8-1 powerpoint presentation by douglas cloud professor emeritus of accounting pepperdine university...

PowerPoint Presentation by PowerPoint Presentation by Douglas CloudDouglas Cloud

Professor Emeritus of AccountingProfessor Emeritus of AccountingPepperdine UniversityPepperdine University

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Financial AccountingInformation for Decisions

6th edition

Ingram and Albright

F1388The Time The Time Value of Value of MoneyMoney

Financial AccountingA Bridge to Decision MakingA Bridge to Decision Making

Ingram and Albright

6th edition

ObjectivesObjectivesObjectivesObjectives

Once you have completed this chapter, you should be able to—

1. Define future and present value.

ObjectivesObjectivesObjectivesObjectives

2. Determine the future value of a single amount invested at the present time.

3. Determine the future value of an annuity.4. Determine the present value of a single amount

to be received in the future.5. Determine the present value of an annuity.6. Determine investment values and interest

expense or revenue for various periods.

11ObjectiveObjectiveObjectiveObjective

Determine future and present value.

Future ValueFuture ValueFuture ValueFuture Value

The future value of an amount is the value of that

amount at a particular time in

the future.

The future value of an amount is the value of that

amount at a particular time in

the future.

The present value of an amount is the

value of that amount at a particular date

prior to the time the amount is paid or

received.

The present value of an amount is the

value of that amount at a particular date

prior to the time the amount is paid or

received.

Future Value = Present Value (1 + R)

Interest Rate

Future Value = Present Value (1 + R)

Future Value = $1,000(1.05)

If $1,000 is invested on January 1, 2007, at 5% interest, what will be the future value

(the amount that will accumulate) by December 31, 2007?

If $1,000 is invested on January 1, 2007, at 5% interest, what will be the future value

(the amount that will accumulate) by December 31, 2007?

Future Value = $1,050

22Determine the future value of a single amount invested at the present time.

ObjectiveObjectiveObjectiveObjective

Compound InterestCompound InterestCompound InterestCompound Interest

If the accumulated amount ($1,050) is left in the savings account for a second year, until December 31,

2008, how much would the investment be worth at that time?

If the accumulated amount ($1,050) is left in the savings account for a second year, until December 31,

2008, how much would the investment be worth at that time?

FV = $1,050(1.05)FV = $1,102.50

Interest earned in one period on interest earned in an earlier period is known as compound interest.

Assume you invest $500 for three years at 8% interest. How much would your investment

be worth at the end of three years?

Assume you invest $500 for three years at 8% interest. How much would your investment

be worth at the end of three years?

FV = PV(1 + R)t

FV = $500(1.08)³

FV = $500(1.08)(1.08)(1.08)

FV = $629.86

To calculate a future value, a future value of a single amount

table, such as the one in the next slide, can be used.

To calculate a future value, a future value of a single amount

table, such as the one in the next slide, can be used.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09PeriodInterest RateInterest Rate

1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090

1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188

1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295

Future Value of a Single Amount

Note: Due to space limitations, the tables in this chapter have the table values rounded to three decimal places.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period

1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090

1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188

1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295

Interest RateInterest Rate

1.2601.260

FV = $500 x 1.260 = $630 (rounded)

Interest Table for an Investment of $500 for Three Years at 8%

A B C DA B C D

Value atValue at Interest EarnedInterest Earned FV at YearendFV at YearendYearYear Beginning of YearBeginning of Year (B x Interest Rate)(B x Interest Rate) (B + C)(B + C)

1 500.00 40.00 540.00

2 540.00 43.20 583.20

3 583.20 46.66 629.86

TotalTotal 129.86129.86

Exhibit 1Exhibit 1Exhibit 1Exhibit 1

Exercise 8-2Exercise 8-2Exercise 8-2Exercise 8-2

Click the button to skip this exercise.If you experience trouble making the button work, type 20 and press “Enter.”

Assume that you borrow $25,000 on April 1, 2007, at an annual rate of 7%. How much will you owe on March 31, 2008 if you make no payments until that date?

Press “Enter” or left click the mouse for solution.

