for future value of a single amount.

the future value of $1,000 at the end of three years:

What table do we use?

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What factor do we use?

Present Value Factor Future Value

$1,000 x 1.29503 = $1,295.03

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Appendix

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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?

SO 2 Solve for future value of a single amount.

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Present Value Factor Future Value

$20,000 x 2.85434 = $57,086.80

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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 Annuity

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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

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Appendix

A- 17 SO 3 Solve for future value of an annuity.

Solution on notes page

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Annual Investment Factor Future Value

$2,000 x 3.15250 = $6,305

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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 Variables

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

Formula for present value

i = interest rate for one period

n = number of periods

Present Value of a Single Amount

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Appendix

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would compute the present value of $1,000 for one year

as follows:

SO 5 Solve for present value of a single amount.

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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

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Appendix

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Future Value Factor Present Value

$1,000 x 90909 = $909.09

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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

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Appendix

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$1,000 x 82645 = $826.45

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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

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Appendix

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savings account, paying 9% interest, in order to accumulate

$5,000,000 four years from today

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

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The value now of a series of future receipts or

payments, discounted assuming compound interest.

Present Value of an Annuity

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Appendix

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annually for three years at a time when the discount rate is

10%

SO 6 Solve for present value of an annuity.

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Appendix

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Annual Receipts Factor Present Value

$1,000 x 2.48685 = $2,486.85

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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?

$6,000 x 3.60478 = $21,628.68

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Appendix

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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 Discounting

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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 Decision

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Appendix

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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?

SO 7 Compute the present values in capital budgeting situations.

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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.

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Appendix

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Notice 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.

Accepted

SO 7 Compute the present values in capital budgeting situations.

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Using Financial Calculators

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Appendix

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Present Value of a Single Sum

Assume that you want to know the present value of

$84,253 to be received in five years, discounted

at 11% compounded annually.

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

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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%.

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Appendix

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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.

Useful Applications – Auto Loan

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

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Useful Applications – Mortgage Loan

You 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?

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Appendix

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