Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money...
-
Upload
meaghan-cords -
Category
Documents
-
view
214 -
download
2
Transcript of Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money...
![Page 1: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/1.jpg)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Time Value of Money
Concepts
6
![Page 2: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/2.jpg)
6-2
Time Value of Money
Interest is therent paid for the useof money over time.
That’s right! A dollartoday is more valuable
than a dollar to bereceived in one year.
![Page 3: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/3.jpg)
6-3
Learning Objectives
Explain the difference between simple and compound interest.
![Page 4: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/4.jpg)
6-4
Simple Interest
Interest amount = P × i × n
Assume you invest $1,000 at 6% simple interest for 3 years.
You would earn $180 interest.
($1,000 × .06 × 3 = $180)(or $60 each year for 3 years)
![Page 5: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/5.jpg)
6-5
Compound Interest
Compound interest includes interest not only on the initial investment but also on the
accumulated interest in previous periods.
Principal Interest
![Page 6: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/6.jpg)
6-6
Assume we will save $1,000 for three years and earn 6% interest compounded annually.
What is the balance inour account at the
end of three years?
Compound Interest
![Page 7: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/7.jpg)
6-7
Compound Interest
![Page 8: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/8.jpg)
6-8
Learning Objectives
Compute the future value of a single amount.
![Page 9: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/9.jpg)
6-9
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 will save $1,000 for three years and earn 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
![Page 10: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/10.jpg)
6-10
Writing in a more efficient way, we can say . . . .
$1,000 × 1.06 × 1.06 × 1.06 = $1,191.02
or
$1,000 × [1.06]3 = $1,191.02
Future Value of a Single Amount
![Page 11: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/11.jpg)
6-11
$1,000 × [1.06]3 = $1,191.02
We can generalize this as . . .
FV = PV (1 + i)n
FutureValue
FutureValue
Present Value
Present Value
InterestRate
InterestRate
Numberof
Compounding Periods
Numberof
Compounding Periods
Future Value of a Single Amount
![Page 12: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/12.jpg)
6-12
Find the Future Value of $1 table in
your textbook.
Future Value of a Single Amount
Find the factor for 6% and 3 periods.
![Page 13: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/13.jpg)
6-13
Find the factor for 6% and 3 periods.
Solve our problem like this. . .
FV = $1,000 × 1.19102
FV = $1,191.02
FV $1
Future Value of a Single Amount
![Page 14: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/14.jpg)
6-14
Learning Objectives
Compute the present value of a single amount.
![Page 15: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/15.jpg)
6-15
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.
Present Value of a Single Amount
![Page 16: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/16.jpg)
6-16
Remember our equation?
FV = PV (1 + i) n
We can solve for PV and get . . . .
FV
(1 + i)nPV =
Present Value of a Single Amount
![Page 17: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/17.jpg)
6-17
Find the Present Value of $1 table in
your textbook.
Hey, it looks familiar!
Present Value of a Single Amount
![Page 18: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/18.jpg)
6-18
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 todaytoday in order to
accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?
Present Value of a Single Amount
![Page 19: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/19.jpg)
6-19
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 a Single Amount
![Page 20: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/20.jpg)
6-20
Learning Objectives
Solving for either the interest rate or the number of compounding periods when present value and future value of a single amount are
known.
![Page 21: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/21.jpg)
6-21
FV = PV (1 + i)n
FutureValue
FutureValue
PresentValue
PresentValue
InterestRate
InterestRate
Numberof Compounding
Periods
Numberof Compounding
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 Values
![Page 22: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/22.jpg)
6-22
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%
Determining the Unknown Interest Rate
![Page 23: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/23.jpg)
6-23
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%
Determining the Unknown Interest Rate
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.
![Page 24: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/24.jpg)
6-24
Monetary assets and monetary liabilities are valued at the
present value of future cash flows.
Accounting Applications of Present Value Techniques—Single Cash Amount
Monetary Assets
Money and claims to receive money, the
amount which is fixed or determinable
Monetary Liabilities
Obligations to pay amounts of cash, the amount of which is
fixed or determinable
![Page 25: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/25.jpg)
6-25
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 a loan of this type to use
as the interest rate.
No Explicit Interest
![Page 26: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/26.jpg)
6-26
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
× Risk-Free Rate of InterestPresent Value
Expected Cash Flow Approach
![Page 27: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/27.jpg)
6-27
Learning Objectives
Explain the difference between an ordinary annuity and an annuity due.
