Module 8: Current and long-term liabilities
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)
Module 8: Current and long-term liabilities - Content Links
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
Module 8 Test Your Knowledge solutions
a.
1. Incorrect. The obligation is a present one, incurred as a result of a past transaction.
2. Correct. There are three crucial elements to the definition of a liability. First, it arises from a
past transaction or event. Second, it constitutes a present obligation. Third, it requires a future sacrifice of assets or services for settlement of the obligation.
3. Incorrect. The obligation is a present one, requiring future settlement.
4. Incorrect. There are three crucial elements to the definition of a liability. First, it arises from a past transaction or event. Second, it constitutes a present obligation. Third, it requires a future sacrifice of assets or services for settlement of the obligation.
b.
1. Incorrect. The discount is subtracted from the par value to arrive at carrying value. 2. Incorrect. The premium is added to the par value to arrive at carrying value.
3. Correct. The Bond discount account is a contra liability account. Its balance is subtracted from
the par value of the bond, as represented by the Bonds payable account, to determine the carrying (or book) value of the bond.
4. Incorrect. The carrying value must be adjusted by either the addition of the unamortized premium or the subtraction of the unamortized discount.
c.
1. Incorrect. $10,000 (= 500,000 × 8% × 3/12) is the actual interest payment for only the 3-month coupon period ending June 30, 2011. Total interest expense for the year must also include the interest payment for the 6-month coupon period ending December 31, 2011.
2. Incorrect. $20,000 (= 500,000 × 8% × 6/12) is the actual interest payment for only the 6-month coupon period ending December 31, 2011. Total interest expense for the year must also include the interest payment for the 3-month partial coupon period ending June 30, 2011.
3. Correct. [500,000 × 8% × (3/12)] + [500,000 × 8% × (6/12)] = 10,000 + 20,000 = 30,000.
Although the bonds were dated January 1, they were not sold until April 1. The first coupon period only covers 3 months, from April 1 to June 30.
4. Incorrect. At year end 2011, the bond has only been outstanding for 9 months, from April 1 to December 31. $40,000 (= 500,000 × 8% × 12/12) represents interest expense for 12 months. d.
1. Incorrect. The relevant amount of premium or discount is determined at the date of sale (issuance date) of the bond. Subsequent changes to the market interest rate have no impact on the Bond Premium account.
2. Incorrect. On each coupon payment date for the life of the bond, the Bond premium account will decrease as the premium is amortized. The full amount in this account at December 31, 2011 will not be written off.
3. Incorrect. The Bond premium account will decrease over time as the premium is amortized at each coupon payment date, using either the straight-line or effective-interest method or amortization.
4. Correct. The Bonds payable account remains at the par value of $20 million for the full 3-year
life of the bond. The Bond premium account is a separate accretion (or adjunct liability) account which will decrease over time as the bond premium is amortized at each coupon payment date. e.
1. Incorrect. The present value is calculated on both the principal and the interest. To find the PV of the principal: FV = 80,000,000; i = 5/4 = 1.25; n = 10 × 4 = 40; Compute PV. To find the PV of the interest: PMT = 80,000,000 × 4% × (3/12) = 800,000; i = 5/4; n = 10 × 4; Compute PV. PV = $73,734,613.
2. Correct. To find the PV of the principal: FV = 80,000,000; i = 5/4 = 1.25; n = 10 × 4 = 40;
Compute PV. To find the PV of the interest: PMT = 80,000,000 × 4% × (3/12) = 800,000; i = 5/4; n = 10 × 4; Compute PV. PV = $73,734,613.
3. Incorrect. To find the PV of the principal: FV = 80,000,000; i = 5/4 = 1.25; n = 10 × 4 = 40; Compute PV. To find the PV of the interest: PMT = 80,000,000 × 4% × (3/12) = 800,000; i = 5/4; n = 10 × 4; Compute PV. PV = $73,734,613.
4. Incorrect. To find the PV of the principal: FV = 80,000,000; i = 5/4 = 1.25; n = 10 × 4 = 40; Compute PV. To find the PV of the interest: PMT = 80,000,000 × 4% × (3/12) = 800,000; i = 5/4; n = 10 × 4; Compute PV. PV = $73,734,613.
8.1 Liabilities
Learning objectiveDefine 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, define 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.
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; and 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 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)
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.
