Appendix C- 1. Appendix C- 2 Time Value of Money Financial Accounting, Seventh Edition Appendix C

Appendix C- 1

Appendix C- 2

Time Value of MoneyTime Value of Money

Financial Accounting, Seventh Edition

Appendix Appendix CCAppendix Appendix CC

Appendix C- 3

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 value of notes and bonds.

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

Study ObjectivesStudy ObjectivesStudy ObjectivesStudy Objectives

Appendix C- 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 C- 5

Payment for the use of money.

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

Variables involved in financing transaction:

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

2. Interest Rate (i) – An annual percentage of the principal.

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

Nature of Interest

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

Appendix C- 6

Interest computed on the principal only.

SO 1 Distinguish between simple and compound interest.SO 1 Distinguish between simple and compound interest.

Simple InterestSimple InterestSimple InterestSimple Interest

ILLUSTRATION: Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ withdraw assuming the investment earns simple interest?

Full Full YearYear

Principal $4,000.00Annual interest rate 5.00%Annual Interest $200.00

Appendix C- 7

Simple Interest – Multiple YearsSimple Interest – Multiple YearsSimple Interest – Multiple YearsSimple Interest – Multiple Years


ILLUSTRATION continued: Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ earn as interest through the end of the third year using simple interest calculations?

Multiple Multiple YearYear

Principal $4,000.00Annual interest rate 5.00%Annual Interest $200.00Duration in years 32011 interest $600.00

Appendix C- 8 SO 1 Distinguish between simple and compound interest.SO 1 Distinguish between simple and compound interest.

Compound InterestCompound InterestCompound InterestCompound Interest

ILLUSTRATION: Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ withdraw assuming the investment earns interest compounded annually? (Round to two decimal places.)

Principal $4,000.00Future value factor for 10 periods at 5% 1.62889Annual Interest $6,515.56


Compound Interest ProofCompound Interest ProofCompound Interest ProofCompound Interest Proof

EOY 1 [Principal + (Principal × 5%)] $4,200.00EOY 2 [Balance + (Balance × 5%)] $4,410.00EOY 3 [$4,410.00 + ($4,410.00 × 5%)] $4,630.50EOY 4 [$4,630.50 + ($4,630.50 × 5%)] $4,862.03EOY 5 [$4,862.03 + ($4,862.03 × 5%)] $5,105.13EOY 6 [$5,105.13 + ($5,105.13 × 5%)] $5,360.39EOY 7 [$5,360.39 + ($5,360.39 × 5%)] $5,628.41EOY 8 [$5,628.41 + ($5,628.41 × 5%)] $5,909.83EOY 9 [$5,909.83 + ($5,909.83 × 5%)] $6,205.32EOY 10 [$6,205.32 + ($6,205.32 × 5%)] $6,515.59

EOY – End of year

Appendix C- 10

Interest computed on the principal only.


Partial Year InterestPartial Year InterestPartial Year InterestPartial Year Interest

ILLUSTRATION: On April 1, 2011, Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ earn as interest in year 2011?

Partial Partial YearYear

Principal $4,000.00Annual interest rate 5.00%Annual Interest $200.009 months of 12 months 9/122011 interest $150.00

Appendix C- 11

Computes interest on

the principal and

any interest earned that has not been paid or withdrawn.

Most business situations use compound interest.

With simple interest Russ earned $600.00 through the end of the third year while he earned $630.50 in the same duration using compound interest calculations.

Compound InterestCompound InterestCompound InterestCompound Interest


Appendix C- 12 SO 2 Solve future value of a single amount.SO 2 Solve future value of a single amount.

Future Value ConceptsFuture Value ConceptsFuture Value ConceptsFuture Value Concepts

Future Value of a Single Amount

The value at a future date of a given amount invested assuming compound interest.

FV = p x (1 + i )n

Illustration C-3Formula for future value

FV = future value of a single amount p = principal (or present value) i = interest rate for one period n = number of periods



Future Value of a Single Amount

The value at a future date of a given amount invested assuming compound interest.

Exercise: Racine Company signed a lease for an office building for a period of 10 years. Under the lease agreement, a security deposit of $10,000 is made. The deposit will be returned at the expiration of the lease with interest compounded at 4% per year. What amount will Racine receive at the time the lease expires?

Appendix C- 14

Exercise: Racine’s deposit of $10,000 will earn 4% per year, compounded annually, during the 10-year lease, what amount will Racine receive at the end of the lease?

0 2 4 6 8 10 12

Present Value $10,000

What table do we use?

Future Value?

