Chapter 13 — Long-Term Liabilities
The module's primary reading · ~40–50 minutes · Objective 8 (account for long-term liabilities, including bonds issued at face, at a discount, and at a premium, and for stockholders' equity, including stock issuance, dividends, and treasury stock), with Objective 4 (complete the accounting cycle: prepare an income statement, a statement of retained earnings, and a classified balance sheet, journalize closing entries, and prepare a post-closing trial balance) and Objective 7 (account for long-lived assets, including cost, depreciation by three methods, and disposal, and for current liabilities, including payroll) called back · Read it first this week; the lecture, the slides, the tutorial, the quiz, and the workshop all build on it.
In plain language
Sometimes a business needs more money than one bank will lend, for longer than a year. It can borrow from many lenders at once by selling bonds (long-term promises to pay interest every period and to repay a fixed amount at the end). The lenders may pay exactly that fixed amount, less, or more, depending on the return they want compared with the interest the bond pays. This week you learn to record all three cases, to follow each period's interest, and to report the debt on the balance sheet. You also learn why paying less up front means a bigger total cost of borrowing.
Why you already care about this
Picture the bicycle shop after a later expansion. It needs $100,000 for five years, more than one lender will cover, so it sells bonds to many lenders at once. On the day it sells them, the shop might receive $100,000, $96,000, or $104,000 for exactly the same promise. All three promise $3,000 of interest every half-year and $100,000 at the end.
You already know a small version of why the price can move. Suppose a friend offers to pay you $100 a year from now. Would you hand over $100 today? Probably not, because $100 today could earn something for you over that year. You would pay a little less. Lenders think the same way about a bond, and the interest they want decides how much less, or how much more, they will pay.
By the end of this chapter you will be able to:
- read a bond's face value, stated rate, maturity date, and market rate;
- explain a bond's price as the present value of its cash flows, and check it step by step;
- tell from two rates whether bonds sell at face, at a discount, or at a premium;
- record the issue, each period's interest, and the repayment for all three cases;
- amortize a discount or premium by the straight-line method and follow the carrying value to face;
- describe the effective-interest method and an installment note in words;
- report bonds in the right section of the balance sheet.
Carry this sentence with you: the stated rate sets the cash; the market rate sets the price.
Where we are
- Already covered: Week 2 defined a liability as an obligation to transfer resources to others. Week 5 split the balance sheet into current and long-term sections. Week 11 spread a van's cost evenly with the straight-line method. Week 12 recorded short-term notes payable and the current portion of long-term debt.
- This week: bonds, their terms and prices, bonds issued at face, at a discount, and at a premium, interest expense and amortization, the effective-interest method and installment notes in words, and debt on the balance sheet.
- How they connect: a bond is a long-term note payable, its amortization spreads one amount evenly the way straight-line depreciation does, and it lands in the long-term liabilities section Week 5 built.
- Where we're going next: Week 14, Stockholders' Equity, turns from what the shop owes lenders to what it owes its owners.
Week 12 gave you the borrower's side of a note. A note payable is a written promise to repay a sum, usually with interest, by a stated date. The program you met in Week 12 owed its interest for three months, so it paid $90, not a full year's interest. This week's debts run for years, and the lenders are many people instead of one. You also lean on Week 5's rule that a long-term liability is one not due within one year or the operating cycle.
1. Borrow for years with a bond
Think of a city that wants to build a new bridge. It cannot pay for the bridge out of one year's taxes, and no single bank wants to lend the whole amount. So the city sells thousands of small, identical promises to repay, each with interest. Anyone can buy one. Businesses do the same thing.
Those promises have a name.
A bond is a long-term note that a business or a government issues to many lenders at once, promising interest every period and the face value at maturity. The lenders who buy it are the bondholders. The borrower records its promise in Bonds Payable, the long-term liability account for the face value of the bonds it has issued.
Worked example — the shop's decision (Dataset J, illustrative). After a later expansion, the bicycle shop needs $100,000 for five years.
- What happened: the shop decides to borrow by issuing $100,000 of 5-year bonds, instead of one large bank loan.
- Which account changes: when it sells them, the shop will record Bonds Payable, a liability, for the $100,000 it must repay.
