Module 8: Current and long-term liabilities

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Overview

In previous modules, you learned how to account for assets. Assets are what a business uses or sells to earn revenues. Recall that the accounting equation (A = L + E) tells us that assets are financed by liabilities and/or equity. Modules 8 and 9 will cover the topics of liabilities and equity.

Liabilities represent obligations to pay money or deliver goods or services to another party at a later date. Sometimes the amount of a liability is known with certainty (such as a bank loan); other times, the amount must be estimated (for example, the cost of providing a five-year warranty on a new car).

Test your knowledge

Begin your work on this module with a set of test-your-knowledge questions designed to help your gauge the depth of study required.

Learning objectives

8.1 Define liabilities, explain the difference between current and long-term liabilities, and describe the uncertainties related to some liabilities. (Level 1)

8.2 Identify and describe known (determinable) liabilities. (Level 2)

8.3 Record and report short-term notes payable. (Level 1)

8.4 Record and report estimated liabilities such as warranties and income taxes, and report contingent liabilities. (Level 2)

8.5 Describe the various characteristics of different bonds. (Level 2) 8.6 Record the issue of bonds at par. (Level 1)

8.7 Describe the time value of money. (Level 2)

8.8 Calculate the price of bonds issued at either a discount or a premium, and describe their effects on the issuer's financial statements. (Level 1)

8.9 Record the retirement of bonds. (Level 2)

Assignment reminder: Assignment 3 (see Module 9) is due at the end of week 9

(see Course Schedule). You may wish to take a look at it now in order to

familiarize yourself with the requirements and to prepare for any necessary work in advance.

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8.1 Liabilities

Learning objective

● Define liabilities, explain the difference between current and long-term liabilities, and describe the uncertainties related to some liabilities. (Level 1)

Required reading

● Chapter 13, pages 652-656

LEVEL 1

CICA Handbook, paragraphs 1000.32-33, defines liabilities as follows:

Liabilities are obligations of an entity arising from past transactions or events, the settlement of which may result in the transfer or use of assets, provision of services or other yielding of economic benefits in the future.

Liabilities have three essential characteristics:

a. They embody a duty or responsibility to others that entails settlement by future transfer or use of assets, provision of services or other yielding of economic benefits, at a specified or determinable date, on occurrence of a specified event, or on

demand.

b. The duty or responsibility obligates the entity leaving it little or no discretion to avoid it.

c. The transaction or event obligating the entity has already occurred.

At a very basic level, liabilities represent obligations to deliver money, goods, or services to another party at a later date. However, as you progress through more advanced accounting courses, you will find that in many cases, whether a specific situation gives rise to a liability, as opposed to equity, for example, is not clear cut. For this reason, it is advisable to

routinely apply the criteria listed in paragraph 1000.33 to the situation to verify that the item is in fact a liability. See Example 8-1 for an illustration.

The example may seem trivial. Everyone knows that a bank loan is a liability. However, as you progress through your program of studies, you will be faced with many instances in which the answers are not obvious. Often, it is only through rigorously applying the criteria to the situation that you can determine the correct classification of the item.

Current and long-term liabilities

Current liabilities are debts or other obligations that are due within one year of the

balance sheet date or within the company’s operating cycle, whichever is longer. In other words, current liabilities are expected to be discharged by using current assets or creating other current liabilities. Examples of current liabilities include accounts payable, short-term

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8.1 Liabilities

notes payable, wages payable, dividends payable, product warranty liabilities for repairs expected to be performed within 12 months of the balance sheet date, payroll taxes and other taxes payable, and unearned revenues.

Long-term liabilities are obligations that are not expected to be paid within one year or a

longer operating cycle. In other words, these obligations do not require the use of a current asset or the creation of a current liability to satisfy the debt. Examples of long-term

liabilities include leases, long-term notes payable, product warranty liabilities for repairs expected to be performed more than one year after the balance sheet date, and bonds payable.

Long-term liabilities requiring partial repayment in the year immediately following the

balance sheet date must be separated on the balance sheet into their current and long-term components. Exhibit 13.3 on page 655 demonstrates the process; Exhibit 13.5 on page 656 illustrates the balance sheet presentation of the current and long-term segments.

Textbook activities

● Checkpoint Questions 1, 2, and 3 on page 656 (Solutions on page 671) ● Quick Study 13-1 and 13-2 on page 678 (Solutions)

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8.2 Known (determinable) liabilities

● Identify and describe known (determinable) liabilities. (Level 2)

Textbook erratum:

The Goods and Services Tax was reduced from 6% to 5% effective January 1, 2008. The Harmonized Sales Tax was reduced from 14% to 13% effective the same date. You should use these current rates in assignments and other questions.

LEVEL 2

Known liabilities are those where the payee, the timing, and the amount are determinable. Examples are trade accounts payable, payroll liabilities, sales taxes payable, unearned revenues, and notes payable. The nature of these liabilities and the accounting are detailed on pages 656-661.

Textbook activities

● Checkpoint Question 4 on page 661 (Solution on page 671) ● Quick Study 13-3 to 13-7 on pages 678-679 (Solutions)

● Mid-Chapter Demonstration Problem on pages 662-663

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8.3 Short-term notes payable

● Record and report short-term notes payable. (Level 1)

LEVEL 1

Short-term notes payable are current liabilities supported by a written promissory note.

There are two types of short-term notes payable — trade notes and short-term promissory notes. Accounting for short-term notes payable is described on pages 663-665.

Trade notes

Trade notes are obligations due to suppliers for goods and services used in business

operations. For example, on November 23, Weston Holdings secures a payment extension with TechNology Inc. on an account payable, which will be paid by a 60-day, 12%, $6,000 note payable. The following journal entry would be made by Weston Holdings:

Suppose a different payment schedule is negotiated, whereby TechNology Inc. agrees to receive $1,000 cash and a 60-day, 12%, $5,000 note payable to replace the account payable. This entry is shown near the bottom of page 663.

LEVEL 2

Accrued interest expense

An expense that has been incurred during an accounting period but has not been paid or recorded must be accrued at the end of the period. In the previous example, if Weston’s year end is December 31, interest for 38 days must be accrued on December 31

(November 23 to 30 = 7 days, plus 31 days in December). The December 31 entry on page 664 shows the interest expense of $62.47 ($5,000 × 12% × 38/365).

On January 22, the payment date, an additional 22 days of interest expense, $36.16 ($5,000 × 12% × 22/365), must be recorded as shown in the entry at the bottom of

page 664. Exhibit 13.10 on page 665 clarifies the matching of the interest expense over two accounting periods, 2011 and 2012.

