BUS103: Introduction to Financial Accounting

The price of a bond issue often differs from its face value. The amount a bond sells for above face value is a premium. The amount a bond sells for below face value is a discount. A difference between face value and issue price exists whenever the market rate of interest for similar bonds differs from the contract rate of interest on the bonds. The effective interest rate (also called the yield) is the minimum rate of interest that investors accept on bonds of a particular risk category. The higher the risk category, the higher the minimum rate of interest that investors accept. The contract rate of interest is also called the stated, coupon, or nominal rate. Firms state this rate in the bond indenture, print it on the face of each bond, and use it to determine the amount of cash paid each interest period. The market rate fluctuates from day to day, responding to factors such as the interest rate the Federal Reserve Board charges banks to borrow from it; government actions to finance the national debt; and the supply of, and demand for, money.

Market and contract rates of interest are likely to differ. Issuers must set the contract rate before the bonds are actually sold to allow time for such activities as printing the bonds. Assume, for instance, that the contract rate for a bond issue is set at 12 percent. If the market rate is equal to the contract rate, the bonds will sell at their face value. However, by the time the bonds are sold, the market rate could be higher or lower than the contract rate. As shown in Exhibit 43, if the market rate is lower than the contract rate, the bonds will sell for more than their face value. Thus, if the market rate is 10 percent and the contract rate is 12 percent, the bonds will sell at a premium as the result of investors bidding up their price. However, if the market rate is higher than the contract rate, the bonds will sell for less than their face value. Thus, if the market rate is 14 percent and the contract rate is 12 percent, the bonds will sell at a discount. Investors are not interested in bonds bearing a contract rate less than the market rate unless the price is reduced. Selling bonds at a premium or a discount allows the purchasers of the bonds to earn the market rate of interest on their investment.

Computing long-term bond prices involves finding present values using compound interest. The appendix to this chapter explains the concepts of future value and present value. If you do not understand the present value concept, read the appendix before continuing with this section.

Buyers and sellers negotiate a price that yields the going rate of interest for bonds of a particular risk class. The price investors pay for a given bond issue is equal to the present value of the bonds. To compute present value, we discount the promised cash flows from the bonds – principal and interest using the market, or effective, rate. We use the market rate because the bonds must yield at least this rate or investors are attracted to alternative investments. The life of the bonds is stated in interest (compounding) periods. The interest rate is the effective rate per interest period, which is found by dividing the annual rate by the number of times interest is paid per year. For example, if the annual rate is 12 percent, the semiannual rate would be 6 percent.

Issuers usually quote bond prices as percentages of face value – 100 means 100 percent of face value, 97 means 97 percent of face value, and 103 means 103 percent of face value. For example, one hundred USD 1,000 face value bonds issued at 103 have a price of USD 103,000. Regardless of the issue price, at maturity the issuer of the bonds must pay the investor(s) the face value of the bonds.

	Market Rate	Contract Rate
Bonds sell at a premium if market rate < contract rate	10%	12%
Bonds sell at a face value if market rate = contract rate	12%	12%
Bonds sell at a discount if market rate > contract rate	14%	12%

Exhibit 43: Bond premiums and discounts

Bonds issued at face value The following example illustrates the specific steps in computing the price of bonds. Assume Carr Company issues 12 percent bonds with a USD 100,000 face value to yield 12 percent. Dated and issued on 2010 June 30, the bonds call for semiannual interest payments on June 30 and December 31 and mature on 2013 June 30. The bonds would sell at face value because they offer 12 percent and investors seek 12 percent. Potential purchasers have no reason to offer a premium or demand a discount. One way to prove the bonds would be sold at face value is by showing that their present value is USD 100,000:

	Cash Flow x Present value Factor	= Present value
Principal of $100,000 due in six interest periods multiplied by present value factor for 6% from Table A.3 of the Appendix (end of text)	$100,000 X 0.70496	=$70,496
Interest of $6,000 due at the end of six interest periods multiplied by present value factor for 6% from Table A.4 of the Appendix (end of text)	6,000 X 4.91732	=29,504
Total price (present value)		$100,000

According to this schedule, investors who seek an effective rate of 6 percent per six-month period should pay USD 100,000 for these bonds. Notice that the same number of interest periods and semiannual interest rates occur in discounting both the principal and interest payments to their present values. The entry to record the sale of these bonds on 2010 June 30, debits Cash and credits Bonds Payable for USD 100,000.