SO 2 Solve future value of a single amount.SO 2 Solve future value of a single amount.


Appendix C- 15

What factor do we use?



TABLE 1Future Value of 1

Interest: 4% 5% 6% 8%Periods 1 1.04000 1.05000 1.06000 1.08000

2 1.08160 1.10250 1.12360 1.16640 3 1.12486 1.15763 1.19102 1.25971 4 1.16986 1.21551 1.26248 1.36049 5 1.21665 1.27628 1.33823 1.46933 6 1.26532 1.34010 1.41852 1.58687 7 1.31593 1.40710 1.50363 1.71382 8 1.36857 1.47746 1.59385 1.85093 9 1.42331 1.55133 1.68948 1.99900

10 1.48024 1.62889 1.79085 2.15892 11 1.53945 1.71034 1.89830 2.33164 12 1.60103 1.79586 2.01220 2.51817



$10,000 x 1.48024 = $14,802.40Present value x Future value factor = Future amount



2 1.04040 1.08160 1.12360 1.16640 3 1.06121 1.12486 1.19102 1.25971 4 1.08243 1.16986 1.26248 1.36049 5 1.10408 1.21665 1.33823 1.46933 6 1.12616 1.26532 1.41852 1.58687 7 1.14869 1.31593 1.50363 1.71382 8 1.17166 1.36857 1.59385 1.85093 9 1.19509 1.42331 1.68948 1.99900

10 1.21899 1.48024 1.79085 2.15892 11 1.24337 1.53945 1.89830 2.33164 12 1.26824 1.60103 2.01220 2.51817


Compound Interest ProofCompound Interest ProofCompound Interest ProofCompound Interest Proof

EOY 1 [Principal + (Principal × 4%)] $10,400.00EOY 2 [Balance + (Balance × 4%)] $10,816.00EOY 3 [$10,816.00 + ($10,816.00 × 4%)] $11,248.60EOY 4 [$11,248.60 + ($11,248.60 × 4%)] $11,698.50EOY 5 [$11,698.50 + ($11,698.50 × 4%)] $12,166.50EOY 6 [$12,166.50 + ($12,166.50 × 4%)] $12,653.20EOY 7 [$12,653.20 + ($12,653.20 × 4%)] $13,159.30EOY 8 [$13,159.30 + ($13,159.30 × 4%)] $13,685.70EOY 9 [$13,685.70 + ($13,685.70 × 4%)] $14,233.10EOY 10 [$14,233.10 + ($14,233.10 × 4%)] $14,802.40

EOY – End of year (Rounded at each step)

Appendix C- 18

Exercise: Racine’s deposit of $10,000 will earn 4% per year, compounded semiannually, during the 10-year lease, what amount will Racine receive at the end of the lease?

0 2 4 6 8 10 12

Present Value $10,000


Future Value?



Appendix C- 19

What factor do we use? • 20 compounding periods

• 2% interest per period





2 1.04040 1.08160 1.12360 1.16640 9 1.19509 1.42331 1.68948 1.99900

10 1.21899 1.48024 1.79085 2.15892 11 1.24337 1.53945 1.89830 2.33164 12 1.26824 1.60103 2.01220 2.51817 18 1.42825 2.02582 2.85434 3.99602 19 1.45681 2.10685 3.02560 4.31570 20 1.48595 2.19112 3.20714 4.66096 21 1.51567 2.27877 3.39956 5.03383

Appendix C- 20






2 1.04040 1.08160 1.12360 1.16640 9 1.19509 1.42331 1.68948 1.99900

10 1.21899 1.48024 1.79085 2.15892 11 1.24337 1.53945 1.89830 2.33164 12 1.26824 1.60103 2.01220 2.51817 18 1.42825 2.02582 2.85434 3.99602 19 1.45681 2.10685 3.02560 4.31570 20 1.48595 2.19112 3.20714 4.66096 21 1.51567 2.27877 3.39956 5.03383

Appendix C- 21

(1) Periodic payments or receipts of the same amount,

(2) Same-length interval between payments or receipts,

(3) Compounding of interest each interval.

Annuity requires the following:

SO 3 Solve for future value of an annuity.SO 3 Solve for future value of an annuity.

The future value of an annuity is the sum of all the payments (receipts) plus the accumulated compoundinterest on them.


Appendix C- 22

Future Value of an Annuity

Rents occur at the end of each period.

No interest during 1st period.

0 1

Present Value

2 3 4 5 6 7 8

$20,000

20,000 20,000 20,000 20,000 20,000 20,000 20,000

Future Value



Appendix C- 23

Exercise: Chaffee Company issued $1,000,000, 10-year bonds and agreed to make annual sinking fund deposits of $75,000. The deposits are made at the end of each year into an account paying 6% annual interest. What amount will be in the sinking fund at the end of 10 years?