LEVEL 1

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8.3 Short-term notes payable

Short-term promissory notes

Short-term promissory notes are given in exchange for the loan of cash from a bank or

other financial institutions. Page 665 shows the journal entry on September 30 to record a loan note that has a face value equal to the amount borrowed, sometimes referred to as an interest-bearing note. The entry includes a debit to Cash and a credit to Notes payable.

A discounted bank loan or noninterest-bearing note, however, is one from which interest is deducted at the time of borrowing. This type of note will be covered in FA2. Note that Appendix 13A is not required reading.

Textbook activities

● Checkpoint Questions 5 and 6 on page 665 (Solutions page 671) ● Quick Study 13-8 and 13-9 on page 679 (Solutions)

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8.4 Estimated and contingent liabilities

● Record and report estimated liabilities such as warranties and income taxes, and report contingent liabilities. (Level 2)

On page 670, the second last sentence requires clarification:

"For example, a plaintiff in a lawsuit should not disclose any expected gain until the courts settle the matter."

Contingent gains like this can be disclosed if the settlement is likely.

LEVEL 2

Estimated liabilities

In most cases, the amount of liabilities can be easily determined from invoices and contracts, although to whom and when the liability is due may be uncertain. Obligations may exist, however, in which the amount to be paid is uncertain. These liabilities are called

estimated liabilities. Estimated liabilities include product warranty liabilities and income

taxes payable, which are explained on pages 665-668.

Contingent liabilities

Contingencies are uncertainties as to possible gains or losses that will be resolved in the

future, when one or more events occur or fail to occur. Examples of these events include lawsuits, notes receivable discounted with recourse, and guaranteeing another company’s debt.

It is important to distinguish between contingent liabilities and estimated liabilities. A

contingent liability may never materialize because it is contingent on the outcome of

future events. In contrast, estimated liabilities are actual liabilities that will definitely occur, although the exact amount is not known with certainty.

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8.4 Estimated and contingent liabilities

Contingent liabilities may need to be recorded under some circumstances. The

full-disclosure principle requires financial statements and their accompanying footnotes to

contain all relevant information about the operations and financial position of the entity. Therefore, an indication of any contingent liability that would have a material effect is required, and it is typically disclosed by footnotes. Exhibit 13.11 on page 670 clearly

summarizes these disclosure requirements. Note that the illustration includes three primary categories of contingent liabilities compared to two noted on page 669. The addition is the category of contingent liabilities that is likely to become payable but the amount cannot

reasonably be estimated. Disclosure for this type of possibility is required in the notes to the

financial statements.

Textbook activities

● Checkpoint Questions 7 and 8 on page 667, question 9 on page 668, and questions

10 and 11 on page 670 (Solutions on page 671)

● Quick Study 13-10 to 13-15 on pages 679-680 (Solutions)

● Demonstration Problem on pages 672-674

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8.5 Bonds payable and other long-term liabilities

● Describe the various characteristics of different bonds. (Level 2)

● Chapter 17, pages 834-840 and 860 (Level 2)

● Chapter 17, pages 861-865, "Installment Notes, Mortgage Notes, and Lease Liabilities" (Level 3)

LEVEL 2

Bonds payable

Bonds payable are one manner in which large corporations and governments borrow

money for longer periods of time.1_{The minimum amount of a bond issue is normally $100}

million. The issue is then apportioned and sold in smaller quantities to many different lenders (investors). As such, the issuer of the bond (such as General Motors) is borrowing directly from the investing public. This contrasts sharply with a note payable, which is borrowed from one creditor, such as a bank.

The bond is a form of note. This note is a legal contract to pay monies in the future that sets out the terms (the bond indenture) of the loan. The indenture typically includes the principal amount to be repaid and the date of payment, the interest rate and the frequency of payment, the security pledged (if any), undertakings of the issuer (known as restrictive covenants), and any other unique features.

The text (pages 835-840) provides a comprehensive coverage on bonds, including the advantages and disadvantages of borrowing in this manner, the types of bonds that are commonly sold, how bonds are sold (issued), and some pricing terminology. Note that the convention for quoting bond prices is as a percentage of face value, but that the percent sign is typically omitted. Thus, if you buy a $1,000 bond at 98, this means that you pay $980 or 98% of the par value of the bond.

Bonds are one form of long-term indebtedness. There are many others including some bank loans, interest-bearing long-term notes (see text page 860), and leases.

LEVEL 3

Other long-term liabilities

The text details various other forms of long-term liabilities, including instalment notes, mortgage notes, and lease liabilities on pages 861-865.

Textbook activities

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8.5 Bonds payable and other long-term liabilities

● Checkpoint Questions 1, 2, and 3 on page 840 (Solutions on page 866) ● Quick Study 17-1, 17-2, and 17-3 on page 874 (Solutions)

1 _{While there is no legal limitation on the minimum time to maturity of a bond, there are}

practical ones. Issuing bonds is an expensive process. As such, companies are loath to sell bonds for a short period of time, preferring instead to set a maturity date for

periods such as 5, 10, or 15 years hence.

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8.6 Issuing bonds at par

● Record the issue of bonds at par. (Level 1)

LEVEL 1

At the time that bonds are authorized, a memorandum is entered in the Bonds payable account. The interest payment dates are calculated from the date printed on the bonds, not from the date the bonds are actually sold, because they may be sold at a later date. A bond dated October 1, for example, may not be sold until December 1 due to unfavourable

market conditions or delays in obtaining the necessary regulatory approvals.

Selling bonds at par on a stated date

Study the journal entries in the example on pages 840 and 841. On January 1, the date the Barnes Corp. bonds are issued, the cash received and the bonds payable are recorded at par. Bond interest expense and cash paid are recorded on each interest payment date as illustrated for the first interest payment date on June 30, 2011. At

maturity, January 1, 2031, the par value of the bonds is paid. If an enterprise closes its books between interest payment dates, an adjusting entry will be required to recognize any accrued interest expense.

Selling bonds between interest dates

When the bond is sold at a later date than that printed on the bond, the purchaser is required to pay any interest that has accrued on the bonds up to the date of sale. The nature of accounting for bonds issued between issue dates is detailed on pages 841-842.

Textbook activities

● Checkpoint Question 4 on page 842 (Solution on page 866) ● Quick Study 17-4 and 17-5 on page 875 (Solutions)

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8.7 Time value of money

● Describe the time value of money. (Level 2)

On page 869, the second table incorrectly has the same heading as the first table and reads: Table 17A.1: Present Value of 1 Due in n Periods.

It should read: Table 17A.2: Present Value of an Annuity of 1 per n Periods.

● Chapter 17, pages 842-844 ● Appendix 17A, page 869

● Reading 8-1: Present and future values

Note:

In this module, the solutions to numerical computations are demonstrated using the most common format of data entry for financial calculators. The method of input may differ slightly across brands and models of calculators. Always refer to your owner’s manual for specific instructions.