- Where it goes: the debt is due in five years, so it belongs with the long-term liabilities, not the current ones.
In words: a bond lets the shop borrow from many bondholders at once, and Bonds Payable is the long-term liability that records what it owes them.
Misconception check. Students often think a business that issues bonds is selling a piece of itself, the way it sells shares of stock. It is tempting, because both are "sold to investors." A bondholder is a lender, not an owner. The shop owes bondholders interest and their money back, and it owes them nothing more. Owners and their shares are next week's topic.
2. Read a bond's four terms
A bond is a promise, and every promise has terms. Picture the paper certificate a bondholder might once have framed: it named an amount, a rate, and a date. Those three, plus one more rate set by the market, are all you need.
- The face value, also called par value, is the amount a bond promises to repay at maturity. The shop's face value is $100,000.
- The stated rate, also called the contract rate, is the annual rate printed in the bond's terms. It sets the cash interest paid each period. The shop's stated rate is 6 percent a year.
- The maturity date is the day the face value is due to be repaid.
- The market rate is the return investors require on bonds like these on the day the bonds are sold. It sets the bond's price.
Worked example — the shop's cash interest (Dataset J, illustrative). The shop's bonds pay interest semiannually, which means twice a year. So each payment covers one half-year, called a period.
- Cash interest each period: 100,000 × 6% ÷ 2 = $3,000.
- Number of periods: 5 years × 2 = 10 periods.
- Maturity: the $100,000 face is due at the end of the 10th period.
In words: every half-year for five years, the shop pays its bondholders $3,000, and at the end of the last half-year it repays the $100,000.
Notice what the stated rate does not depend on. The shop pays $3,000 a period whether it sold the bonds for $100,000, $96,000, or $104,000. The cash interest always comes from the face value times the stated rate.
Misconception check. Students often think the stated rate is what investors earn on any bond. The stated rate only sets the cash. An investor who paid less than face still receives the same $3,000 a period, plus a bigger gain at maturity, so that investor earns more than 6 percent. Hold on to the memory hook: the stated rate sets the cash; the market rate sets the price.
3. Price a bond by its present value
Go back to the friend's offer of $100 a year from now. You would pay less than $100 today, because money you hold now can earn a return. The further away the money, and the higher the return you want, the less you would pay for it today.
That idea has a name.
Present value is what an amount due in the future is worth today at a given rate. You find it by discounting the amount for each period until it arrives, which means dividing it by one plus the rate, once per period.
The price of a bond is the present value of its cash flows at the market rate. A bond's cash flows are its 10 interest payments plus its face value. Each one is discounted for the time until it arrives, and the results are added.
Worked example — the at-face check (Dataset J, illustrative). Suppose the market rate equals the stated rate, 6 percent a year. Per period that is 6% ÷ 2 = 3%. Discount each cash flow at 3 percent a period.
- One $3,000 payment due in one period: 3,000 ÷ 1.03 = $2,912.62 today. Dividing by 1.03 removes one period of 3 percent return.
- The $100,000 face, due in 10 periods: divide by 1.03 once for each period, which is the same as dividing by 1.03¹⁰. So 100,000 ÷ 1.03¹⁰ = $74,409.39 today.
- The 10 interest payments, each discounted the same way for its own number of periods, add up to $25,590.61 today.
- Price: 74,409.39 + 25,590.61 = $100,000.00.
In words: when the market rate equals the stated rate, the present value of everything the bond pays is exactly its face value, so the bond sells at face.
Now see what changes when the market rate moves. If investors require more than 6 percent, every cash flow is divided by a larger number, so the total falls below $100,000. If they require less, the total rises above $100,000. The cash flows never change; only the rate used to discount them does.
Dataset J pins two such prices for the shop, $96,000 and $104,000. They are illustrative prices, and this course does not compute a market rate for them. What you can say about each is its direction: $96,000 means the market rate was higher than 6 percent, and $104,000 means it was lower.
In practice (your tools). In a free spreadsheet such as Google Sheets, type =100000/1.03^10 to discount the face; it shows 74409.39 when formatted to two decimals. The built-in present value function does the whole bond in one cell: =PV(0.03, 10, -3000, -100000) returns 100000. The minus signs tell the function that the payments are cash flowing out of the borrower.