Present Value Payments (in thousands) Future value




0$75 75 75 75 75 75 75 75 75 75 ?0 1 2 3 4 5 6 7 8 9 10

Appendix C- 24



Future Value ConceptsFuture Value ConceptsFuture Value ConceptsFuture Value ConceptsTable 2

Value of an Annuity of 1Interest 4% 5% 6% 8%

Period 1 1.00000 1.00000 1.00000 1.00000 2 2.04000 2.05000 2.06000 2.08000 3 3.12160 3.15250 3.18360 3.24640 4 4.24646 4.31013 4.37462 4.50611 5 5.41632 5.52563 5.63709 5.86660 6 6.63298 6.80191 6.97532 7.33592 7 7.89829 8.14201 8.39384 8.92280 8 9.21423 9.54911 9.89747 10.63663 9 10.58280 11.02656 11.49132 12.48756

10 12.00611 12.57789 13.18079 14.48656 11 13.48635 14.20679 14.97164 16.64549 12 15.02581 15.91713 16.86994 18.97713

Appendix C- 25 SO 3 Solve for future value of an annuity.SO 3 Solve for future value of an annuity.



Table 2Value of an Annuity of 1

Interest 4% 5% 6% 8%Period 1 1.00000 1.00000 1.00000 1.00000

2 2.04000 2.05000 2.06000 2.08000 3 3.12160 3.15250 3.18360 3.24640 4 4.24646 4.31013 4.37462 4.50611 5 5.41632 5.52563 5.63709 5.86660 6 6.63298 6.80191 6.97532 7.33592 7 7.89829 8.14201 8.39384 8.92280 8 9.21423 9.54911 9.89747 10.63663 9 10.58280 11.02656 11.49132 12.48756

10 12.00611 12.57789 13.18079 14.48656 11 13.48635 14.20679 14.97164 16.64549 12 15.02581 15.91713 16.86994 18.97713

Appendix C- 26 SO 4 Identify the variables fundamental to solving present value SO 4 Identify the variables fundamental to solving present value

problems.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 received in the future,

2. Length of time until amount is received, and

3. Interest rate (the discount rate).

Present Value ConceptsPresent Value ConceptsPresent Value ConceptsPresent Value Concepts

Appendix C- 27

Present Value of a Single Amount

PV = FV / (1 + i )n Illustration C-9Formula for present value

PV = present value of a single

amount FV = future value of a single amount p = principal (or present value) i = interest rate for one period n = number of periods


SO 5 Solve for present value of a single amount.SO 5 Solve for present value of a single amount.

Appendix C- 28 SO 5 Solve for present value of a single amount.SO 5 Solve for present value of a single amount.

Present Value of a Single Amount

Multiply the present value factor by the future value.

Exercise: Gonzalez Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Gonzalez Company pay for this investment in order to earn a 10% return?


Appendix C- 29

Exercise: Gonzalez Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Gonzalez Company pay for this investment in order to earn a 10% return?

0 1 2 3 4 5 6

Present Value?


Future Value $500,000



Appendix C- 30




TABLE 3Present Value of 1

Interest 8% 9% 10% 11%Period 1 0.92593 0.91743 0.90909 0.90090

2 0.85734 0.84168 0.82645 0.81162 3 0.79383 0.77218 0.75132 0.73119 4 0.73503 0.70843 0.68301 0.65873 5 0.68058 0.64993 0.62092 0.59345 6 0.63017 0.59627 0.56447 0.53464 7 0.58349 0.54703 0.51316 0.48166 8 0.54027 0.50187 0.46651 0.43393 9 0.50025 0.46043 0.42410 0.39092

10 0.46319 0.42241 0.38554 0.35218 11 0.42888 0.38753 0.35049 0.31728 12 0.39711 0.35554 0.31863 0.28584



$500,000 x 0.62092 = $310,460.00Future value x Present value factor = Future amount


Interest 8% 9% 10% 11%Period 1 0.92593 0.91743 0.90909 0.90090

2 0.85734 0.84168 0.82645 0.81162 3 0.79383 0.77218 0.75132 0.73119 4 0.73503 0.70843 0.68301 0.65873 5 0.68058 0.64993 0.62092 0.59345 6 0.63017 0.59627 0.56447 0.53464 7 0.58349 0.54703 0.51316 0.48166 8 0.54027 0.50187 0.46651 0.43393 9 0.50025 0.46043 0.42410 0.39092

10 0.46319 0.42241 0.38554 0.35218

Appendix C- 32

Exercise: Gonzalez Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Gonzalez Company pay for this investment in order to earn a 10% return if interest is compounded semiannually?

