Lecture Issues in financial accounting – Lecture 24: Accounting and the time value of money

Lecture 24 - Accounting and the time value of money. The contents of this chapter include all of the following: Compute interest and future values, compute present values, use a financial calculator to solve time value of money problems.

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Accounting and the Time

Value of Money

PART II: Corporate Accounting Concepts and

Issues

Lecture 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 Objectives

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Future value

of a single sum

Present value

of a single sum

Solving for other

Accounting 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 Concepts

Time Value of Money

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1 Notes

2 Leases

3 Pensions and Other

Postretirement Benefits

4 Long-Term Assets

Applications to Time Value Concepts:

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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

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 Interest

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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

= $10,000 x 08 x 3

= $2,400

Total Interest

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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 Year

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Future Value of a Single Amount Future 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.

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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

Future Value

Future Value Invested at Invested at Amount Amount InterestInterestRateRate

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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 × 1.19102

FV = $1,191.02

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Present Value of a Single Amount Present 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 )n

PV =

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Present Value of a Single Amount

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, at 8% 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

Future Value

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Determining the Unknown

Interest Rate

Determining the Unknown

Interest 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?

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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

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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.

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

Compound Interest

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

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Determine the number of periods by multiplying the number

of years involved by the number of compounding periods

per year

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9% annual interest compounded daily provides a 9.42%

yield

Effective Yield for a $10,000 investment.

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Value at a future date of a given amount invested, assuming

compound interest

Single-Sum Problems

FV = future value

PV = present value (principal or single sum)

= future value factor for n periods at i interest

FVF n,i

Where:

Future Value of a Single Sum

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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

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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

x 1.68506 = $84,253

Future Value of a Single Sum Calculation Alternate

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

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Present Value Factor Future Value

$15,000 x 1.25971 = $18,896

i=8%

n=3

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Beginning Previous Year-End Year Balance Rate Interest Balance Balance

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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?

Present Value $15,000

What table do we use?

Future Value?

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$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

PV = present value (principal or single sum)

= present value factor for n periods at i interest

PVF n,i

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Present 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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What table

do we use?

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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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?

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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

What table do we use?

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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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

noninterestbearing note, the note does, in fact, include interest.

Accounting Applications of Present Value

Techniques—Single Cash Amount

Accounting Applications of Present Value

Techniques—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

Present Value

Expected Cash Flow Approach

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