Misconception check. Students often think a bond's price is set by its stated rate, so a 6 percent bond should always sell for its face. The stated rate fixes the cash flows, but the market rate discounts them. Two bonds with the same stated rate can sell for different prices on days when investors want different returns.
Pause and think. Choose one: (a) Think of something you paid for now but will only enjoy later, such as a concert ticket bought months ahead. Would you have paid the same price on the day of the concert? Why or why not? (b) Think of money someone owes you, or you owe someone, that is due a while from now. Would you trade it for a smaller amount today? How much smaller, and why?
4. Record bonds issued at face
Start with the simplest day. Investors want exactly the 6 percent the bonds pay, so they pay exactly the face.
Bonds issued at face are sold for exactly the face value. That happens when the market rate equals the stated rate.
Worked example — the shop's bonds at face (Dataset J, illustrative). Walk each transaction the same way: what happened, which accounts change, the debit and the credit.
- The issue: the shop receives $100,000 cash and owes $100,000. Cash, an asset, goes up; Bonds Payable, a liability, goes up.
- Each period: the shop pays $3,000 of interest. Interest Expense goes up; Cash goes down.
- Over the bonds' life: the interest expense totals 10 × 3,000 = $30,000.
| Entry | Account | Debit | Credit |
|---|---|---|---|
| Issue | Cash | 100,000 | |
| Bonds Payable | 100,000 | ||
| Issued $100,000 of 5-year, 6 percent bonds at face. | |||
| Each period | Interest Expense | 3,000 | |
| Cash | 3,000 | ||
| Paid one period's cash interest. |
Each entry balances: debits 100,000 = credits 100,000, and debits 3,000 = credits 3,000.
In words: at face, the shop's interest expense each period is exactly the $3,000 of cash it pays, and borrowing the $100,000 for five years costs it $30,000 in all.
Misconception check. Students often record the bond issue as revenue, because cash came in. Borrowing is not earning. The shop must give every dollar back, so the $100,000 is a liability, Bonds Payable. Revenue comes from doing the shop's work, such as repairs and sales.
5. Record bonds issued at a discount
Now suppose investors want more than 6 percent on the day the shop sells its bonds. The bonds still pay only $3,000 a period. So investors pay less than $100,000, and they make up the difference when they collect the full face at maturity.
Bonds issued at a discount are sold for less than the face value. That happens when the market rate is higher than the stated rate, and the shortfall is the discount.
The shop records the shortfall in its own account. Discount on Bonds Payable is a contra liability account with a debit balance that holds the amount by which bonds sold below face value. A contra liability carries a debit balance and is subtracted from the liability it is paired with, the way Accumulated Depreciation is subtracted from an asset.
That gives the number the balance sheet uses. The carrying value of bonds is Bonds Payable minus any unamortized discount, or plus any unamortized premium.
Worked example — the shop's bonds at a discount (Dataset J, illustrative). The shop receives $96,000.
- The discount: 100,000 − 96,000 = $4,000.
- What happened: Cash goes up by $96,000; Bonds Payable goes up by the full $100,000 face; the $4,000 gap goes to Discount on Bonds Payable.
- The entry balances: debits 96,000 + 4,000 = 100,000 = credits 100,000.
- The carrying value on the day of issue: 100,000 − 4,000 = $96,000.
| Entry | Account | Debit | Credit |
|---|---|---|---|
| Issue | Cash | 96,000 | |
| Discount on Bonds Payable | 4,000 | ||
| Bonds Payable | 100,000 | ||
| Issued $100,000 of 5-year, 6 percent bonds for $96,000. |
In words: the shop owes $100,000 but received $96,000, so on the day of issue its bonds are carried at $96,000, and the $4,000 discount is interest it will pay later.
Misconception check. Students often read a bond discount as a loss, or even as a gain, because the shop "sold something for less" or "owes more than it got." Neither is right on the day of issue. The discount is part of the cost of borrowing. The shop borrows $96,000 and repays $100,000, so the $4,000 is extra interest, and it reaches the income statement as interest expense over the bonds' life.
6. Amortize the discount by the straight-line method
The $4,000 discount is interest the shop pays at maturity, but the shop uses the borrowed money in every period. So the extra interest belongs a little in each period, not all at the end. This is Week 4's matching idea again: an expense goes in the period it helps.
