1 Accounting and the Time Value of Money Instructor Adnan Shoaib PART II: Corporate Accounting Concepts and Issues Lecture 24

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Accounting and the Time Value of Money

InstructorInstructorAdnan ShoaibAdnan Shoaib

PART II: Corporate Accounting Concepts and PART II: Corporate Accounting Concepts and IssuesIssues

Lecture 24Lecture 24

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1. Identify accounting topics where the time value of money is relevant.

2. Distinguish between simple and compound interest.

3. Use appropriate compound interest tables.

4. Identify variables fundamental to solving interest problems.

5. Solve future and present value of 1 problems.

Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives

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Future value of a single sum

Present value of a single sum

Solving for other unknowns

Basic Time Value

Concepts

Single-Sum Problems

Applications

The nature of interest

Simple interest

Compound interest

Fundamental variables

Accounting and the Time Value of MoneyAccounting and the Time Value of MoneyAccounting and the Time Value of MoneyAccounting and the Time Value of Money

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A relationship between time and money.

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

LO 1 Identify accounting topics where the time value of money is relevant.

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1. Notes

2. Leases

3. Pensions and Other Postretirement Benefits

4. Long-Term Assets

Applications to Time Value Concepts:


5. Shared-Based Compensation

6. Business Combinations

7. Disclosures

8. Environmental Liabilities


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Payment for the use of money.

Excess cash received or repaid over the amount

borrowed (principal).

The Nature of Interest



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Interest computed on the principal only.

LO 2 Distinguish between simple and compound interest.


Simple Interest

Illustration: Barstow Electric Inc. borrows $10,000 for 3 years

at a rate of 8% per year. Compute the total interest to be paid

for the 1 year.

Federal law requires the disclosure of interest rates on an annual basis.

Interest = p x i x n

= $10,000 x .08 x 1

= $800

Annual Annual InterestInterest

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Simple Interest

Illustration: Barstow Electric Inc. borrows $10,000 for 3 years

at a rate of 8% per year. Compute the total interest to be paid

for the 3 years.

Federal law requires the disclosure of interest rates on an annual basis.


= $10,000 x .08 x 3

= $2,400

Total Total InterestInterest

9 LO 2 Distinguish between simple and compound interest.


Simple Interest

Illustration: On October 1, 2012, Barstow Electric Inc. borrows

$10,000 for 3 months at a rate of 7% per year. Compute the

total interest to be paid for the year ended Dec. 31, 2012.


= $10,000 x .08 x 3/12

= $200

Partial Partial YearYear


10 LO 2 Distinguish between simple and compound interest.


Compound Interest

Computes interest on

► principal and

► interest earned that has not been paid or

withdrawn.

Most business situations use compound interest.

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

The future value of a single amount is the amount of money that a dollar will grow to at some point in

the future.

Assume we deposit $1,000 for three years that earns 6% interest compounded annually.

$1,000.00 × 1.06 = $1,060.00

and

$1,060.00 × 1.06 = $1,123.60

and

$1,123.60 × 1.06 = $1,191.02

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Writing in a more efficient way, we can say . . . .

$1,191.02 = $1,000 × [1.06]3

FV = PV (1 + i)n

FutureValue

FutureValue

Amount Invested at

the Beginning of the Period

Amount Invested at

the Beginning of the Period

InterestRate

InterestRate

Numberof Compounding

Periods


Periods

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Using the Future Value of $1 Table, we find the factor for 6% and 3 periods is 1.19102. So, we can solve our problem like this. . .

FV = $1,000 × 1.19102FV = $1,191.02


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

Instead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a

known future amount.

This is a present value question.

Present value of a single amount is today’s equivalent to a particular amount in the future.

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Remember our equation?

FV = PV (1 + i) n

We can solve for PV and get . . . .

FV

(1 + i)nPV =

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Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at

that time.What amount must you invest today in order to

accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?

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i = .08, n = 5

Present Value Factor = .68058

$20,000 × .68058 = $13,611.60

If you deposit $13,611.60 now, at8% annual interest, you will have

$20,000 at the end of 5 years.

Present Value of $1 Table

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FV = PV (1 + i)n

FutureValue

FutureValue

PresentValue

PresentValue

InterestRate

InterestRate


Periods


Periods

There are four variables needed when determining the time value of money.