0 1 2 3 4 5 6

Present Value?


Future Value $500,000



Appendix C- 33





Interest 4% 5% 6% 8%Period 1 0.96154 0.95238 0.94340 0.92593

2 0.92456 0.90703 0.89000 0.85734 3 0.88900 0.86384 0.83962 0.79383 4 0.85480 0.82270 0.79209 0.73503 5 0.82193 0.78353 0.74726 0.68058 6 0.79031 0.74622 0.70496 0.63017 7 0.75992 0.71068 0.66506 0.58349 8 0.73069 0.67684 0.62741 0.54027 9 0.70259 0.64461 0.59190 0.50025

10 0.67556 0.61391 0.55839 0.46319 11 0.64958 0.58468 0.52679 0.42888 12 0.62460 0.55684 0.49697 0.39711



$500,000 x 0.61391 = $306,955.00Future value x Present value factor = Future amount


Interest 4% 5% 6% 8%Period 1 0.96154 0.95238 0.94340 0.92593

2 0.92456 0.90703 0.89000 0.85734 3 0.88900 0.86384 0.83962 0.79383 4 0.85480 0.82270 0.79209 0.73503 5 0.82193 0.78353 0.74726 0.68058 6 0.79031 0.74622 0.70496 0.63017 7 0.75992 0.71068 0.66506 0.58349 8 0.73069 0.67684 0.62741 0.54027 9 0.70259 0.64461 0.59190 0.50025

10 0.67556 0.61391 0.55839 0.46319

Appendix C- 35

Present Value of an Annuity

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.SO 6 Solve for present value of an annuity.


Appendix C- 36

Exercise: Bosco Company is considering investing in an annuity contract that will return $30,000 annually at the end of each year for 15 years. What amount should Bosco Company pay for this investment if it earns a 6% return?

0 1

Present Value


2 3 4 14 15

$30,000 30,000 30,000 30,000 30,000

. . . . .30,000



Appendix C- 37



Present Value ConceptsPresent Value ConceptsPresent Value ConceptsPresent Value ConceptsTABLE 4

Present Value of an Annuity of 1Interest 4% 5% 6% 8%

Period: 1 0.96154 0.95238 0.94340 0.92593 2 1.88609 1.85941 1.83339 1.78326 3 2.77509 2.72325 2.67301 2.57710 7 6.00205 5.78637 5.58238 5.20637 8 6.73274 6.46321 6.20979 5.74664 9 7.43533 7.10782 6.80169 6.24689

10 8.11090 7.72173 7.36009 6.71008 14 10.56312 9.89864 9.29498 8.24424 15 11.11839 10.37966 9.71225 8.55948 16 11.65230 10.83777 10.10590 8.85137 17 12.16567 11.27407 10.47726 9.12164

Appendix C- 38

$30,000 x 9.71225 = $291,367.50Receipt x Present value factor = Present value


Present Value ConceptsPresent Value ConceptsPresent Value ConceptsPresent Value ConceptsTABLE 4


Period: 1 0.96154 0.95238 0.94340 0.92593 2 1.88609 1.85941 1.83339 1.78326 3 2.77509 2.72325 2.67301 2.57710 7 6.00205 5.78637 5.58238 5.20637 8 6.73274 6.46321 6.20979 5.74664 9 7.43533 7.10782 6.80169 6.24689

10 8.11090 7.72173 7.36009 6.71008 14 10.56312 9.89864 9.29498 8.24424 15 11.11839 10.37966 9.71225 8.55948 16 11.65230 10.83777 10.10590 8.85137 17 12.16567 11.27407 10.47726 9.12164

Appendix C- 39 SO 7 Compute the present value of notes and bonds.SO 7 Compute the present value of notes and bonds.

Two Cash Flows:

Periodic interest payments (annuity).

Principal paid at maturity (single-sum).

0 2 4 6 8 18 20

5,000 5,000 5,000$5,000

. . . . .5,000 5,000

100,000

Present Value of a Long-term Note or Bond


Appendix C- 40

Exercise: Midwest Railroad Co. is about to issue $100,000 of 10-year bonds paying a 10% interest rate, with interest payable semiannually. The discount rate for such securities is 8%. How much can Midwest expect to receive from the sale of these bonds?