To amortize a discount or premium is to spread it over the periods of the bond's life. A discount is added to interest expense; a premium is subtracted from it. Straight-line amortization spreads it in equal amounts to each interest period: the discount or premium divided by the number of periods.
If that sounds familiar, it should. Week 11's straight-line method spread the van's depreciable cost evenly over its years. Straight-line amortization spreads the discount evenly over the bonds' periods in exactly the same way.
Worked example — each period at a discount (Dataset J, illustrative). Walk one period.
- Amortization per period: 4,000 ÷ 10 = $400.
- Interest expense per period: 3,000 + 400 = $3,400.
- The entry: debit Interest Expense 3,400; credit Discount on Bonds Payable 400; credit Cash 3,000. Debits 3,400 = credits 400 + 3,000 = 3,400.
- Carrying value after the first period: 96,000 + 400 = $96,400.
- Carrying value after 10 periods: 96,000 + 10 × 400 = $100,000.
The credit to Discount on Bonds Payable shrinks the contra account by $400, so the carrying value grows by $400 every period. After the last period, the discount is gone and the carrying value equals the face.
| Period | Carrying value at start | Cash interest | Amortization | Interest expense | Carrying value at end |
|---|---|---|---|---|---|
| 1 | 96,000 | 3,000 | 400 | 3,400 | 96,400 |
| 2 | 96,400 | 3,000 | 400 | 3,400 | 96,800 |
| 3 | 96,800 | 3,000 | 400 | 3,400 | 97,200 |
| 4 | 97,200 | 3,000 | 400 | 3,400 | 97,600 |
| 5 | 97,600 | 3,000 | 400 | 3,400 | 98,000 |
| 6 | 98,000 | 3,000 | 400 | 3,400 | 98,400 |
| 7 | 98,400 | 3,000 | 400 | 3,400 | 98,800 |
| 8 | 98,800 | 3,000 | 400 | 3,400 | 99,200 |
| 9 | 99,200 | 3,000 | 400 | 3,400 | 99,600 |
| 10 | 99,600 | 3,000 | 400 | 3,400 | 100,000 |
| Total | 30,000 | 4,000 | 34,000 |
Foot the schedule. The cash interest column totals 10 × 3,000 = $30,000, the amortization column 10 × 400 = $4,000, and the expense column 10 × 3,400 = $34,000, which is 30,000 + 4,000.
Now check the total cost of borrowing another way. The shop pays 10 × 3,000 + 100,000 = $130,000 in all, and it received $96,000. The difference, 130,000 − 96,000 = $34,000, is the same total interest expense.
In practice (your tools). In a spreadsheet, put the period numbers 1 to 10 in column A and the starting carrying value, 96000, in B2. In C2 type =3000, in D2 =4000/10, in E2 =C2+D2, and in F2 =B2+D2. In B3 type =F2, then fill each formula down to row 11. A total row with =SUM(E2:E11) should show 34000, and F11 should show 100000.
Misconception check. Students often think the bondholders who paid $96,000 earn the 6 percent stated rate. They receive the same $3,000 a period as everyone else, and then $100,000 for bonds that cost them $96,000. That extra $4,000 means they earn more than 6 percent, which is exactly why the shop's interest expense, $3,400, is higher than its cash interest.
7. Record bonds issued at a premium
Flip the story. On the day the shop sells, investors want less than 6 percent. A bond that pays $3,000 a period is worth more than face to them, so they pay more.
Bonds issued at a premium are sold for more than the face value. That happens when the market rate is lower than the stated rate, and the excess is the premium. Premium on Bonds Payable is an account with a credit balance that holds the amount by which bonds sold above face value. It is added to Bonds Payable.
Worked example — the shop's bonds at a premium (Dataset J, illustrative). The shop receives $104,000.
- The premium: 104,000 − 100,000 = $4,000.
- The issue: debit Cash 104,000; credit Bonds Payable 100,000; credit Premium on Bonds Payable 4,000. Debits 104,000 = credits 100,000 + 4,000 = 104,000.
- The carrying value on the day of issue: 100,000 + 4,000 = $104,000.