FV = $25,000 x (1.07) = $26,7501

ContinuedContinuedContinuedContinued

How much will you owe on March 31, 2009 if you make no payments until that date?

FV = $25,000 x (1.07) = $28,622.502

If you pay the interest incurred for the first year on March 31, 2008, how much will you owe on March 31, 2009 if you make no other payments until that date?

FV = $25,000 x (1.07) = $26,7501

If the interest incurred during the first year is paid off before the second year begins, interest will

accrue only on the $25,000 during Year 2.

33Determine the future value of an annuity.

An annuity is a series of equal amounts received or

paid over a specified number of equal time periods.

An annuity is a series of equal amounts received or

paid over a specified number of equal time periods.

Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity

If $500 is invested at the end of each year for three years, how much

would the investment be worth at the end of three years if the interest

earned is 8% per year?

If $500 is invested at the end of each year for three years, how much

would the investment be worth at the end of three years if the interest

earned is 8% per year?

End of Year 1 End of Year 2 End of Year 3 FV at End of Year 3

Invested for 2 years ($500 x 1.08²) $ 583.20

Invested for 1 years ($500 x 1.08¹) 540.00

Invested for 0 years 500.00

Future value of total investment $1,623.20

Total amount invested over 2 years 1,500.00

Interest earned over 2 years

$ 123.20

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090

3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.2783.2463.246

FVA = Amount invested (A) x Interest factor (IF)FVA = $500 x 3.246 (rounded to three decimal places) FVA = $1,623 (or $1,623.20 if a four-decimal table is

A B C D EA B C D E

Value Value Interest EarnedInterest Earned AmountAmount FV at FV at at Beginningat Beginning (Column B x(Column B x Invested atInvested at End of End of

Year Year of Yearof Year Interest Rate)Interest Rate) End of YearEnd of Year YearYear

1 0.00 0.00 500.00 500.00

2 500.00 40.00 500.00 1,040.00

3 1,040.00 83.20 500.00 1,623.20

TotalTotal 123.20123.20 1,500.001,500.00

Interest Table for an Annuity of $500 at the End of Each Year for Three Years at 8%

How much would you need to invest each year to accumulate $1,000 at the

end of three years to take a trip to Mexico after you graduate from

college? Assume you can earn 6% on your investment.

How much would you need to invest each year to accumulate $1,000 at the

end of three years to take a trip to Mexico after you graduate from

college? Assume you can earn 6% on your investment.

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090

3.030 3.060 3.091 3.122 3.153 1.191 1.225 1.260 1.295

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period

3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.2783

3.1843.184

FVA = Amount invested (A) x Interest factor (IF)$1,000 = A x 3.184 (using three decimal places) A = $1,000 ÷ 3.184 A = $314 (or $314.11 if 3.1836 is used)

Optimism, Inc. anticipates the need for factory expansion four years from today. The firm has determined that it will have the necessary funds for expansion if it puts $400,000 per year into a stock portfolio expected to earn 9% per year. Deposits will be made at the end of the year.

a) How much is the company planning to raise toward factory expansion with this plan?

FV of an annuity = Amount x Interest Factor= $400,000 x 4.57313= $1,829,252

9%, 4 years

b) What amount would the company expect to raise if it could invest $400,000 per year for seven years?FV of an annuity = Amount x Interest Factor

= $400,000 x 9.20043= $3,680,172

9%, 7 years

c) Why is the answer to part b more than twice as large as the answer to part a even though the length of the annuity is less than twice as long?

The future value of an annuity grows from the contribution of additional deposits and by the compounding of interest on the existing balances. In short, interest on interest contributes substantially to the annuity’s future value.

44Determine the present value of a single amount to be received in the future.

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

A company offered to sell you an investment that pays $3,000 at the end of three years. You want to

earn 8% return on your investment. How much would you be willing to

pay for the investment?

A company offered to sell you an investment that pays $3,000 at the end of three years. You want to

earn 8% return on your investment. How much would you be willing to

pay for the investment?

FV = PV(1+R) t

$3,000 = PV(1+R)³

PV = $3,000 x 1/(1.08)³

PV = $3,000 ÷ (1.08)³ PV = $2,381.50

$3,000 = PV(1.08)³

Using Excel, the present value of an investment that pays $3,000 at the end of

three years at 8% can be calculated by entering =3000*(1/(1.08^3)) in a cell.