0 1

Present Value

2 3 4 9 10

5,000 5,000 5,000$5,000

. . . . .5,000 105,000

SO 7 Compute the present value of notes and bonds.SO 7 Compute the present value of notes and bonds.


Appendix C- 41

$5,000 x 13.59033 = $67,951.65Interest Payment x PV factor = Present value


Present Value Concepts - InterestPresent Value Concepts - InterestPresent Value Concepts - InterestPresent Value Concepts - InterestTABLE 4


Period: 1 0.96154 0.95238 0.94340 0.92593 2 1.88609 1.85941 1.83339 1.78326 3 2.77509 2.72325 2.67301 2.57710 8 6.73274 6.46321 6.20979 5.74664 9 7.43533 7.10782 6.80169 6.24689

10 8.11090 7.72173 7.36009 6.71008 11 8.76048 8.30641 7.88687 7.13896 12 9.38507 8.86325 8.38384 7.53608 18 12.65930 11.68959 10.82760 9.37189 19 13.13394 12.08532 11.15812 9.60360 20 13.59033 12.46221 11.46992 9.81815

Appendix C- 42

$100,000 x 0.45639 = $45,639.00Principal x Present value factor = Present value


Present Value Concepts - PrincipalPresent Value Concepts - PrincipalPresent Value Concepts - PrincipalPresent Value Concepts - Principal


Interest 4% 5% 6% 8%Period 1 0.96154 0.95238 0.94340 0.92593

2 0.92456 0.90703 0.89000 0.85734 3 0.88900 0.86384 0.83962 0.79383 8 0.73069 0.67684 0.62741 0.54027 9 0.70259 0.64461 0.59190 0.50025

10 0.67556 0.61391 0.55839 0.46319 11 0.64958 0.58468 0.52679 0.42888 12 0.62460 0.55684 0.49697 0.39711 18 0.49363 0.41552 0.35034 0.25025 19 0.47464 0.39573 0.33051 0.23171 20 0.45639 0.37689 0.31180 0.21455

Appendix C- 43

Exercise: Midwest Railroad Co. is about to issue $100,000 of 10-year bonds paying a 10% interest rate, with interest payable semiannually. The discount rate for such securities is 8%. How much can Midwest expect to receive from the sale of these bonds?

Present value of principal $45,693.00

Present value of interest 67,951.65

Bond present value $113,590.65



Date Account Title Debit Credit Cash 113,590.65

Bonds Payable 100,000.00

Premium on Bonds Payable 13,590.65

Appendix C- 44 SO 8 Use a financial calculator to solve time value of money SO 8 Use a financial calculator to solve time value of money

problems.problems.

Using Financial CalculatorsUsing Financial CalculatorsUsing Financial CalculatorsUsing Financial Calculators

Illustration C-22Financial calculator keysN = number of periods

I = interest rate per period

PV = present value (occurs at the beginning of the first period)

PMT = payment (all payments are equal, and none are skipped)

FV = future value (occurs at the end of the last period.


problems.problems.


Interest Rate for an Investment

Reba McEntire wishes to invest $19,000 on July 1, 2011, and have it accumulate to $49,000 by July 1, 2021. Use a financial calculator to determine at what exact annual rate of interest Reba must invest the $19,000.

10 0 49,000?? 19,000

9.94%


problems.problems.


Present Value of an AnnuityOn June 1, 2011, Shelley Long purchases lakefront property from her neighbor, Joey Brenner, and agrees to pay the purchase price in seven payments of $16,000 each, the firstpayment to be payable June 1, 2012. (Assume that interest compounded at an annual rate of 7.35% is implicit in the payments.) What is the purchase price of the property? 0-16,0007 ??

85,186.34

7.35


problems.problems.


Useful Applications – Auto LoanBill Schroeder owes a debt of $35,000 from the purchase of his new sport utility vehicle. The debt bears annual interest of 9.1% compounded monthly. Bill wishes to pay the debt and interest in equal monthly payments over 8 years, beginning one month hence. What equal monthly payments will pay off the debt and interest?

8 × 12 9.1 ÷ 12 35,000

-514.57


problems.problems.


Useful Applications – BondsOn January 1, 2011, Cooke Corporation purchased 200 of the $1,000 face value, 8% coupon, 10-year bonds of Howe Inc. The bonds mature on January 1, 2021, and pay interest annually beginning January 1, 2012. Cooke purchased the bonds to yield 10.65%. How much did Cooke pay for the bonds?

10.65

-168,323.64

? 16,000 200,00010

Appendix C- 49

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Appendix C- 1. Appendix C- 2 Time Value of Money Financial Accounting, Seventh Edition Appendix C