- Amortization per period: 4,000 ÷ 10 = $400.
- Interest expense per period: 3,000 − 400 = $2,600.
- Each period: debit Interest Expense 2,600; debit Premium on Bonds Payable 400; credit Cash 3,000. Debits 2,600 + 400 = 3,000 = credits 3,000.
- Carrying value after the first period: 104,000 − 400 = $103,600.
- Total interest expense: 10 × 2,600 = $26,000, which equals 130,000 − 104,000 = $26,000.
| Entry | Account | Debit | Credit |
|---|---|---|---|
| Issue | Cash | 104,000 | |
| Bonds Payable | 100,000 | ||
| Premium on Bonds Payable | 4,000 | ||
| Issued $100,000 of 5-year, 6 percent bonds for $104,000. | |||
| Each period | Interest Expense | 2,600 | |
| Premium on Bonds Payable | 400 | ||
| Cash | 3,000 | ||
| Paid one period's cash interest and amortized $400 of premium. |
The debit to Premium on Bonds Payable shrinks the premium by $400 a period. After 10 periods the premium is gone, and the carrying value has fallen from $104,000 to the $100,000 face.
In words: the shop pays $3,000 a period but records only $2,600 of interest expense, because the extra $4,000 it received at issue pays back $400 of each period's interest.
Misconception check. Students often treat a premium as extra interest expense, because "premium" sounds like paying more. It is the investors who paid more. The shop received $104,000 and repays only $100,000, so its total cost of borrowing is lower, and each period's interest expense, $2,600, is less than the $3,000 of cash it pays.
8. Compare the effective-interest method, in words
Straight-line gives the same $400 of amortization every period, and that keeps the arithmetic clean. But the shop's debt is not the same size every period. In the discount case it grows from $96,000 toward $100,000. A second method ties each period's interest to the size of the debt at that moment.
That method has a name.
The effective-interest method is the amortization method GAAP calls for. Under it, each period's interest expense is the carrying value at the start of the period times the market rate for one period. The amortization is the difference between that interest expense and the cash interest. Straight-line amortization is acceptable when its results are not materially different.
Worked example — the two methods side by side, in words (Dataset J, illustrative). Follow the discount case for its whole life.
- Cash interest: the same under both methods, $3,000 a period, because the stated rate sets it.
- Interest expense: under straight-line, $3,400 every period. Under the effective-interest method, a little less than that in the early periods and a little more in the later ones, because the carrying value it is figured on grows each period.
- Total amortized: the same $4,000 under both methods.
- At maturity: both bring the carrying value to the $100,000 face.
When the bonds mature, every method and every issue price end the same way. The shop repays the face: debit Bonds Payable 100,000; credit Cash 100,000. By then the discount or premium has been fully amortized, so Bonds Payable is the only account left to close out.
One caveat about this section: it deliberately has no effective-interest figures. This course computes straight-line amortization and teaches the effective-interest method in words, so you can describe its pattern without carrying its decimals.
Misconception check. Students often think the two methods give different total interest, so one must "cost more." They do not. Both spread the same $4,000 and reach the same $100,000 at maturity. The methods differ only in how the total is split among the periods, and neither is ranked above the other here.
9. Repay an installment note, in words
Not every long-term debt is repaid in one amount at the end. Think of a car loan: you pay the same amount every month, and the balance shrinks a little every time.
That shape of loan has a name.
An installment note is a loan repaid in a series of payments over its term. When the payments are equal, each one covers that period's interest and the rest reduces the principal.
Worked example — a farm cooperative's harvester note, in words (illustrative). A farm cooperative signs a note for a new harvester and agrees to repay it in equal payments over several years.
- The first payment: the balance owed is at its largest, so the interest on it is large too. Most of the payment is interest, and a small part reduces the principal.
- A later payment: the balance has shrunk, so its interest is smaller. The same payment now reduces the principal by more.
- The last payment: almost all of it is principal, and it brings the balance to zero.
- On the balance sheet: the part of the principal due within the next year is a current liability, the current portion of long-term debt from Week 12, and the rest stays long-term.
In words: equal payments shift from mostly interest to mostly principal over the life of an installment note, because each period's interest is figured on a smaller balance.