This module introduces the following abbreviations: ● PV — present value

● FV — future value

● PMT — the amount of the annuity payment ● I — the interest rate per period

● N — the number of periods

● PV, FV, PMT, I, or N = ? — you should solve for the desired variable ● ? = a number — the displayed solution

Financial calculators generally use the cash flow sign convention. To properly use this

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convention, you must first determine if the problem is an investment or a loan. An

investment will have the initial cash flow as a negative amount because it is an amount paid for the investment. The reverse is true of a loan. So when using a financial calculator, enter a cash outflow as a negative number and a cash inflow as a positive number.

LEVEL 2

For supplementary material on present and future values, refer to Reading 8-1.

From an accounting perspective, liabilities are initially valued at the present value of the future payment stream. In practice, this is how financial instruments, such as bonds, are valued in the marketplace by investors. When a company issues (sells) a bond, the price it receives is what investors determine that the future payments, consisting of the interest payments over time and the return of principal at maturity, is worth to them, given their alternatives for investing in the financial marketplace.

Bond pricing using present value techniques is covered on pages 842-844 and is supplemented below.

Would you rather have a dollar now or a dollar next year? $1 today is worth more than $1 at a later date because the $1 today (the present value) could be invested to grow to a larger sum (the future value). This concept is known as the time value of money.

From a bond pricing perspective, we are interested in the present value (what something is worth in today’s terms) of the future value (the amount that we will actually receive at a later date) of the payment stream.

Single payments — Present value of a single amount

For a single payment, such as the maturity value of the bond, the relationship between present value (PV) and future value (FV) is expressed as:

PV = FV/(1 + i)n

where

i = interest rate

n = number of periods

Annuities — Present value of an annuity

An annuity is a series of equal amounts to be received at equal periodic intervals. For a series of payments, such as the interest payments on a bond, the relationship between the present value of the annuity (PVA) and the periodic payments (PMT) is expressed as

PVA = PMT{[1–(1/(1+ i)n_]/i}

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where

i = interest rate

n = number of periods PMT = periodic payments

Note that to value a bond, two components need to be assessed separately — the value of the lump-sum payment at the maturity of the bond and the value of the periodic interest payments.

Note:

The PV tables in Appendix 17A on page 869 as well as the formula and calculator modes refer to the number of periods and the interest rate per period. The period may or may not be a year. This is important because bonds typically pay interest semi-annually. Therefore, the number of years to maturity needs to be expressed as the number of periods to

maturity, the interest rate per year as an interest rate per period, and the interest payment as an interest payment per period.

Computing present values using the table method and the calculator

method

To demonstrate both methods, assume Tech Inc. had an 8%, $600,000 bond available for issue on October 1, 2011, due in four years. Interest at the rate of 4% is to be paid semi-annually. Calculate the issue price (the PV) assuming the market interest rate is 6%. Table method

Table 17A.1 on page 869 of the text is used when you want to calculate the present value of a single payment; Table 17A.2 is used when you want to calculate the present value of an ordinary annuity.

These are the steps to follow when using the table method:

1. There are two cash flows: the principal or lump sum of $600,000 plus the interest annuity. The PV of the principal will be calculated first. Determine the correct table to use: PV of 1, Table 17A.1 on page 869.

2. Determine the interest rate per period (6% annually/2 = 3% semi-annually). Locate this amount in the first row: 3%.

3. Determine the number of periods (4 years × 2 payments per year = 8 periods). Locate this amount in the first column: 8.

4. Find the intersect of the specified rate and number of periods and note the number: 0.7894. This is the factor for $1.

5. Multiply the factor of $1 by the value of concern. This yields the solution: $600,000 × 0.7894 = $473,640.00.

6. Second, the PV of the interest annuity is calculated by determining the correct table to use: PV of an Annuity of 1 per n Periods, Table 17A.2 on page 869.

7. Determine the interest rate per period (6% annually/2 = 3% semi-annually). Locate this amount in the first row: 3%.

8. Determine the number of periods (4 years × 2 payments per year = 8 periods).

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Locate this amount in the first column: 8.

9. Find the intersect of the specified rate and number of periods and note the number: 7.0197. This is the factor for $1.

10. Multiply the factor of $1 by the interest annuity per period ($600,000 × 4% =

$24,000 interest per semi-annual period). This yields the solution: $24,000 × 7.0197 = 168,472.80.

11. The total PV is $642,112.80, the sum of $473,640 + $168,472.80. This process is summarized as follows:

Cash flow Table Table value Amount Present value

Par value 17A.1 0.7894 $600,000 $473,640.00

Interest (annuity) 17A.2 7.0197 24,000 168,472.80

Total $642,112.80

Calculator method

Using the same information provided above, the calculations will be repeated using the calculator method. First, confirm that you are in financial mode and that you have fully cleared all the mode registers. Then enter the following data:

Future value (FV) 600000

Number of periods (N) 8

Payment amount (PMT) 24000

Interest rate (I) 3

PV = ?

? = 642,118.1531

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8.8 Issuing bonds at a discount and premium

● Calculate the price of bonds issued at either a discount or a premium, and describe their effects on the issuer’s financial statements. (Level 1)

● Chapter 17, pages 844-845 "Issuing Bonds at a Discount" and 849-850 "Issuing Bonds at a Premium" (Level 1)

● Chapter 17, pages 845-849 "Amortizing a Bond Discount" and pages 850-854 (not examinable)

LEVEL 1

Bonds sold at a discount

If the contract rate on the bond is less than the prevailing market rate, the bonds will sell at a discount, that is, for less than their face value. Accounting for bonds sold at a discount is covered on pages 844-845.

LEVEL 1

Bonds sold at a premium

When the market rate of interest is less than the contract rate stated on the bond, the cash received will exceed the face value. This excess (called bond premium) is recorded as a credit, thus increasing the carrying value of the liability. Accounting for bonds sold at a premium is explained on pages 849-850.

Textbook activities

● Checkpoint Question 5 on page 844, questions 6 and 7 on page 849, and question 10

on page 854 (Solutions on page 866)

● Quick Study 17-6 and 17-7 on page 875 (Solutions)

● Mid-Chapter Demonstration Problem, Parts 1 and 2 only, on pages 856-858.

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8.9 Retiring bonds

● Record the retirement of bonds. (Level 2)

LEVEL 2

Retiring bonds

Bonds providing for early redemption at the issuing corporation’s option are callable

bonds. If interest rates fall, the company can repurchase the bond and finance the cash

redemption by issuing new bonds at a lower interest rate. The text suggests that even if bonds are not callable, the issuing corporation can retire its bonds by purchasing them in the open market. While true, there would be no benefit to doing so if they had to finance the purchase by issuing new bonds. This aspect of bonds is beyond the scope of this course; it is dealt with in FN2.