An accounting perspective:

Business insight

Some persons estimate that Social Security will be broke by the year 2025 unless changes are made. Therefore, you may want to set aside funds during your working career to provide for retirement.

Over the last 60 years, the inflation rate has averaged about 3 percent per year, treasury bills have averaged a little under 4 percent per year, corporate bonds have averaged about a little over 5 percent per year, and stocks have averaged a little over 10 percent per year. Using the tables at the end of the text we can determine how much you would have at age 65 if you invested USD 2,000 each year for 45 years in treasury bills, corporate bonds, or stocks, beginning at age 20.

To do this calculation for treasury bills, for instance, we would first use Table A.2 to determine the future value of an annuity of USD 2,000 for 30 periods at 4 percent (USD 2,000 X 56.08494 = USD 112,170). (We would have used 45 periods, but the table only went up to 30 periods.) Then we would use Table A.1 to find the value of this lump sum of USD 112,170 for another 15 years at 4 percent (USD 112,170 X 1.80094 = USD 202,011). Then we cannot forget that we have another 15 years of USD 2,000 annuity to consider. Thus, we go back to Table A.2 and calculate the future value of an annuity of USD 2,000 for 15 periods at 4 percent (USD 2,000 X 20.02359 = USD 40,047). Then we add the USD 202,011 and the USD 40,047 to get the total future value of USD 242,058. (You would have invested USD 2,000 X 45 years = USD 90,000.) Would you be pleased? Not when you see what you could have had at age 65 if you invested in stocks.

If you had invested in corporate bonds at 5 percent, you would have USD 319,401. However, if you had invested in stocks at 10 percent, you would have USD 1,437,810 at age 65. Can you use the tables in the back of the text to verify these amounts?

Bonds issued at a discount Assume the USD 100,000, 12 percent Carr bonds are sold to yield a current market rate of 14% annual interest, or 7 percent per semiannual period. Carr computes the present value (selling price) of the bonds as follows:

	Cash Flow x Present value Factor	= Present value
Principal of $100,000 due in six interest periods multiplied by present value factor for 7% from Table A.3 of the Appendix (end of text)	$100,00 0 X0.66630	=$66,634
Interest of $6,000 due at the end of six interest periods multiplied by present value factor for 7% from Table A.4 of the Appendix (end of text)	6,000 X4.76654	=28,559
Total price (present value)		$95,233

Note that in computing the present value of the bonds, Carr uses the actual USD 6,000 cash interest payment that will be made each period. The amount of cash the company pays as interest does not depend on the market interest rate. However, the market rate per semiannual period – 7 percent – does change, and Carr uses this new rate to find interest factors in the tables.

The journal entry to record issuance of the bonds is:

2010 June 30	Cash (+A)	95,233
	Discount on bonds payable (-L; Contra-account)	4,767
	Bonds payable (+L)	100,000
	To record bonds issued at a discount.

In recording the bond issue, Carr credits Bonds Payable for the face value of the debt. The company debits the difference between face value and price received to Discount on Bonds Payable, a contra account to Bonds Payable. Carr reports the bonds payable and discount on bonds payable in the balance sheet as follows:

Long-term liabilities:
Bonds payable, 12%, due 2009 June 30	$100,000
Less: Discount on bonds payable	4,767	$95,233

The USD 95,233 is the carrying value, or net liability, of the bonds. Carrying value is the face value of the bonds minus any unamortized discount or plus any unamortized premium. The next section discusses unamortized premium on bonds payable.

Bonds issued at a premium Assume that Carr issued the USD 100,000 face value of 12 percent bonds to yield a current market rate of 10 percent. The bonds would sell at a premium calculated as follows:

	Cash Flow x Present value Factor	= Present value
Principal of $100,000 due in six interest periods multiplied by present value factor for 5% from Table A.3 of the Appendix (end of text)	$100,00 0 X 0.74622	=$74,622
Interest of $6,000 due at the end of six interest periods multiplied by present value factor for 5% from Table A.4 of the Appendix (end of text)	6,000 X 5.07569	=30,454
Total price (present value)		$105,076

The journal entry to record the issuance of the bonds is:

2010 June 30	Cash (+A)	105,076
	Bonds payable (+L)	100,000
	Premium on bonds payable (+L)	5,076
	To record bonds issued at a premium.