If you know any three of these, the fourth can be determined.

Solving for Other ValuesSolving for Other ValuesSolving for Other ValuesSolving for Other Values

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Determining the UnknownDetermining the UnknownInterest RateInterest Rate

Determining the UnknownDetermining the UnknownInterest RateInterest Rate

Suppose a friend wants to borrow $1,000 today and promises to repay you $1,092 two years from now. What is the annual interest rate you would be agreeing to?

a. 3.5%

b. 4.0%

c. 4.5%

d. 5.0%

Present Value of $1 Table$1,000 = $1,092 × ?

$1,000 ÷ $1,092 = .91575Search the PV of $1 table

in row 2 (n=2) for this value.

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Illustration: Tomalczyk Company deposits $10,000 in the Last National Bank, where it will earn simple interest of 9% per year. It deposits another $10,000 in the First State Bank, where it will earn compound interest of 9% per year compounded annually. In both cases, Tomalczyk will not withdraw any interest until 3 years from the date of deposit.

Year 1 $10,000.00 x 9% $ 900.00 $ 10,900.00

Year 2 $10,900.00 x 9% $ 981.00 $ 11,881.00

Year 3 $11,881.00 x 9% $1,069.29 $ 12,950.29



21 LO 3 Use appropriate compound interest tables.

Table 1 - Future Value of 1

Table 2 - Present Value of 1

Table 3 - Future Value of an Ordinary Annuity of 1

Table 4 - Present Value of an Ordinary Annuity of 1

Table 5 - Present Value of an Annuity Due of 1

Compound Interest Tables

Number of Periods = number of years x the number of compounding periods per year.

Compounding Period Interest Rate = annual rate divided by the number of compounding periods per year.



How much principal plus interest a dollar accumulates to at the end of

each of five periods, at three different rates of compound interest.


Compound Interest



Formula to determine the future value factor (FVF) for 1:

Where:

= future value factor for n periods at i interest

n = number of periods

i = rate of interest for a single period

FVFn,i

Compound Interest



Determine the number of periods by multiplying the number of years involved by the number of compounding periods per year.

Compound Interest


9% annual interest compounded daily provides a 9.42% yield.

Effective Yield for a $10,000 investment.


Compound Interest

26 LO 4 Identify variables fundamental to solving interest problems.

Rate of Interest

Number of Time Periods

Future Value

Present Value

Fundamental Variables


27 LO 5 Solve future and present value of 1 problems.

Single-Sum ProblemsSingle-Sum ProblemsSingle-Sum ProblemsSingle-Sum Problems

Unknown Future Value

Two Categories

Unknown Present Value

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Value at a future date of a given amount invested, assuming compound interest.

LO 5 Solve future and present value of 1 problems.


FV = future value

PV = present value (principal or single sum)

= future value factor for n periods at i interestFVF n,i

Where:

Future Value of a Single Sum


Future Value of a Single SumFuture Value of a Single SumFuture Value of a Single SumFuture Value of a Single Sum

Illustration: Bruegger Co. wants to determine the future

value of $50,000 invested for 5 years compounded annually at

an interest rate of 11%.

= $84,253



What table do we use?

Alternate Calculation

Illustration: Bruegger Co. wants to determine the future

value of $50,000 invested for 5 years compounded annually at

an interest rate of 11%.

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What factor do we use?

$50,000

Present Value Factor Future Value

x 1.68506 = $84,253

Future Value of a Single SumFuture Value of a Single SumFuture Value of a Single SumFuture Value of a Single Sum Alternate Calculation

i=11%n=5


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Bob Anderson invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?

0 1 2 3 4 5 6

Present Value $15,000


Future Value?





$15,000 x 1.25971 = $18,896


i=8%n=3


Beginning Previous Year-EndYear Balance Rate Interest Balance Balance

1 15,000$ x 8% = 1,200 + 15,000 = 16,200$ 2 16,200 x 8% = 1,296 + 16,200 = 17,496 3 17,496 x 8% = 1,400 + 17,496 = 18,896

Beginning Previous Year-EndYear Balance Rate Interest Balance Balance

1 15,000$ x 8% = 1,200 + 15,000 = 16,200$ 2 16,200 x 8% = 1,296 + 16,200 = 17,496 3 17,496 x 8% = 1,400 + 17,496 = 18,896

PROOF

Bob Anderson invested $15,000 today in a fund that earns 8%

compounded annually. To what amount will the investment

grow in 3 years?