Any remaining discount or premium account must be brought up to date and closed as part of the retirement entry as illustrated in the example on page 855.

Textbook activities

● Checkpoint Question 14 on page 856 (Solution on page 866) ● Quick Study 17-18 and 17-19 on page 878 (Solutions)

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Module summary

Module 8 summary

Current and long-term liabilities

Define liabilities, explain the difference between current and long-term

liabilities, and describe the uncertainties related to some liabilities.

● Current liabilities are due within one year of the balance sheet date or within one operating cycle, whichever is longer.

● The liquidation of current liabilities requires the use of existing assets or the creation of other current liabilities.

● Long-term liabilities do not have to be paid within one year or one operating cycle.

● In many cases, the amount of liabilities can be easily determined from invoices and contracts, although to whom and when the liability is due may be uncertain. Obligations may exist, however, in which the amount to be paid is uncertain, for example, product warranties and income taxes payable.

Identify and describe known (determinable) liabilities.

● A liability is definite when you know the answer to all three of these questions: ❍ Who will be paid?

❍ When is payment due? ❍ How much will be paid?

● Short-term notes payable are an example of a known liability.

Record and report short-term notes payable.

● Short-term notes payable are recorded at their face amount when the stated interest rates of the note are a reasonable approximation of the current market rates of interest.

● When the note is non-interest-bearing, or the stated rate of interest does not reflect the current market rate, the note is recorded at its present value.

Record and report estimated liabilities such as warranties and income

taxes, and report contingent liabilities.

When the amount to be paid is not precisely known, the obligation is called an estimated liability.

● A liability is established based on our best estimate of the amount to be actually paid. ● When more information becomes available, the liabilities are adjusted to reflect the

amount actually owing.

Describe the various characteristics of different bonds.

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Module summary

● Serial bonds are bonds that mature at different dates with the result that the entire debt is repaid gradually over a number of years.

● Registered bonds are bonds whose ownership is recorded by the issuing company. Cheques for interest payments are mailed to the registered owner.

● Bearer bonds are not registered and the holder, or bearer, of the bond is presumed to be the rightful owner.

● Coupon bonds are bonds that have interest coupons attached to the bond

certificate and do not require that ownership be recorded. When interest is due, the coupons are detached and presented by the bearer for payment.

● Debenture bonds are unsecured bonds that are supported by only the general credit standing of the issuer.

● Secured bonds are bonds backed by collateral to protect bondholders in case of default.

● Callable bonds are bonds that give the borrower the right to redeem the bond at a fixed price prior to maturity. A call provision usually requires the borrower to pay a call premium in addition to the face value of the bond as a penalty for depriving the lender of the right to earn the full interest payments.

Record the issue of bonds at par.

● When bonds are issued for an amount that equals the contract rate, the cash proceeds will equal the face amount of the bond. The Bonds payable account is credited for the par value of the bonds and the Cash account is debited for the sales proceeds.

● If the market rate for a corporation’s bonds is more than the contract rate, the bonds will sell at a discount.

❍ When sold at a discount, the Bonds payable account is credited for the par value of the bonds and the difference between the cash proceeds and the par value is debited to Discount on bonds payable. Each time interest is paid, the discount is amortized, the effect being to increase interest expense.

● If the market rate for a corporation’s bonds is less than the contract rate, the bonds will sell at a premium.

❍ When sold at a premium, the Bonds payable account is credited for the par value of the bonds and the difference between the cash proceeds and the par value is credited to Premium on bonds payable. Each time interest is paid, the discount is amortized, the effect being to decrease interest expense.

Describe the time value of money.

● A present value is the amount that you need to invest today at the market rate of interest to receive a specified sum at a future date.

● The present value of a series of payments is the sum of the present values of each payment.

● A bond embodies two financial instruments: the series of interest payments and the lump-sum payment of the face value at maturity.

● The present value of a bond is the sum of the value of the two components. They are determined by discounting the series of interest payments and the face value to be received at maturity by the market rate of interest.

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Module summary

Calculate the price of bonds issued at either a discount or a premium, and

describe their effects on the issuer’s financial statements.

● If a company issues a $1,000 bond that offers a coupon rate that is less/more than the prevailing market rate, the bond will sell for less/more than $1,000.

● Investors will pay an amount equal to the present value of the bonds so that they will earn the same return available to them on comparable investments.

● The face value of the bond less/plus the discount/premium is called the carrying value of the bond.

Record the retirement of bonds.

● Companies sometimes retire their bonds before maturity through open market purchases or exercising a call feature.

● At the time of retirement, the liability and any remaining discount or premium is removed from the books.

● The cash outflow from the purchase of the bonds is recorded and compared to the carrying value to determine any gain or loss.

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Self-test

Module 8 Self-test

Question 1

Exercise 17-17, page 881 Solution

Question 2

Exercise 13-3, pages 680-681 Solution

Question 3

Exercise 17-25, page 883 Solution

Question 4

Problem 13-3B, page 688 Solution

Question 5

Question 6

Complete the Mini Cases to develop your analytic and decision-making skills. Remember the suggested solution is just a guide; there is not a single right answer. Use your own

judgement. Refer to the Critical Thinking Model in the front cover of your textbook.

Question 7

Critical Thinking Mini Case, Chapter 13, page 691

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Self-test Solution

Question 8

Critical Thinking Mini Case, Chapter 17, page 894

Solution

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Test your knowledge

Module 8 Test your knowledge

a. Which of the following statements best describes liabilities?

1. Future obligations for future payments likely to result from future transactions 2. Present obligations for future payments that result from past transactions 3. Past obligations that arose out of past transactions that are paid already 4. Present payments for obligations that might arise from future transactions b. Which of the following statements about carrying value is true?

1. The carrying value of a bond equals its face value plus the discount. 2. The carrying value of a bond equals its face value minus the premium. 3. The carrying value of a bond equals its face value minus the discount. 4. The carrying value of a bond is not affected by the discount or premium. c. Juanita Corporation sold $500,000 of 8%, 7-year bonds at par on April 1, 2011. The

bonds were dated January 1, 2011 and pay interest semiannually. What is the interest expense for the year ended December 31, 2011?

1. $10,000 2. $20,000 3. $30,000 4. $40,000

d. On January 1, 2011, FNEDC Global Inc. issued 3-year, 7.5% bonds for $20 million, at a premium of $800,000. The bonds pay interest semiannually. On December 31, 2011, the market interest rate increased to 8%, thus making the bond coupon interest rate lower than the current market rate. Which of the following statements best describes the effect on bonds payable and the related accounts on December 31, 2011?

1. On December 31, 2011, the entire premium account will be written off and a bond discount account will be created to reflect the decrease in market value. 2. On December 31, 2011, the entire premium account will decrease in market

value.