8.2 Known (determinable) liabilities
Learning objectiveIdentify and describe known (determinable) liabilities. (Level 2)
Required reading
Chapter 13, pages 656-661
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
8.3 Short-term notes payable
Learning objectiveRecord and report short-term notes payable. (Level 1)
Required reading
Chapter 13, pages 663-665
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
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)
8.4 Estimated and contingent liabilities
Learning objectiveRecord and report estimated liabilities such as warranties and income taxes, and report contingent liabilities. (Level 2)
Required reading
Chapter 13, pages 665-670
Textbook erratum:
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.
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
8.5 Bonds payable and other long-term liabilities
Learning objectiveDescribe the various characteristics of different bonds. (Level 2)
Required reading
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, notes payable due in more than one year, and leases.
LEVEL 3
Other long-term liabilities
The text details various other forms of long-term liabilities, including interest-bearing notes, instalment notes, mortgage notes, and lease liabilities on pages 860-865.
Textbook activities
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)
8.6 Issuing bonds at par
Learning objectiveRecord the issue of bonds at par. (Level 1)
Required reading
Chapter 17, pages 840-842
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
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.
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)
8.7 Time value of money
Learning objectiveDescribe the time value of money. (Level 2)
Textbook erratum:
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.
Required reading
Chapter 17, pages 842-844 Appendix 17A, page 869
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 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 (To view the content from this link go to end of document.).
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} 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.
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). 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:
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:
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
Future value (FV) 600000
Number of periods (N) 8
Payment amount (PMT) 24000
Interest rate (I) 3
PV = ?
8.8 Issuing bonds at discount and premium
Learning objectiveCalculate the price of bonds issued at either a discount or a premium, and describe their effects on the issuer’s financial statements. (Level 1)
Required reading
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.
8.9 Retiring bonds
Learning objectiveRecord the retirement of bonds. (Level 2)
Required reading
Chapter 17, pages 854-856
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)
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.
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.
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.
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.
Module 8 Self-test
Question 1
Exercise 17-17, page 881 SolutionQuestion 2
Exercise 13-3, pages 680-681Solution
Question 3
Exercise 17-25, page 883 SolutionQuestion 4
Problem 13-3B, page 688 SolutionQuestion 5
Problem 17-1B, page 889 SolutionQuestion 6
Problem 13-1B, page 687 SolutionComplete 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 judgment. Refer to the Critical Thinking Model in the front cover of your textbook.
Question 7
Critical Thinking Mini Case, Chapter 13, page 691
Solution
Question 8
Critical Thinking Mini Case, Chapter 17, page 894
Solution
Solution 1
Solution 2
Part 1(a)
a. Size of semiannual payment = $25,000 × 8% × 1/2 = $1,000 b. Number of payments = 15 years × 2 = 30
c. The 8% contract rate is greater than the 6% market rate; therefore, the bonds were issued at a premium.
d. Calculation of the market price at the issue date: Table method
*The table values are based on a discount rate of 3% (half the annual market rate) and 30 periods/payments.
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:
Cash flow Table
Table
value* Amount
Present value
Par value 17A.1 0.4120 $25,000 $10,300
Interest (annuity) 17A.2 19.6004 1,000 19,600
Total $29,900
Future value (FV) 25000
Number of periods (N) 30
Payment amount (PMT) 1000
Interest rate (I) 3
PV = ?
? = 29,900.11034
e. 2011
Sept. 1 Cash... 29,900
Premium on bonds payable.... 4,900
Bonds payable... 25,000
Sold bonds at a premium on the original issue date.
2011
Jan. 2 Land... 120,000
Part 1(b)
Part 2
Solution 3
To record issuance of 6%, 3-year note.
2011
Dec. 31 Notes payable... 37,693
Interest expense... 7,200
Cash... 44,893
To record annual payment on note payable.
Liabilities:
Current liabilities:
Current portion of long-term note $39,955
Solution 6
Solution 7
Problem:
The financial statements are not correct because of a number of recording errors and misclassification. Goal:*
To restate the financial statement amounts to ensure correct values are reported. Principles:
The matching, conservatism, realization, and full disclosure principles have been violated and need to be complied with.
December 31,
2011 2012 2013 2014
Current liabilities:
Current portion of long-term debt $53,868 $59,254 $65,180 $71,698
Interest payable 25,000 19,613 13,688 7,170
Long-term liabilities:
Facts:
As reported in the mini case.
Current assets should be $120,000 – $34,000 = $86,000.