Using Excel, the present value of an investment that pays $3,000 at the end of

three years at 8% can be calculated by entering =3000*(1/(1.08^3)) in a cell.

The present value of a single amount table also could be

used to determine the present value of the $3,000.

The present value of a single amount table also could be

used to determine the present value of the $3,000.

0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917

0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period

0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.7723

PV = FV x IFPV = $3,000 x 0.794 (rounded to three decimal places) PV = $2,381.49

0.7940.794

Interest Table for a Present Value of $2,381.49 for Three Years at 8%

A B C DA B C D

Present Value atPresent Value at Interest EarnedInterest Earned Value at EndValue at EndYearYear Beginning of YearBeginning of Year (B x Interest Rate)(B x Interest Rate) (B + C)(B + C)

1 2,381.49 190.52 2,572.01

2 2,572.01 205.76 2,777.77

3 2,777.77 222.23 3,000.00

Assume that you received a loan on July 1, 2007. The lender charges annual interest of 6%. On June 30, 2012, you owe the lender $802.93. Assuming that you made no payments for principal or interest on the loan during the five years, how much did you borrow?

Press “Enter” or click the left mouse button for solution.

The present value of $802.93 at 6% for five years is $802.93 x 0.74726 = $600.

6%, 5 years

You borrowed $600.

55Determine the present value of an annuity.

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

Assume that you could purchase an investment that would pay $1,000 at the

end of each year for three years, and you expect to earn a return of 8%.

Assume that you could purchase an investment that would pay $1,000 at the

end of each year for three years, and you expect to earn a return of 8%.

How much would you be willing to pay for the investment?

$ 925.93 = $1,000 ÷ (1.08) $1,000

Present Value atBeginning of Year 1 End of Yr. 1

$ 925.93

857.34 = $1,000 ÷ (1.08) $1,000

$ 925.93

857.34

793.83 = $1,000 ÷ (1.08) $1,000

Present Value atBeginning of Year 1

$3,000.00 Total amount received over three years 2,577.10 Present value of total investment$ 422.90 Interest earned over three years

$ 925.93

857.34

793.83

$2,577.10 Present value of total investment

You would be willing to pay

$2,577.10.

You would be willing to pay

$2,577.10.

The PV function in Excel can be used to calculate the present value of an annuity. The function can be entered in the pop-up box or

directly into the cell.

The PV function in Excel can be used to calculate the present value of an annuity. The function can be entered in the pop-up box or

directly into the cell.

If you purchase an investment that paid $1,000 each year for three years at

8% interest, type =PV(0.08,3,–1000) in a cell

and press Enter.

If you purchase an investment that paid $1,000 each year for three years at

8% interest, type =PV(0.08,3,–1000) in a cell

and press Enter.

Or, you can use the present value

of an annuity table.

Or, you can use the present value

of an annuity table.

Interest Rate

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period

2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.5313

2.5772.577

PVA = FV x IFPVA = $1,000 x 2.577 (table value read to three decimal

places) PVA = $2,577 ($2,577.10 if five decimal places used)

0.990 0.981 0.971 0.962 0.952 0.943 0.935 0.926 0.917

1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759

A B C D FA B C D F

Present Value Present Value Interest EarnedInterest Earned Total AmountTotal Amount Value at Value at at Beginningat Beginning (Column B x(Column B x InvestedInvested End of End of

Year Year of Yearof Year Interest Rate)Interest Rate) (B + C)(B + C) YearYear

1 2,577.10 206.17 2,783.27 1,783.27

Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%

$2,783.27 – $1,000.00Note: Column E was

omitted because of limited space.