3. There will be no change in the premium account and it will be $800,000 on December 31, 2011.

4. There will be no change in the bonds payable account on December 31, 2011. e. Beta Capital Inc. issued $80 million of 4% 10-year coupon bonds to yield 5%. The

bonds pay interest quarterly. What is the issue price of the bonds? 1. $48,673,067 2. $73,734,613 3. $73,822,612 4. $86,566,937 Solutions file:///F|/Courses/2009-10/CGALU/FA1/06course/01mod/fa10910/module08/m08tyk.htm [16/06/2009 4:32:21 PM]

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Example 8-1

Example 8-1

Assume that you borrowed $10,000 from the bank yesterday. The loan, together with interest at 6% per annum, is to be repaid in one month’s time. Is this a liability? In comparing the underlying circumstances to the characteristics, note that

1. you have an obligation to transfer assets (cash) at a determinable date (one month from now);

2. you have little discretion to avoid payment. If you choose not to pay the bank back, it has the right to pursue legal action to enforce payment of the debt; and 3. the transaction has already occurred as you borrowed the money yesterday. Because all three criteria are met, the bank loan is a liability. Note that this is an and situation — that is, all three criteria must be met for the item to be classified as a liability. In the example, if you intend to borrow the money one week from now, only two of the criteria are met — the transaction has not yet occurred, and as such, you have not yet incurred a liability.

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APPENDIX

IV

IV - 1 Appendix IV Present and Future Values

P r e s e n t a n d

F u t u r e V a l u e s

A p p e n d i x P r e v i e w

The concepts of present value are described and applied in Chapter 17. This appendix helps to supplement that discussion with added explanations, illustra-tions, computaillustra-tions, present value tables, and additional assignments. We also give attention to illustrations, definitions, and computations of future values.

P r e s e n t a n d F u t u r e V a l u e C o n c e p t s

There’s an old saying, time is money. This say-ing reflects the notion that as time passes, the assets and liabilities we hold are changing. This change is due to interest. Interest is the payment to the owner of an asset for its use by a borrower. The most common example of this type of asset is a savings account. As we keep a balance of cash in our accounts, it earns interest that is paid to us by the financial institution. An example of a liability is a car loan. As we carry the bal-ance of the loan, we accumulate interest costs on this debt. We must ultimately repay this loan with interest.

Present and future value computations are a way for us to estimate the inter-est component of holding assets or liabilities over time. The present value of an amount applies when we either lend or borrow an asset that must be repaid in full at some future date, and we want to know its worth today. The future value of an amount applies when we either lend or borrow an asset that must be repaid in full at some future date, and we want to know its worth at a future date.

The first section focuses on the present value of a single amount. Later sec-tions focus on the future value of a single amount, and then both present and future values of a series of amounts (or annuity).

Learning Objectives

LO

1 _{Describe the earning} of interest and the concepts of present and future values.

LO

2 _{Apply present value} concepts to a single amount by using interest tables.

LO

3 _{Apply future value} concepts to a single amount by using interest tables.

LO

4 _{Apply present value} concepts to an annuity by using interest tables.

LO

5 _{Apply future value} concepts to an annuity by using interest tables.

LO

1 Describe the earning of interest and the concepts of present and future values.

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Appendix IV Present and Future Values IV - 2

LO

2 _{Apply present} value concepts to a single amount by using interest tables.

Exhibit IV.1

Present Value of a Single Amount f • • Time p ↑ ↑ Today Future

Exhibit

IV.2

Present Value of a Single Amount Formula

f p

(1 i)n

1_{Interest is also called a discount, and an interest rate is also called a discount rate.} (i 0.10) f $220 • • p ? p f $220 $200 (1 i)n ₍₁_.10)1

P r e s e n t V a l u e o f a S i n g l e A m o u n t

We graphically express the present value (p) of a single future amount (f) received or paid at a future date in Exhibit IV.1.

The formula to compute the present value of this single amount is shown in Exhibit IV.2 where: p present value; ƒ future value; i rate of interest per period; and n number of periods.

To illustrate the application of this formula, let’s assume we need $220 one period from today. We want to know how much must be invested now, for one period, at an interest rate of 10% to provide for this $220.1_{For this illustration the}

p, or present value, is the unknown amount. In particular, the present and future values, along with the interest rate, are shown graphically as:

Conceptually, we know p must be less than $220. This is obvious from the answer to the question: Would we rather have $220 today or $220 at some future date? If we had $220 today, we could invest it and see it grow to something more than $220 in the future. Therefore, if we were promised $220 in the future, we would take less than $220 today. But how much less?

To answer that question we can compute an estimate of the present value of the $220 to be received one period from now using the formula in Exhibit IV.2 as:

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This means we are indifferent between $200 today or $220 at the end of one period. We can also use this formula to compute the present value for any number of periods. To illustrate this computation, we consider a payment of $242 at the end of two periods at 10% interest. The present value of this $242 to be received two periods from now is computed as:

These results tells us we are indifferent between $200 today, or $220 one period from today, or $242 two periods from today.

The number of periods (n) in the present value formula does not have to be expressed in years. Any period of time such as a day, a month, a quarter, or a year can be used. But, whatever period is used, the interest rate (i) must be com-pounded for the same period. This means if a situation expresses n in months, and i equals 12% per year, then we can assume 1% of an amount invested at the begin-ning of each month is earned in interest per month and added to the investment. In this case, interest is said to be compounded monthly.

A present value table helps us with present value computations. It gives us present values for a variety of interest rates (i) and a variety of periods (n). Each present value in a present value table assumes the future value (f) is 1. When the future value (f) is different than 1, we can simply multiply present value (p) by that future amount to give us our estimate.

The formula used to construct a table of present values of a single future amount of 1 is shown in Exhibit IV.3.

This formula is identical to that in Exhibit IV.2 except that f equals 1. Table IV.1 at the end of this appendix is a present value table for a single future amount. It is often called a present value of 1 table. A present value table involves three fac-tors2_{: p, i, and n. Knowing two of these three factors allows us to compute the}

third. To illustrate, consider the three possible cases.