Property, plant and equipment appear to be correctly stated at $840,000. Intangibles appear to be correctly stated at $50,000.
Current liabilities should be $72,000 + $80,000 + $5,000 + $40,000 + $196,000 = $393,000. Long-term liabilities should be $660,000 – $34,000 = $626,000 – 196,000 = $430,000. Equity should be $278,000 – $80,000 – $5,000 – $40,000 = $153,000.
Revenues should be $960,000 – $80,000 = $880,000.
Expenses should be $890,000 + $5,000 + $40,000 = $935,000.
Net income of $960,000 – $890,000 = $70,000 is really a net loss of $880,000 – $935,000 = $55,000. Total liabilities are 84% of total assets after the corrections ($393,000 + $430,000 = $823,000/
$976,000) in comparison to 72% before the corrections ($72,000 + $660,000 = $732,000/$1,010,000), which means the balance sheet was actually not as strong as it originally was reported.
The current ratio was $86,000/$393,000 = 0.219:1 after the corrections and $120,000/$72,000 = 1.667:1 before the corrections, indicating that the company is not able to meet its short-term obligations in contrast to what was originally reported.
*The goal is highly dependent on “perspective.” Conclusions/Consequences:
The facts show that the company is really in a net loss position as to the net income that was originally reported.
The balance sheet was not as strong as originally reported in terms of debit vs equity financing. The current ratio shows that the company is unable to meet its short-term obligations, which is in
significant contrast to what was originally reported.
A consequence of these errors/misclassifications is that decision makers, both internal and external, may have made very different decisions had they been given the correct information.
A concern is that the financial statements in error reported a favourable scenario relative to the corrected financial statements, which raises the question of how these errors were made and if they were in fact errors — hard questions need to be asked and answered in this regard.
Problem:
There appears to be a discrepancy between how the bond is reported on the balance sheet and the total bond interest expense disclosed in Note 7.
Goal:*
To resolve the discrepancy between how the bond is reported on the balance sheet and the total bond interest expense disclosed in Note 7.
Principles:
Financial statements must be prepared based on GAAP. Facts:
As noted in the mini case.
The actual total interest paid on the note will be $500,000 (see amortization schedule below); the total bond interest expense will be $640,472 (see amortization schedule below), which is $140,472 greater than the actual total interest paid on the note because the bond was issued at a discount. When the bond is repaid at maturity, bondholders will receive $1,000,000, which is $140,472 greater than what they actually paid. This difference represents an additional cost to 5-Star Adventures Inc.
Conclusions/Consequences:
The total bond interest expense is $140,472 greater than what is reported in Note 7 of the financial statements; this will require correction.
Because of the error in Note 7, the entries regarding the bond should be reviewed to ensure the discount has been amortized appropriately.
*The goal is highly dependent on “perspective.”
Mid-term assignment: Dista Co.
Note: This assignment integrates concepts covered in Modules 1 through 7 inclusive. It is worth 15 marks.
Prepare the answers to these assignment questions in Word and save them as one document on your hard drive. See “Submit assignments and quizzes” under the How To tab for the recommended format and filename. When your file is complete and you are ready to submit it for marking, click the link to the drop box for this assignment in the navigation pane.
Question 1 (10 marks)
It is May 1, 2008, the first business day of the month, and you have just been hired as the accountant for Dista Co., which operates with monthly accounting periods. For simplicity, assume that Dista Co. sells one product. All of the company's accounting work has been completed through the end of April, 2008. The post-closing trial balance as at April 30, 2008 follows. The company’s fiscal year end is May 31.
You have determined that Dista Co. uses the moving weighted average cost flow assumption under a perpetual system to account for merchandise inventory and that the terms of all credit sales are 2/10, n/30. Merchandise sells for $50.00 per unit.
During your first month on the job, the following events occurred:
Post-closing Trial Balance
April 30, 2008
Cash 108,859.00
Accounts receivable1 12,348.00
Allowance for doubtful accounts 940.00
Merchandise inventory3 19,470.00 Office supplies 1,300.00 Store supplies 8,600.00 Prepaid insurance 6,400.00 Interest receivable5 35.00 Office equipment4 28,740.00 Accumulated amortization, office equipment 19,394.00 Store equipment4 79,500.00 Accumulated amortization, store equipment 20,566.00 Note receivable5 14,000.00 Accounts payable2 47,960.00
Rona Dista, capital 190,392.00
279,252.00 279,252.00
1 See the Accounts receivable subsidiary ledger under Sub-ledgers (To view the content from this link
you must go on-line.) for details regarding customer balances.