A B C D FA B C D F

1 2,577.10 206.17 2,783.27 1,783.27

2 1,783.27 142.66 1,925.93 925.93

$1,925.93 – $1,000.00

Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%

A B C D FA B C D F

1 2,577.10 206.17 2,783.27 1,783.27

2 1,783.27 142.66 1,925.93 925.93

3 925.93 74.07 1,000.00 0.00

Exhibit 4Exhibit 4Exhibit 4Exhibit 4 Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%

A wealthy uncle has offered to give you either of two assets: (a) an asset that pays $500 at the end of three years or (b) an asset that pays $100 at the end of each year for five years. Assume that both assets earn a 7% annual rate of return. Which asset should you choose?

a. $500 x 0.81630 (from Table 3) = $408.15

7%, 3 years

b. $100 x 4.10020 (from Table 4) = $410.02

7%, 5 years

The annuity (b) has a slightly higher present value. The alternatives are approximately the same, however. (Note: One consideration may be expected investment opportunities at the end of three years. Since there is little difference between a. and b., a. may be the better choice since the $500 could be reinvested sooner than in b.)

66Determine investment values and interest expense or revenue for various periods.

Loan Payments and AmortizationLoan Payments and Amortization

You negotiate with a dealer to purchase a

car for $5,000, which you arrange to

borrow at the bank.

You negotiate with a dealer to purchase a

car for $5,000, which you arrange to

borrow at the bank.

The bank charges 12% interest on the loan, which is to be repaid in two years in equal monthly payments.

How much will your payments be each month?

We are looking for the present value of multiple payments (an annuity),

therefore, Table 4 can be used to solve this problem.

We are looking for the present value of multiple payments (an annuity),

therefore, Table 4 can be used to solve this problem.

0.990 10 0.98039 0.97087 0.96154 0.95238

1.97040 1.94156 1.91347 1.88609 1.85941

2.94099 2.88388 2.82861 2.77509 2.72325

0.01 0.02 0.03 0.04 0.05 Period

24 21.24339 18.91393 16.93554 15.24696 13.79864

0.99010

1.97040

2.94099

0.01 0.01

0.99010

1.97040

2.94099

If the annual interest rate is 12 percent, then interest is 1 percent per month.

Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization

21.24339

24 21.24339 18.91393 16.93554 15.24696 13.7986421.24339

0.990 10 0.98039 0.97087 0.96154 0.95238

1.97040 1.94156 1.91347 1.88609 1.85941

2.94099 2.88388 2.82861 2.77509 2.72325

0.01 0.02 0.03 0.04 0.05 Period

0.99010

1.97040

2.94099

0.01 0.01

0.99010

1.97040

2.94099

24 21.24339 18.91393 16.93554 15.24696 13.79864

There are 24 monthly periods in two years.

21.24339

Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization PVA = A x IF (Table 4)

$5,000 = A x 21.24339A = $5,000 ÷ 21.24339A = $235.37

24 21.24339 18.91393 16.93554 15.24696 13.7986421.24339

0.990 10 0.98039 0.97087 0.96154 0.95238

1.97040 1.94156 1.91347 1.88609 1.85941

2.94099 2.88388 2.82861 2.77509 2.72325

0.01 0.02 0.03 0.04 0.05 Period

0.99010

1.97040

2.94099

0.01 0.01

0.99010

1.97040

2.94099

24 21.24339 18.91393 16.93554 15.24696 13.7986421.24339

Thus, the answer to the question

(How much would you pay each month?) is

$235.37.

Thus, the answer to the question

(How much would you pay each month?) is

$235.37.

Enter =PMT(.01,24,5000) in the cell and press Enter.Enter =PMT(.01,24,5000) in the cell and press Enter.

How would you determine the monthly car payment

by using the payment function in Excel?

How would you determine the monthly car payment

by using the payment function in Excel?

How much interest will you pay over the two years?

To answer this question, let’s walk through Exhibit 5 (p. 296)

from the textbook.

To answer this question, let’s walk through Exhibit 5 (p. 296)

from the textbook.

A B C D FA B C D F

Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of

MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth

1 5,000.00 50.00 235.37 4,814.63

Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month

$5,000.00 – ($235.37 – $50.00)

Note: Column E was omitted

because of limited space.

1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.41

$4,814.63 – ($235.37 – $48.15)

A B C D FA B C D F

TotalTotal 648.81648.81 5,648.815,648.81

1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32

23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00

A B C D FA B C D F

TotalTotal 648.81648.81 5,648.815,648.81

1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32

23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00

A B C D EA B C D E

The total interest incurred over the life of the loan is $648.81.