![Page 28: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/28.jpg)
6-28
An annuity is a series of equal periodic payments.
Basic Annuities
![Page 29: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/29.jpg)
6-29
An annuity with payments at the end of the period is known as an ordinary annuity.
EndEnd EndEnd
Ordinary Annuity
![Page 30: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/30.jpg)
6-30
An annuity with payments at the beginning of the period is known as an annuity due.
Beginning Beginning Beginning
Annuity Due
![Page 31: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/31.jpg)
6-31
Learning Objectives
Compute the future value of both an ordinary annuity and an annuity due.
![Page 32: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/32.jpg)
6-32
Future Value of an Ordinary Annuity
To find the future value of an
ordinary annuity, multiply the
amount of a single payment or receipt by the future value
of an ordinary annuity factor.
![Page 33: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/33.jpg)
6-33
We plan to invest $2,500 at the end of each of the next 10 years. We can earn 8%, compounded
annually, on all invested funds.
What will be the fund balance at the end of 10 years?
Future Value of an Ordinary Annuity
![Page 34: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/34.jpg)
6-34
Future Value of an Annuity Due
To find the future value of an annuity
due, multiply the amount of a single payment or receipt by the future value
of an ordinary annuity factor.
![Page 35: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/35.jpg)
6-35
Compute the future value of $10,000 invested at the beginning of each of the
next four years with interest at 6% compounded annually.
Future Value of an Annuity Due
![Page 36: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/36.jpg)
6-36
Learning Objectives
Compute the present value of an ordinary annuity, an annuity due, and a deferred
annuity.
![Page 37: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/37.jpg)
6-37
You wish to withdraw $10,000 at the end of each of the next 4 years from a
bank account that pays 10% interest compounded annually.
How much do you need to invest today to meet this goal?
Present Value of an Ordinary Annuity
![Page 38: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/38.jpg)
6-38
PV1PV2PV3PV4
$10,000 $10,000 $10,000 $10,000
1 2 3 4Today
Present Value of an Ordinary Annuity
![Page 39: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/39.jpg)
6-39
If you invest $31,698.60 today you will be able to withdraw $10,000 at the end of
each of the next four years.
PV of $1 PresentAnnuity Factor Value
PV1 10,000$ 0.90909 9,090.90$ PV2 10,000 0.82645 8,264.50 PV3 10,000 0.75131 7,513.10 PV4 10,000 0.68301 6,830.10 Total 3.16986 31,698.60$
Present Value of an Ordinary Annuity
![Page 40: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/40.jpg)
6-40
PV of $1 PresentAnnuity Factor Value
PV1 10,000$ 0.90909 9,090.90$ PV2 10,000 0.82645 8,264.50 PV3 10,000 0.75131 7,513.10 PV4 10,000 0.68301 6,830.10 Total 3.16986 31,698.60$
Can you find this value in the Present Value of Ordinary Annuity of $1 table?
Present Value of an Ordinary Annuity
More Efficient Computation $10,000 × 3.16986 = $31,698.60
![Page 41: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/41.jpg)
6-41
How much must a person 65 years old invest today at 8% interest compounded annually to provide for an annuity of $20,000 at the end of each of the next 15 years?a. $153,981
b. $171,190
c. $167,324
d. $174,680
Present Value of an Ordinary Annuity
![Page 42: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/42.jpg)
6-42
How much must a person 65 years old invest today at 8% interest compounded annually to provide for an annuity of $20,000 at the end of each of the next 15 years?a. $153,981
b. $171,190
c. $167,324
d. $174,680
PV of Ordinary Annuity $1Payment $ 20,000.00PV Factor × 8.55948Amount $171,189.60
Present Value of an Ordinary Annuity
![Page 43: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/43.jpg)
6-43
Compute the present value of $10,000 received at the beginning of each of the
next four years with interest at 6% compounded annually.
Present Value of an Annuity Due
![Page 44: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/44.jpg)
6-44
In a deferred annuity, the first cash flow is expected to occur more than one
period after the date of the agreement.
Present Value of a Deferred Annuity
![Page 45: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/45.jpg)
6-45
On January 1, 2006, you are considering an investment that will pay $12,500 a year for 2 years beginning on December 31, 2008. If you require a 12% return on
your investments, how much are you willing to pay for this investment?