Case 1 (solve for p when knowing i and n). Our example above is a case in

which we need to solve for p when knowing i and n. To illustrate how we use a present value table, let’s again look at how we estimate the present value of $220 (f) at the end of one period (n) where the interest rate (i) is 10%. To answer this we go to the present value table (Table IV.1) and look in the row for 1 period and in the column for 10% interest. Here we find a present value (p) of 0.9091 based on a future value of 1. This means, for instance, that $1 to be received 1 period from today at 10% interest is worth $0.9091 today. Since the future value is not $1, but is $220, we multiply the 0.9091 by $220 to get an answer of $200.

p f $242 $200 (1 i)n ₍₁_.10)2

Exhibit IV.3

Present Value of 1 Formula 1 p (1 i)n

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b a c k

Answers—p. IV-9

Case 2 (solve for n when knowing p and i). This is a case in which we have,

say, a $100,000 future value (f) valued at $13,000 today (p) with an interest rate of 12% (i). In this case we want to know how many periods (n) there are between the present value and the future value. A case example is when we want to retire with $100,000, but have only $13,000 earning a 12% return. How long will it be before we can retire? To answer this we go to Table IV.1 and look in the 12% interest col-umn. Here we find a column of present values (p) based on a future value of 1. To use the present value table for this solution, we must divide $13,000 (p) by $100,000 (f), which equals 0.1300. This is necessary because a present value table defines f equal to 1, and p as a fraction of 1. We look for a value nearest to 0.1300 (p), which we find in the row for 18 periods (n). This means the present value of $100,000 at the end of 18 periods at 12% interest is $13,000 or, alternatively stated, we must work 18 more years.

Case 3 (solve for i when knowing p and n). This is a case where we have, say,

a $120,000 future value (f) valued at $60,000 (p) today when there are nine peri-ods (n) between the present and future values. Here we want to know what rate of interest is being used. As an example, suppose we want to retire with $120,000, but we only have $60,000 and hope to retire in nine years. What interest rate must we earn to retire with $120,000 in nine years? To answer this we go to the present value table (Table IV.1) and look in the row for nine periods. To again use the present value table we must divide $60,000 (p) by $120,000 (f), which equals 0.5000. Recall this is necessary because a present value table defines f equal to 1, and p as a fraction of 1. We look for a value in the row for nine periods that is nearest to 0.5000 (p), which we find in the column for 8% interest (i). This means the present value of $120,000 at the end of nine periods at 8% interest is $60,000 or, in our example, we must earn 8% annual interest to retire in nine years.

1.A company is considering an investment expected to yield $70,000 after six years. If this company demands an 8% return, how much is it willing to pay for this investment?

F u t u r e V a l u e o f a S i n g l e A m o u n t

We use the formula for the present value of a single amount and modify it to obtain the formula for the future value of a single amount. To illustrate, we mul-tiply both sides of the equation in Exhibit IV.2 by (1 i)n_{. The result is shown in}

Exhibit IV.4.

Future value (f) is defined in terms of p, i, and n. We can use this formula to determine that $200 invested for 1 period at an interest rate of 10% increases to a future value of $220 as follows:

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3 _{Apply future} value concepts to a single amount by using interest tables.

Exhibit IV.4

Future Value of a Single Amount Formula

f p (1 i)n

f p (1 i)n

$200 (1 .10)1

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This formula can also be used to compute the future value of an amount for any number of periods into the future. As an example, assume $200 is invested for three periods at 10%. The future value of this $200 is $266.20 and is computed as:

It is also possible to use a future value table to compute future values (f) for many combinations of interest rates (i) and time periods (n). Each future value in a future value table assumes the present value (p) is 1. As with a present value table, if the future amount is something other than 1, we simply multiply our answer by that amount. The formula used to construct a table of future values of a single amount of 1 is shown in Exhibit IV.5.

Table IV.2 at the end of this appendix shows a table of future values of a sin-gle amount of 1. This type of table is called a future value of 1 table.

It is interesting to point out some items in Tables IV.1 and IV.2. Note in Table IV.2, for the row where n 0, that the future value is 1 for every interest rate. This is because no interest is earned when time does not pass. Also notice that Tables IV.1 and IV.2 report the same information in a different manner. In particular, one table is simply the inverse of the other.

To illustrate this inverse relation let’s say we invest $100 for a period of five years at 12% per year. How much do we expect to have after five years? We can answer this question using Table IV.2 by finding the future value (f) of 1, for five periods from now, compounded at 12%. From the table we find f 1.7623. If we start with $100, the amount it accumulates to after five years is $176.23 ($100 1.7623).

We can alternatively use Table IV.1. Here we find the present value (p) of 1, dis-counted five periods at 12%, is 0.5674. Recall the inverse relation between present value and future value.3_{This means p}_{1/f (or equivalently f 1/p). Knowing this}

we can compute the future value of $100 invested for five periods at 12% as:

A future value table involves three factors: f, i, and n. Knowing two of these three factors allows us to compute the third. To illustrate, consider the three pos-sible cases.

Case 1 (solve for f when knowing i and n). Our example above is a case in

which we need to solve for f when knowing i and n. We found that $100 invested for five periods at 12% interest accumulates to $176.24.

Case 2 (solve for n when knowing f and i). This is a case where we have, say,

$2,000 (p) and we want to know how many periods (n) it will take to accumulate f p (1 i)n $200 (1 .10)3 $266.20

Exhibit IV.5

Future Value of 1 Formula f (1 i)n

3_{Proof of this relation is left for advanced courses.}

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b a c k

Answers—p. IV-9

to $3,000 (f) at 7% (i) interest. To answer this, we go to the future value table (Table IV.2) and look in the 7% interest column. Here we find a column of future values (f) based on a present value of 1. To use a future value table, we must divide $3,000 (f) by $2,000 (p), which equals 1.500. This is necessary because a future value table defines p equal to 1, and f as a multiple of 1. We look for a value near-est to 1.50 (f), which we find in the row for six periods (n). This means $2,000 invested for six periods at 7% interest accumulates to $3,000.

Case 3 (solve for i when knowing f and n). This is a case where we have, say,

$2,001 (p) and in nine years (n) we want to have $4,000 (f). What rate of interest must we earn to accomplish this? To answer this, we go to Table IV.2 and search in the row for nine periods. To use a future value table, we must divide $4,000 (f) by $2,001 (p), which equals 1.9990. Recall this is necessary because a future value table defines p equal to 1, and f as a multiple of 1. We look for a value nearest to 1.9990 (f), which we find in the column for 8% interest (i). This means $2,001 invested for nine periods at 8% interest accumulates to $4,000.

2.Assume you are a winner in a $150,000 cash sweepstakes. You decide to deposit this cash in an account earning 8% annual interest and you plan to quit your job when the account equals $555,000. How many years will it be before you can quit working?

P r e s e n t V a l u e o f a n A n n u i t y

An annuity is a series of equal payments occurring at equal intervals. One exam-ple is a series of three annual payments of $100 each. The present value of an ordi-nary annuity is defined as the present value of equal payments at equal intervals as of one period before the first payment. An ordinary annuity of $100 and its present value (p) is illustrated in Exhibit IV.6.

One way for us to compute the present value of an ordinary annuity is to find the present value of each payment using our present value formula from Exhibit IV.3. We then would add up each of the three present values. To illustrate, let’s look at three, $100 payments at the end of each of the next three periods with an interest rate of 15%. Our present value computations are:

This computation also is identical to computing the present value of each payment (from Table IV.1) and taking their sum or, alternatively, adding the val-ues from Table IV.1 for each of the three payments and multiplying their sum by the $100 annuity payment.