2 See the Accounts payable subsidiary ledger under Sub-ledgers (To view the content from this link you
must go on-line.) for details regarding creditor balances.
3 See the Merchandise inventory subsidiary ledger under Sub-ledgers (To view the content from this link
you must go on-line.) for details of inventory holdings.
4 See the Furniture and equipment subsidiary ledger under Sub-ledgers (To view the content from this
link you must go on-line.) for detailed information.
5 This is a 6% note due April 15, 2013, with payments of $270.66 receivable on the 15th of each month. Refer to the Note Receivable Amortization Schedule for details.
May 1 Issued cheque #3410 to S & R Management Co. in payment of the May rent, $3,700. Use two lines to record the rent component of the transaction. Charge 75% of the rent to Rent expense, selling space and the balance to Rent expense, office space.
2 Sold 300 units of merchandise on credit to Krista Company, invoice #8785.
2 Issued a credit memorandum to Choi Corp. for 5 units of defective merchandise sold on April 26; the returns were discarded and not restored to inventory.
3 Issued cheque #3411 to Meld Corp. regarding the April 17 purchase.
5 Purchased on credit from Avdex Supply Co.: 340 units of merchandise at $41.00 per unit; store supplies, $2,000; and office supplies, $800. Invoice dated May 5, terms 1/10, n/30.
6 Collected the amount owing from Choi Corp.
6 Avdex Supply Co. issued a memorandum regarding the return of 45 defective units of merchandise purchased on May 5.
Required
Note:
Ensure that all entries are appropriately cross-referenced. You can use the working papers provided on this link. Ignore GST and PST.
1. Transcribe the April 30, 2008 balances from the post-closing trial balance to the General Ledger. 2. Enter the May transactions listed above in the General Journal.
7 Sold 415 units to Dunvegan Inc. for cash.
9 Sold store supplies to the merchant next door at cost for cash, $6,850.
10 Purchased office furniture on credit from Avdex Supply Co., invoice dated May 10, terms n/15, $41,000. The office furniture is expected to be replaced in 6 years and then sold for about $3,000. Dista Co. will use the straight-line method calculated to the nearest whole month when amortizing this asset.
11 Received payment from Krista Company for the May 2 sale.
11 Received 600 units of merchandise and an invoice dated May 11 totalling $25,800.00, terms 1/5, n/15, from Xylo, Inc.
12 Received a $1,500 credit memorandum from Avdex Supply Co. for defective office furniture received on May 10 and returned for credit.
14 Issued cheque #3412 to NASD Products to pay for the merchandise received on April 29. 15 Collected the interest and principal regarding the Note Receivable (Hint: Refer to the
amortization schedule).
15 Issued cheque #3413, payable to Payroll, in payment of sales salaries, $2,000 and office salaries, $4,000. Cashed the cheque and paid the employees.
15 Issued cheque #3414 to Avdex Supply to pay for the May 5 purchase. 16 Sold 490 units of merchandise on credit to Krista Company, invoice #8786.
17 Received 600 units of merchandise and an invoice dated May 17, terms 2/10, n/30, from Meld Corp., $40.50 cost per unit.
19 Issued cheque #3415 to Avdex Supply Co. in payment of its May 10 invoice. 19 Issued cheque #3416 to Xylo, Inc. in payment of its May 11 invoice.
22 Sold 50 units of merchandise to Lloyd Services, invoice #8787. 23 Issued cheque #3417 to Meld Corp. in payment of its May 17 invoice.
25 Determined that the customer account belonging to Lumbar Inc. was uncollectible and wrote it off.
25 Received 230 units of merchandise and an invoice dated May 25, terms 1/15, n/30, from NASD Products, $8,970 total cost.
26 Received payment from Krista Company regarding the May 16 sale.
26 Issued cheque #3418 to Trinity Power in payment of the May utility bill, $3,600.
26 The owner, Rona Dista, withdrew $2,000 from the business for personal use, using cheque #3419.
31 Issued cheque #3420, payable to Payroll, in payment of sales salaries, $2,000, and office salaries, $4,000. Cashed the cheque and paid the employees.
3. Post the entries to the General Ledger. For entries that involve accounts receivable, accounts payable, merchandise inventory, or furniture and equipment, update the respective subsidiary ledger accounts as well.