1/1/06 12/31/06 12/31/07 12/31/08 12/31/09 12/31/10
Present Value? $12,500 $12,500
1 2 3 4
Present Value of a Deferred Annuity
![Page 46: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/46.jpg)
6-46
On January 1, 2006, you are considering an investment that will pay $12,500 a year for 2 years beginning on December 31, 2008. If you require a 12% return on
your investments, how much are you willing to pay for this investment?
1/1/06 12/31/06 12/31/07 12/31/08 12/31/09 12/31/10
Present Value? $12,500 $12,500
1 2 3 4
Present Value of a Deferred Annuity
More Efficient Computation
1. Calculate the PV of the annuity as of the beginning of the annuity period.
2. Discount the single value amount calculated in (1) to its present value as of today.
![Page 47: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/47.jpg)
6-47
On January 1, 2006, you are considering an investment that will pay $12,500 a year for 2 years beginning on December 31, 2008. If you require a 12% return on
your investments, how much are you willing to pay for this investment?
1/1/06 12/31/06 12/31/07 12/31/08 12/31/09 12/31/10
Present Value? $12,500 $12,500
1 2 3 4
Present Value of a Deferred Annuity
![Page 48: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/48.jpg)
6-48
Learning Objectives
Solve for unknown values in annuity situations involving present value.
![Page 49: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/49.jpg)
6-49
In present value problems involving annuities, there are four variables:
Solving for Unknown Values in Present Value Situations
Present value of an ordinary annuity or Present value of an
annuity due
The amount of the annuity payment
The number of periods
The interest rate
If you know any three of these, the fourth can be determined.
![Page 50: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/50.jpg)
6-50Solving for Unknown Values in Present Value Situations
Assume that you borrow $700 from a friend and intend to repay the amount in four equal annual
installments beginning one year from today. Your friend wishes to be reimbursed for the time value of money at an 8% annual rate. What is
the required annual payment that must be made (the annuity amount) to repay the loan in four
years?
Today End ofYear 1
Present Value $700
End ofYear 2
End ofYear 3
End ofYear 4
![Page 51: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/51.jpg)
6-51Solving for Unknown Values in Present Value Situations
Assume that you borrow $700 from a friend and intend to repay the amount in four equal annual
installments beginning one year from today. Your friend wishes to be reimbursed for the time value of money at an 8% annual rate. What is
the required annual payment that must be made (the annuity amount) to repay the loan in four
years?
![Page 52: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/52.jpg)
6-52
Learning Objectives
Briefly describe how the concept of the time value of money is incorporated into the
valuation of bonds, long-term leases, and pension obligations.
![Page 53: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/53.jpg)
6-53
Because financial instruments typically specify equal periodic
payments, these applications quite often involve annuity situations.
Accounting Applications of Present Value Techniques—Annuities
Long-term Bonds
Long-term Leases
Pension Obligations
![Page 54: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/54.jpg)
6-54
Valuation of Long-term Bonds
Calculate the Present Value of the Lump-sum Maturity
Payment (Face Value)
Calculate the Present Value of the Annuity Payments
(Interest)
Cash Flow Table Table Value Amount
Present Value
Face value of the bondPV of $1
n=10; i=6% 0.5584 1,000,000$ 558,400$
Interest (annuity)
PV of Ordinary
Annuity of $1n=10; i=6% 7.3601 50,000 368,005
Price of bonds 926,405$
On January 1, 2006, Fumatsu Electric issues 10% stated rate bonds with a face value of $1 million. The bonds
mature in 5 years. The market rate of interest for similar issues was 12%.
Interest is paid semiannually beginning on June 30, 2006. What is the price of
the bonds?
![Page 55: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/55.jpg)
6-55
Valuation of Long-term Leases
Certain long-term leases require the
recording of an asset and corresponding
liability at the present value of future lease
payments.
![Page 56: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/56.jpg)
6-56
Valuation of Pension Obligations
Some pension plans create obligations during
employees’ service periods that must be paid during their retirement periods. The amounts contributed during the employment period are determined
using present value computations of the
estimate of the future amount to be paid during
retirement.
![Page 57: Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6.](https://reader031.fdocuments.us/reader031/viewer/2022013100/551a815f55034643688b5703/html5/thumbnails/57.jpg)
6-57
End of Chapter 6