LO

4 Apply present value concepts to an annuity by using interest tables.

Exhibit IV.6

Present Value of an Ordinary Annuity $100 $100 $100 • • • • Time p ↑ ↑ ↑ ↑

Today Future (n 1) Future (n 2) Future (n 3)

p $100 $100 $100 $228.32 (1 _.15)1 ₍₁_.15)2 ₍₁_.15)3

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4_{The formula for the present value of an annuity of 1 is: p}

1 i

1 ₍₁_i)n

From Table IV.1 From Table IV.3

i 15%, n 1... 0.8696 i 15%, n 2... 0.7561 i 15%, n 3... 0.6575 Total ... 2.2832 i 15%, n 3 ... 2.2832

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5 _{Apply future} value concepts to an annuity by using interest tables.

Exhibit IV.7

Future Value of an Ordinary Annuity $100 $100 $100 • • • • Time f ↑ ↑ ↑ ↑

Today Future (n 1) Future (n 2) Future (n 3)

f $100 (1 .15)2_{$100 (1 .15)}1_{$100 (1 .15)}0_$347.25

b a c k

Answers—p. IV-9

A more direct way is to use a present value of annuity table. Table IV.3 at the end of this appendix is one such table. If we look at Table IV.3 where n 3 and i 15%, we see the present value is 2.2832. This means the present value of an annuity of 1 for 3 periods, with a 15% interest rate, is 2.2832.

A present value of annuity formula is used to construct Table IV.3. It can also be constructed by adding the amounts in a present value of 1 table.4_{To illustrate,}

we use Tables IV.1 and IV.3 to confirm this relation for the prior example.

We can also use business calculators or spreadsheet computer programs to find the present value of an annuity.

3.A company is considering an investment paying $10,000 every six months for three years. The first payment would be received in six months. If this company requires an annual return of 8%, what is the maximum amount they are willing to invest?

F u t u r e V a l u e o f a n A n n u i t y

We can also compute the future value of an annuity. The future value of an ordi-nary annuity is the accumulated value of each annuity payment with interest as of the date of the final payment. To illustrate, let’s consider the earlier annuity of three annual payments of $100. Exhibit IV.7 shows the point in time for the future value (f). The first payment is made two periods prior to the point where future value is determined, and the final payment occurs on the future value date.

One way to compute the future value of an annuity is to use the formula to find the future value of each payment and add them together. If we assume an interest rate of 15%, our calculation is:

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From Table IV.2 From Table IV.4

i 15%, n 0... 1.0000 i 15%, n 1... 1.1500 i 15%, n 2... 1.3225

Total ... 3.4725 i 15%, n 3 ... 3.4725

5_{The formula for the future value of an annuity of 1 is: f}(1 i)n 1

i

b a c k

Answers—p. IV-9

This is identical to using Table IV.2 and finding the sum of the future values of each payment, or adding the future values of the three payments of 1 and mul-tiplying the sum by $100.

A more direct way is to use a table showing future values of annuities. Such a table is called a future value of an annuity of 1 table. Table IV.4 at the end of this appendix is one such table. We should note in Table IV.4 that when n 1, the future values are equal to 1 (f 1) for all rates of interest. That is because the annuity consists of only one payment and the future value is determined on the date of that payment — no time passes between the payment and its future value. A formula is used to construct Table IV.4.5_{We can also construct it by adding}

the amounts from a future value of 1 table. To illustrate, we use Tables IV.2 and IV.4 to confirm this relation for the prior example:

Note the future value in Table IV.2 is 1.0000 when n 0, but the future value in Table IV.4 is 1.0000 when n 1. Is this a contradiction? No. When n 0 in Table IV.2, the future value is determined on the date where a single payment occurs. This means no interest is earned, since no time has passed, and the future value equals the payment. Table IV.4 describes annuities with equal payments occurring at the end of each period. When n 1, the annuity has one payment, and its future value equals 1 on the date of its final and only payment. Again, no time passes from the payment and its future value date.

4.A company invests $45,000 per year for five years at 12% annual interest. Compute the value of this annuity investment at the end of five years.

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Q u i c k S t u d y

S u m m a r y o f A p p e n d i x I V

G U I D A N C E A N S W E R S T O

1.$70,000 0.6302 $44,114 (using Table IV.1,

i 8%, n 6).

2.$555,000/$150,000 3.7000; Table IV.2 shows this value is not achieved until after 17 years at 8% interest.

3. $10,000 5.2421 $52,421 (using Table IV.3,

i 4%, n 6).

4. $45,000 6.3528 $285,876 (using Table IV.4,

i 12%, n 5).

LO

1 Describe the earning of interest and the

concepts of present and future values. Interest is

payment to the owner of an asset for its use by a borrower. Present and future value computations are a way for us to estimate the interest component of holding assets or liabilities over a period of time.

LO

2 Apply present value concepts to a single

amount by using interest tables. The present

value of a single amount to be received at a future date is the amount that can be invested now at the specified interest rate to yield that future value.

LO

3 Apply future value concepts to a single amount

by using interest tables. The future value of a

single amount invested at a specified rate of interest is the amount that would accumulate by a future date.

LO

4 Apply present value concepts to an annuity by

using interest tables. The present value of an

annuity is the amount that can be invested now at the specified interest rate to yield that series of equal periodic payments.

LO

5 Apply future value concepts to an annuity by

using interest tables. The future value of an

annuity to be invested at a specific rate of interest is the amount that would accumulate by the date of the final equal periodic payment.

b a c k

QS IV-1 Identifying interest rates in tables

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1 QS IV-2 Present value of an amount

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2 QS IV-3 Future value of an amount

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3 QS IV-4 Present value of an annuity

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4

You are asked to make future value estimates using the future value of 1 table (Table IV.2). Which interest rate column do you use when working with the following rates?

a. 8% compounded quarterly

b. 12% compounded annually

c. 6% compounded semiannually

d. 12% compounded monthly

Flaherty is considering an investment that, if paid for immediately, is expected to return $140,000 five years hence. If Flaherty demands a 9% return, how much is she willing to pay for this investment?

CII, Inc., invested $630,000 in a project expected to earn a 12% annual rate of return. The earnings will be reinvested in the project each year until the entire investment is liquidated 10 years hence. What will the cash proceeds be when the project is liquidated?

Beene Distributing is considering a contract that will return $150,000 annually at the end of each year for six years. If Beene demands an annual return of 7% and pays for the investment immediately, how much should it be willing to pay?