Misconception check. Students often record each whole installment payment as a reduction of the note, as if all of it paid down the principal. Part of every payment is interest, an expense of that period. Only the rest reduces Notes Payable.
10. Report debt on the balance sheet
The last step hands the balance sheet a number a lender can read. Bonds sit in the long-term liabilities section, at their carrying value, until they come close to maturity.
Worked example — the discount case after the first period (Dataset J, illustrative). After one period of amortization, 4,000 − 400 = $3,600 of the discount remains.
| Long-term liabilities | ||
|---|---|---|
| Bonds Payable | $100,000 | |
| Less: Discount on Bonds Payable | (3,600) | |
| Carrying value of bonds | $96,400 |
The arithmetic: 100,000 − 3,600 = $96,400, the same carrying value the amortization schedule shows at the end of Period 1.
For the premium case, the premium is added instead: after the first period, the remaining $3,600 of premium is added to Bonds Payable for a carrying value of $103,600.
When the bonds come within one year of maturity, they are due within the year, so they move to current liabilities. That is the same current-versus-long-term line you drew in Week 5 and again for a note's current portion in Week 12. The debt itself does not change; only its classification does.
Here is the honest limitation of this one section: a real balance sheet carries far more than one bond issue. Each debt is classified by when it is due, and a reader adds the pieces to see the whole.
Misconception check. Students often report bonds at their face value no matter what they sold for. The balance sheet shows the carrying value, the face minus any unamortized discount or plus any unamortized premium. For the shop's discounted bonds after one period, that is $96,400, not $100,000.
The whole week fits in one sentence. All three issues borrow against the same $100,000 face and pay the same $3,000 of cash interest a period, but because the shop receives $100,000, $96,000, or $104,000 at the start, its total interest expense is $30,000, $34,000, or $26,000.
Pause and think. Choose one: (a) If you were lending to the shop, would you rather read its bonds at face value or at carrying value on the balance sheet, and why? (b) If you were a founder, would the three possible issue prices change how you feel about borrowing, even though the cash interest is the same in each? Explain your thinking.
Key terms
- Bond — A long-term note that a business or a government issues to many lenders at once, promising interest every period and the face value at maturity. (first used: 1. Borrow for years with a bond)
- Bondholders — The lenders who buy a bond and so are owed its interest payments and, at maturity, its face value. (first used: 1. Borrow for years with a bond)
- Bonds Payable — The long-term liability account in which a borrower records the face value of the bonds it has issued. (first used: 1. Borrow for years with a bond)
- Face value — The amount a bond promises to repay at maturity, also called its par value; the stated rate is applied to it to set the cash interest. (first used: 2. Read a bond's four terms)
- Stated rate — The annual interest rate printed in a bond's terms, also called the contract rate, which sets the cash interest paid each period. (first used: 2. Read a bond's four terms)
- Maturity date — The day a bond's face value is due to be repaid to its bondholders. (first used: 2. Read a bond's four terms)
- Market rate — The return investors require on bonds of similar risk and term on the day the bonds are sold; it sets the bond's price. (first used: 2. Read a bond's four terms)
- Present value — What an amount due in the future is worth today at a given rate, found by discounting the amount for each period until it arrives. (first used: 3. Price a bond by its present value)
- Issued at face — Sold for exactly the face value, which happens when the market rate equals the stated rate. (first used: 4. Record bonds issued at face)
- Issued at a discount — Sold for less than the face value, which happens when the market rate is higher than the stated rate; the shortfall is the discount. (first used: 5. Record bonds issued at a discount)
- Discount on Bonds Payable — A contra liability account with a debit balance that holds the amount by which bonds sold below face value; it is subtracted from Bonds Payable. (first used: 5. Record bonds issued at a discount)
- Contra liability — An account that carries a debit balance and is subtracted from the liability it is paired with, the way Discount on Bonds Payable reduces Bonds Payable. (first used: 5. Record bonds issued at a discount)
- Carrying value — The amount at which bonds are reported: Bonds Payable minus any unamortized discount or plus any unamortized premium. (first used: 5. Record bonds issued at a discount)
- Amortize — To spread a bond discount or premium over the periods of the bond's life, adding a discount to interest expense or subtracting a premium from it. (first used: 6. Amortize the discount by the straight-line method)
- Straight-line amortization — Spreading a bond discount or premium in equal amounts to each interest period, found as the discount or premium divided by the number of periods. (first used: 6. Amortize the discount by the straight-line method)
- Issued at a premium — Sold for more than the face value, which happens when the market rate is lower than the stated rate; the excess is the premium. (first used: 7. Record bonds issued at a premium)
- Premium on Bonds Payable — An account with a credit balance that holds the amount by which bonds sold above face value; it is added to Bonds Payable. (first used: 7. Record bonds issued at a premium)
- Effective-interest method — The amortization method GAAP calls for, in which each period's interest expense is the carrying value at the start of the period times the market rate for one period. (first used: 8. Compare the effective-interest method, in words)
- Installment note — A loan repaid in a series of payments over its term; when the payments are equal, each covers that period's interest and the rest reduces the principal. (first used: 9. Repay an installment note, in words)
Summary
- A bond is a long-term note sold to many bondholders at once.