Now let’s determine the

transactions that the bank and the

borrower would record each month.

Now let’s determine the

transactions that the bank and the

borrower would record each month.

The first transaction on April 1 records the amount of the

loan. The second transaction, dated April 30, records the

amount received from you, the customer, and the amount

earned for the first month, $50 ($5,000 x .12 x 1/12).

The first transaction on April 1 records the amount of the

loan. The second transaction, dated April 30, records the

amount received from you, the customer, and the amount

earned for the first month, $50 ($5,000 x .12 x 1/12).

JournalJournal Date Accounts Debits Credits

Apr. 1 Notes Receivable 5,000.00 2007 Cash 5,000.00Apr. 30 Cash 235.37 2007 Notes Receivable 185.37

Interest Revenue 50.00

Click this button or type “88” and press “Enter” to review the amortization table.

Bank’s BooksBank’s BooksBank’s BooksBank’s Books

Effect on Accounting EquationEffect on Accounting Equation

A = L +

4/1 Notes Receivable +5,000.00Cash –5,000.00

4/30 Cash 235.37Notes Receivable –185.37Interest Revenue +50.00

OE CC + RE

Customer’s BooksCustomer’s BooksCustomer’s BooksCustomer’s Books

Apr. 1 Cash 5,000.00 2007 Notes Payable 5,000.00Apr. 30 Notes Payable 185.37 2007 Interest Expense 50.00

Cash 235.37

Click this button or type “89” and press “Enter” to review the amortization table.

Customer’s BooksCustomer’s BooksCustomer’s BooksCustomer’s Books

A = L +

4/1 Cash +5,000.00Notes Payable +5,000.00

4/30 Notes Payable –185.37Interest Expense –50.00

Cash –235.37

OE CC + RE

In the last month of the loan (March 2009), the

bank records would reflect that the note has been fully paid by the

customer.

In the last month of the loan (March 2009), the

bank records would reflect that the note has been fully paid by the

customer.

Mar. 31 Cash 235.30 2009 Notes Receivable 232.97

Interest Revenue 2.33

Bank’s BooksBank’s BooksBank’s BooksBank’s BooksClick this button or type “90” and press “Enter” to review the amortization table.

A = L +

3/31 Cash +235.30Notes Receivable –232.97Interest Revenue +2.33

OE CC + RE

Unequal PaymentsUnequal PaymentsUnequal PaymentsUnequal Payments

Jill Johnson invested a portion of her salary at the beginning of each year for four years.

The amounts she invested in those years were $700, $800, $900, and

$1,000, respectively.

The amounts she invested in those years were $700, $800, $900, and

$1,000, respectively.

How much would her investments be worth at the end of four years if

she earned 6% per year?

How much would her investments be worth at the end of four years if

she earned 6% per year?

$ 833.71

$800 898.88

$900 954.00

$1,000 1,000.00

$700 Four Yearsx 1.19102 (6%, 3 periods)x 1.19102 (6%, 3 periods)

Three Yearsx 1.12360 (6%, 2 periods)x 1.12360 (6%, 2 periods)

Two Yearsx 1.0600 (6%, 1 period)x 1.0600 (6%, 1 period)

x 1.0000x 1.0000

Total $3,686.59

End of

You can purchase an investment that is expected to pay $200, $300,

and $400 at the end of the next three years. You expect to earn 7%

interest. How much should you pay for the investment?

You can purchase an investment that is expected to pay $200, $300,

and $400 at the end of the next three years. You expect to earn 7%

interest. How much should you pay for the investment?

$200$186.92 One Yearx 0.93458x 0.93458

Two Years262.03 $300x 0.87344x 0.87344

$400326.52 Three Yearsx 0.81630x 0.81630

$775.47 Total

PV at Beginning

of YearAmounts Received at End of Each Year

Future and Present Value Concepts

THE ENDTHE END

CCHAPTERHAPTER 8 8

1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32

23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00

A B C D EA B C D E

Click this button or type 73 and press “Enter” to return to Slide 73.

1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32

23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00

A B C D EA B C D E

1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32

23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00

A B C D EA B C D E

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