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Claire Fitch is planning to begin an individual retirement program in which she will invest $1,500 annually at the end of each year. Fitch plans to retire after making 30 annual invest-ments in a program that earns a return of 10%. What will be the value of the program on the date of the last investment?

Ken Francis has been offered the possibility of investing $2,745 for 15 years, after which he will be paid $10,000. What annual rate of interest will Francis earn? (Use Table IV.1.)

Megan Brink has been offered the possibility of investing $6,651. The investment will earn 6% per year and will return Brink $10,000 at the end of the investment. How many years must Brink wait to receive the $10,000? (Use Table IV.1.)

QS IV-5 Future value of an annuity

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5 QS IV-6 Interest rate on an investment

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2 QS IV-7 Number of periods of an investment

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2

E x e r c i s e s

For each of the following situations identify (1) it as either (a) present or future value and

(b) single amount or annuity case, (2) the table you would use in your computations (but do not solve the problem), and (3) the interest rate and time periods you would use. a. You need to accumulate $10,000 for a trip you wish to take in four years. You are able

to earn 8% compounded semiannually on your savings. You only plan on making one deposit and letting the money accumulate for four years. How would you determine the amount of the one-time deposit?

b. Assume the same facts as in (a), except you will make semiannual deposits to your sav-ings account.

c. You hope to retire after working 40 years with savings in excess of $1,000,000. You expect to save $4,000 a year for 40 years and earn an annual rate of interest of 8%. Will you be able to retire with more than $1,000,000 in 40 years?

d. A sweepstakes agency names you a grand prize winner. You can take $225,000 imme-diately or elect to receive annual installments of $30,000 for 20 years. You can earn 10% annually on investments you make. Which prize do you choose to receive?

Bill Thompson expects to invest $10,000 at 12% and, at the end of the investment, receive $96,463. How many years will elapse before Thompson receives the payment? (Use Table IV.2.)

Ed Summers expects to invest $10,000 for 25 years, after which he will receive $108,347. What rate of interest will Summers earn? (Use Table IV.2.)

Betsey Jones expects an immediate investment of $57,466 to return $10,000 annually for eight years, with the first payment to be received in one year. What rate of interest will Jones earn? (Use Table IV.3.)

Exercise IV-1

Using present and future value tables

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1 Exercise IV-2 Number of periods of an investment

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2 Exercise IV-3 Interest rate on an investment

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4

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Keith Riggins expects an investment of $82,014 to return $10,000 annually for several years. If Riggins is to earn a return of 10%, how many annual payments must he receive? (Use Table IV.3.)

Steve Algoe expects to invest $1,000 annually for 40 years and have an accumulated value of $154,762 on the date of the last investment. If this occurs, what rate of interest will Algoe earn? (Use Table IV.4.)

Katherine Beckwith expects to invest $10,000 annually that will earn 8%. How many annual investments must Beckwith make to accumulate $303,243 on the date of the last invest-ment? (Use Table IV.4.)

Sam Weber financed a new automobile by paying $6,500 cash and agreeing to make 40 monthly payments of $500 each, the first payment to be made one month after the purchase. The loan bears interest at an annual rate of 12%. What was the cost of the automobile?

Mark Welsch deposited $7,200 in a savings account that earns interest at an annual rate of 8%, compounded quarterly. The $7,200 plus earned interest must remain in the account 10 years before it can be withdrawn. How much money will be in the account at the end of the 10 years?

Kelly Malone plans to have $50 withheld from her monthly paycheque and deposited in a savings account that earns 12% annually, compounded monthly. If Malone continues with her plan for 2 1/2 years, how much will be accumulated in the account on the date of the last deposit?

Spiller Corp. plans to issue 10%, 15-year, $500,000 par value bonds payable that pay inter-est semiannually on June 30 and December 31. The bonds are dated December 31, 2001, and are to be issued on that date. If the market rate of interest for the bonds is 8% on the date of issue, what will be the cash proceeds from the bond issue?

Starr Company has decided to establish a fund that will be used 10 years hence to replace an aging productive facility. The company will make an initial contribution of $100,000 to the fund and plans to make quarterly contributions of $50,000 beginning in three months. The fund is expected to earn 12%, compounded quarterly. What will be the value of the fund 10 years hence?

McAdams Company expects to earn 10% per year on an investment that will pay $606,773 six years hence. Use Table IV.1 to compute the present value of the investment.

Exercise IV-5 Number of periods of an investment

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5 Exercise IV-7 Number of periods of an investment

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5 Exercise IV-8 Present value of an annuity

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4 Exercise IV-9 Future value of an amount

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3 Exercise IV-10 Future value of an annuity

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4 Exercise IV-11

Present value of bonds

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2, 3

Exercise IV-12

Future value of an amount plus an annuity

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3, 5

Exercise IV-13

Present value of an amount

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Appendix IV Present and Future Values IV - 12 Exercise IV-14 Future value of an amount

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3 Exercise IV-15 Present value of an amount and annuity

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2, 4 Exercise IV-16 Present value of an amount

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2 Exercise IV-17 Present value of an amount

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2 Exercise IV-18 Present values of annuities

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4 Exercise IV-19

Present value with semi-annual compounding

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1, 4

Single Future Number Interest

Case Payment of Years Rate

a. $40,000 3 4% b. 75,000 7 8% c. 52,000 9 10% d. 18.000 2 4% e. 63,000 8 6% f. 89,000 5 2%

Catten, Inc., invests $163,170 at 7% per year for nine years. Use Table IV.2 to compute the future value of the investment nine years hence.

Compute the amount that can be borrowed under each of the following circumstances: a. A promise to pay $90,000 in seven years at an interest rate of 6%.

b. An agreement made on February 1, 2002, to make three payments of $20,000 on February 1 of 2003, 2004, and 2005. The annual interest rate is 10%.

On January 1, 2002, a company agrees to pay $20,000 in three years. If the annual interest rate is 10%, determine how much cash the company can borrow with this promise.

Find the amount of money that can be borrowed with each of the following promises:

C&H Ski Club recently borrowed money and agreed to pay it back with a series of six annual payments of $5,000 each. C&H subsequently borrowed more money and agreed to pay it back with a series of four annual payments of $7,500 each. The annual interest rate for both loans is 6%.

a. Use Table IV.1 to find the present value of these two annuities. (Round amounts to the nearest dollar.)

b. Use Table IV.3 to find the present value of these two annuities.

Otto Co. borrowed cash on April 30, 2002, by promising to make four payments of $13,000 each on November 1, 2002, May 1, 2003, November 1, 2003, and May 1, 2004.

a. How much cash is Otto able to borrow if the interest rate is 8%, compounded semian-nually?

b. How much cash is Otto able to borrow if the interest rate is 12%, compounded semi-annually?

c. How much cash is Otto able to borrow if the interest rate is 16%, compounded semi-annually?