- Face value times the stated rate sets the cash interest.
- The market rate sets the price, the present value of the cash flows.
- Market rate equal to stated rate: the bonds sell at face.
- Market rate higher: a discount. Market rate lower: a premium.
- A discount adds to interest expense; a premium reduces it.
- Straight-line amortization spreads the discount or premium evenly.
- Carrying value moves to face by maturity.
- GAAP calls for the effective-interest method; straight-line is acceptable when not materially different.
- An installment note's equal payments shift from interest to principal.
- Bonds are long-term liabilities until they come due within a year.
Check your understanding
Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.
- A ski resort (illustrative) issues $50,000 of 4-year, 8 percent bonds that pay interest semiannually, at face. Compute the cash interest each period and the total interest expense over the bonds' life, and name the accounts in the entry for each interest payment.
- A recording studio (illustrative) issues $20,000 of 3-year, 5 percent bonds that pay interest semiannually, for $19,400. Compute the discount, the straight-line amortization per period, the interest expense per period, and the carrying value after the first period.
- A community health clinic (illustrative) issues $60,000 of 4-year, 7 percent bonds that pay interest semiannually, for $61,200. Compute the premium, the interest expense per period by the straight-line method, and the total interest expense over the bonds' life.
- A bond's stated rate is 5 percent, and on the day it is sold investors require 7 percent on similar bonds. Without any dollar amounts, explain whether it sells at face, at a discount, or at a premium, and whether its interest expense will be more or less than its cash interest.
Answers (worked reasoning — read after attempting)
- Cash interest each period is 50,000 × 8% ÷ 2 = $2,000. There are 4 × 2 = 8 periods, so total interest expense is 8 × 2,000 = $16,000. Each payment debits Interest Expense 2,000 and credits Cash 2,000. At face, interest expense equals the cash interest, because there is no discount or premium to amortize.
- The discount is 20,000 − 19,400 = $600. Cash interest is 20,000 × 5% ÷ 2 = $500 a period, and there are 3 × 2 = 6 periods, so amortization is 600 ÷ 6 = $100 a period. Interest expense is 500 + 100 = $600 a period. The carrying value after the first period is 19,400 + 100 = $19,500. The studio's expense is higher than its cash interest because it repays $600 more than it received.
- The premium is 61,200 − 60,000 = $1,200. Cash interest is 60,000 × 7% ÷ 2 = $2,100 a period over 4 × 2 = 8 periods, and amortization is 1,200 ÷ 8 = $150 a period. Interest expense is 2,100 − 150 = $1,950 a period, and over the life it totals 8 × 1,950 = $15,600. Check it another way: the clinic pays 8 × 2,100 + 60,000 = $76,800 and received $61,200, and 76,800 − 61,200 = $15,600.
- Investors want 7 percent, but the bond pays cash at only 5 percent of face. To earn 7 percent on that smaller cash, they must pay less than face, so the bond sells at a discount. The discount is extra interest the issuer repays at maturity, so as it is amortized, interest expense each period is more than the cash interest. The memory hook settles it: the stated rate sets the cash; the market rate sets the price.
Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, the quiz, the discussion, and the assignment; next week the rules for issuing stock and paying dividends take up the owners' side of the balance sheet.
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