4. Prepare an unadjusted trial balance in the provided work sheet form and complete the work sheet using the following additional information:
a. The balance in Prepaid insurance represents 4 months of insurance for coverage that commenced on May 1, 2008.
b. A count of the store supplies showed a balance on hand on May 31 of $140. c. Office supplies used during May totalled $1,950.
d. Calculate amortization by referring to the property, plant, and equipment subsidiary ledger. (Round to the nearest whole dollar.)
e. Actual count of ending merchandise inventory was determined to be $35,420.85 — the difference between this amount and your inventory records is due to shrinkage.
f. Calculate accrued interest on the note receivable. (Hint: Refer to the Note Receivable Amortization Schedule).
g. Dista Co. received the following bank statement for May. Last month’s bank reconciliation showed no reconciling items.
Note:
NSF is from Choi Corp. regarding IN#8776 dated April 2, 2008.
h. Management estimates uncollectible accounts receivable based on the following rates of uncollectibility applied to outstanding accounts:
Bank Statement To: Dista Co.
Piggy Bank
Cheques/Charges Deposits/Credits Balance
Apr 30/08 108,859.00 CH#3410 3-May 3,700.00 105,159.00 6-May 10,778.04 115,937.04 NSF 7-May 7,648.64 7-May 20,750.00 129,038.40 9-May 68,500.00 197,538.40 11-May 14,700.00 212,238.40 CH#3412 15-May 7,920.00 15-May 270.66 204,589.06 CH#3413 15-May 6,000.00 198,589.06 CH#3416 20-May 25,800.00 172,789.06 CH#3417 24-May 23,814.00 148,975.06 CH#3419 26-May 2,000.00 26-May 24,010.00 170,985.06 CH#3415 28-May 39,500.00 131,485.06 CH#3411 31-May 39,960.00 91,525.06 SC 31-May 217.72 91,307.34 1-30 days 31-60 days
5. Prepare and post adjusting entries and entries resulting from the bank reconciliation (omit explanations).
6. Prepare the adjusted trial balance column on the work sheet.
7. Prepare a May classified multiple-step income statement, a May statement of owner’s equity, and a May 31 classified balance sheet.
8. Prepare and post the closing entries (omit explanations). 9. Prepare a post-closing trial balance.
Submit the following reports to your marker for assessment (10 marks total): a. General journal (3 marks)
b. General ledger (1 mark) c. Work sheet (0.5 mark)
d. A classified multiple-step income statement for the month ending May 31 (1.5 marks), a statement of owner's equity for the month ending May 31 (0.5 mark), and a classified balance sheet as at May 31 (1.5 marks)
e. Post-closing trial balance (0.5 mark)
f. The Accounts receivable (0.25 mark), Accounts payable (0.25 mark), and Inventory (0.5 mark) sub-ledger accounts, including those that have a nil balance.
g. May 31 bank reconciliation (0.5 mark)
Question 2 (5 marks)
You have the May 31, 2008 financial statements completed and want to understand more about the financial performance of Dista Co. This is a new job for you and there is a lot to learn. You anticipate that Rona, your new boss, will have questions about the year-end results.
Calculate any three ratios that will help you to better understand the company and that you believe will be informative to the company owner.
a. For each ratio, interpret the meaning of the results you calculated and write a brief explanation of what the results tell you about Dista. In your analysis, you may refer to any other source (such as
information in the textbook, online sources, or cases you are familiar with). (3.75 marks — 1.25 mark per ratio)
b. Select one of the ratios and explain how the ratio is affected by the accounting policies Dista selected. (1.25 marks)
Not yet due past due past due Greater than 61 days past due
Mid-term assignment - Content Links
DISTA CO.