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Bob Anderson invested $15,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years?

0 1 2 3 4 5 6

Present Value $15,000


Future Value?





$15,000 x 1.26532 = $18,980


What factor?

i=4%n=6

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Value now of a given amount to be paid or received in the future, assuming compound interest.


Present Value of a Single Sum


Where:

FV = future value

PV = present value (principal or single sum)

= present value factor for n periods at i interestPVF n,i


Present Value of a Single SumPresent Value of a Single SumPresent Value of a Single SumPresent Value of a Single Sum

Illustration: What is the present value of $84,253 to be

received or paid in 5 years discounted at 11% compounded

annually?

= $50,000

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Illustration: What is the present value of $84,253 to be

received or paid in 5 years discounted at 11% compounded

annually?

Alternate Calculation

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$84,253

Future Value Factor Present Value

x .59345 = $50,000


What factor?

i=11%n=5


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Caroline and Clifford need $25,000 in 4 years. What

amount must they invest today if their investment earns

12% compounded annually?



0 1 2 3 4 5 6

Present Value?


Future Value $25,000

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$25,000


x .63552 = $15,888


What factor?

i=12%n=4


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0 1 2 3 4 5 6

Present Value?


Future Value $25,000



Caroline and Clifford need $25,000 in 4 years. What

amount must they invest today if their investment earns

12% compounded quarterly?

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$25,000


x .62317 = $15,579


i=3%n=16


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Solving for Other Unknowns


Example—Computation of the Number of Periods

The Village of Somonauk wants to accumulate $70,000 for the

construction of a veterans monument in the town square. At the

beginning of the current year, the Village deposited $47,811 in a

memorial fund that earns 10% interest compounded annually.

How many years will it take to accumulate $70,000 in the

memorial fund?

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Using the future value factor of 1.46410, refer to Table 6-1 and read

down the 10% column to find that factor in the 4-period row.

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Using the present value factor of .68301, refer to Table 6-2 and

read down the 10% column to find that factor in the 4-period row.

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The Village of Somonauk wants to accumulate $70,000 for the

construction of a veterans monument in the town square. At the

beginning of the current year, the Village deposited $47,811 in a

memorial fund that earns 10% interest compounded annually.

How many years will it take to accumulate $70,000 in the

memorial fund?

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Example—Computation of the Interest Rate

Advanced Design, Inc. needs $1,409,870 for basic research 5

years from now. The company currently has $800,000 to invest

for that purpose. At what rate of interest must it invest the

$800,000 to fund basic research projects of €1,409,870, 5 years

from now?

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Using the future value factor of 1.76234, refer to Table 6-1 and read across the 5-period row to

find the factor.


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Using the present value factor of .56743, refer to Table 6-2 and read across the 5-period row to

find the factor.


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Some notes do not include a stated interest rate. We call these notes

noninterest-bearing notes.

Even though the agreement states it is a noninterest-bearing note, the note

does, in fact, include interest.

We impute an appropriate interest rate for noninterest-bearing notes.

Accounting Applications of Present Value Accounting Applications of Present Value Techniques—Single Cash AmountTechniques—Single Cash Amount

Accounting Applications of Present Value Accounting Applications of Present Value Techniques—Single Cash AmountTechniques—Single Cash Amount

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Statement of Financial Accounting Concepts No. 7

“Using Cash Flow Information and Present Value in Accounting Measurements”

The objective of valuing an asset or

liability using present value is to

approximate the fair value of that asset

or liability.

Expected Cash Flow

×Credit-Adjusted Risk-Free Rate of InterestPresent Value

Expected Cash Flow ApproachExpected Cash Flow ApproachExpected Cash Flow ApproachExpected Cash Flow Approach

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End of Lecture 24End of Lecture 24End of Lecture 24End of Lecture 24

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1 Accounting and the Time Value of Money Instructor Adnan Shoaib PART II: Corporate Accounting Concepts and Issues Lecture 24