Note Receivable Amortization Schedule
Date Collection Principal Interest Balance
15-Apr-08 14,000.00 15-May-08 270.66 200.66 70.00 13,799.34 15-Jun-08 270.66 201.66 69.00 13,597.68 15-Jul-08 270.66 202.67 67.99 13,395.01 15-Aug-08 270.66 203.68 66.98 13,191.32 15-Sep-08 270.66 204.70 65.96 12,986.62 15-Oct-08 270.66 205.73 64.93 12,780.89 15-Nov-08 270.66 206.75 63.90 12,574.14 15-Dec-08 270.66 207.79 62.87 12,366.35 15-Jan-09 270.66 208.83 61.83 12,157.52 15-Feb-09 270.66 209.87 60.79 11,947.65 15-Mar-09 270.66 210.92 59.74 11,736.73 15-Apr-09 270.66 211.98 58.68 11,524.76 15-May-09 270.66 213.04 57.62 11,311.72 15-Jun-09 270.66 214.10 56.56 11,097.62 15-Jul-09 270.66 215.17 55.49 10,882.45 15-Aug-09 270.66 216.25 54.41 10,666.20 15-Sep-09 270.66 217.33 53.33 10,448.87 15-Oct-09 270.66 218.41 52.24 10,230.46 15-Nov-09 270.66 219.51 51.15 10,010.95 15-Dec-09 270.66 220.60 50.05 9,790.35 15-Jan-10 270.66 221.71 48.95 9,568.64 15-Feb-10 270.66 222.82 47.84 9,345.82 15-Mar-10 270.66 223.93 46.73 9,121.89 15-Apr-10 270.66 225.05 45.61 8,896.84 15-May-10 270.66 226.18 44.48 8,670.67 15-Jun-10 270.66 227.31 43.35 8,443.36 15-Jul-10 270.66 228.44 42.22 8,214.92 15-Aug-10 270.66 229.58 41.07 7,985.34 15-Sep-10 270.66 230.73 39.93 7,754.60 15-Oct-10 270.66 231.89 38.77 7,522.72 15-Nov-10 270.66 233.05 37.61 7,289.67 15-Dec-10 270.66 234.21 36.45 7,055.46 15-Jan-11 270.66 235.38 35.28 6,820.08 15-Feb-11 270.66 236.56 34.10 6,583.52 15-Mar-11 270.66 237.74 32.92 6,345.78 15-Apr-11 270.66 238.93 31.73 6,106.85 15-May-11 270.66 240.12 30.53 5,866.72 15-Jun-11 270.66 241.33 29.33 5,625.40 15-Jul-11 270.66 242.53 28.13 5,382.86 15-Aug-11 270.66 243.74 26.91 5,139.12 15-Sep-11 270.66 244.96 25.70 4,894.16 15-Oct-11 270.66 246.19 24.47 4,647.97 15-Nov-11 270.66 247.42 23.24 4,400.55
Working papers
a. General journal (To view the content from this link you must go on-line.)
b. General ledger (To view the content from this link you must go on-line.)
c. Work sheet (To view the content from this link you must go on-line.)
d. Income statement
Statement of owner's equity
Balance sheet (To view the content from this link you must go on-line.)
e. Post-closing trial balance (To view the content from this link you must go on-line.)
f. Sub-ledgers (To view the content from this link you must go on-line.)
Drop box: Mid-term assignment
Note to supplemental, deferred and challenge examination writers:The course examination is worth 100% of your final course mark. If you choose to participate in quizzes and assignments, the marks you receive will not count toward your final course mark.
You must be online to view this course component.
15-Dec-11 270.66 248.66 22.00 4,151.89 15-Jan-12 270.66 249.90 20.76 3,901.99 15-Feb-12 270.66 251.15 19.51 3,650.84 15-Mar-12 270.66 252.41 18.25 3,398.44 15-Apr-12 270.66 253.67 16.99 3,144.77 15-May-12 270.66 254.94 15.72 2,889.84 15-Jun-12 270.66 256.21 14.45 2,633.63 15-Jul-12 270.66 257.49 13.17 2,376.13 15-Aug-12 270.66 258.78 11.88 2,117.36 15-Sep-12 270.66 260.07 10.59 1,857.28 15-Oct-12 270.66 261.37 9.29 1,595.91 15-Nov-12 270.66 262.68 7.98 1,333.23 15-Dec-12 270.66 263.99 6.67 1,069.24 15-Jan-13 270.66 265.31 5.35 803.93 15-Feb-13 270.66 266.64 4.02 537.29 15-Mar-13 270.66 267.97 2.69 269.31 15-Apr-13 270.66 269.31 1.35 0.00
APPENDIX
IV
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.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 FutureExhibit
IV.2
Present Value of a Single Amount Formulaf p
(1 i)n
1Interest 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 $220.1For 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:
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)nb a c k
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:
LO
3 Apply future value concepts to a single amount by using interest tables.Exhibit
IV.4
Future Value of a Single Amount Formulaf p (1 i)n
f p (1 i)n $200 (1 .10)1