The carrying value of these bonds at issuance is USD 105,076, consisting of the face value of USD 100,000 and the premium of USD 5,076. The premium is an adjunct account shown on the balance sheet as an addition to bonds payable as follows:

Long-term liabilities:
Bonds payable, 12%, due 2009 June 30	$100,000
Add: Premium on bonds payable	5,076	$105,076

When a company issues bonds at a premium or discount, the amount of bond interest expense recorded each period differs from bond interest payments. A discount increases and a premium decreases the amount of interest expense. For example, if Carr issues bonds with a face value of USD 100,000 for USD 95,233, the total interest cost of borrowing would be USD 40,767: USD 36,000 (which is six payments of USD 6,000) plus the discount of USD 4,767. If the bonds had been issued at USD 105,076, the total interest cost of borrowing would be USD 30,924: USD 36,000 less the premium of USD 5,076. The USD 4,767 discount or USD 5,076 premium must be allocated or charged to the six periods that benefit from the use of borrowed money. Two methods are available for amortizing a discount or premium on bonds – the straight-line method and the effective interest rate method.

The straight-line method records interest expense at a constant amount; the effective interest rate method records interest expense at a constant rate. APB Opinion No. 21 states that the straight-line method may be used only when it does not differ materially from the effective interest rate method. In many cases, the differences are not material.

An accounting perspective:

Business insight

US government bonds have traditionally offered a fixed rate of interest. In early 1997, the US Treasury began offering inflation indexed bonds. The amount of interest on these bonds is tied to the officially reported rate of inflation. The bonds pay interest every six months, and the interest is based on the inflation-adjusted value of the principal. These bonds are designed to protect purchasers against purchasing power loss due to inflation. At that time, there was some concern by investors that the government had been considering calculating the official rate of inflation differently than in the past in such a way that it would lower the annual increase as compared to the then present method of calculation. This change in calculation, if adopted, would lower the amount of interest earned on these bonds. However, there were some assurances that for this purpose the official rate of inflation would be calculated the "old way".

The straight-line method The straight-line method of amortization allocates an equal amount of discount or premium to each month the bonds are outstanding. The issuer calculates the amount by dividing the discount or premium by the total number of months from the date of issuance to the maturity date. For example, if it sells USD 100,000 face value bonds for USD 95,233, Carr would charge the USD 4,767 discount to interest expense at a rate of USD 132.42 per month (equal to USD 4,767/36). Total discount amortization for six months would be USD 794.52, computed as follows: USD 132.42 X 6. Interest expense for each six-month period then would be USD 6,794.52, calculated as follows: USD 6,000 + (USD 132.42 X 6). The entry to record the expense on 2010 December 31, would be:

2010 Dec. 31	Bond interest expense (-SE)	6,794.52
	Cash (-A)	6,000.00
	Discount on bonds payable ($132.42 x 6) (+L)	794.52
	To record interest payment and discount amortization.

By the maturity date, all of the discount would have been amortized.

To illustrate the straight-line method applied to a premium, recall that earlier Carr sold its USD 100,000 face value bonds for USD 105,076. Carr would amortize the USD 5,076 premium on these bonds at a rate of USD 141 per month, equal to USD 5,076/36. The entry for the first period's semiannual interest expense on bonds sold at a premium is:

2010 Dec. 31	Bond interest expense (-SE)	5,154
	Premium on bonds payable ($141 x 6) (-L)	846
	Cash (-A)	6,000
	To record interest payable and premium amortization.

By the maturity date, all of the premium would have been amortized.

The effective interest rate method APB Opinion No. 21 recommends an amortization procedure called the effective interest rate method, or simply the interest method. Under the interest method, interest expense for any interest period is equal to the effective (market) rate of interest on the date of issuance times the carrying value of the bonds at the beginning of that interest period. Using the Carr example of 12 percent bonds with a face value of USD 100,000 sold to yield 14 percent, the carrying value at the beginning of the first interest period is the selling price of USD 95,233. Carr would record the interest expense for the first semiannual period as follows:

2010 Dec. 31	Bond interest expense ($95,233 x 0.14 x ½) (- SE)	6,666
	Cash ($100,000 x 0.12 x ½) (-A)	6,000
	Discount on bonds payable (+L)	666
	To record discount amortization and interest payment.

Note that interest expense is the carrying value times the effective interest rate. The cash payment is the face value times the contract rate. The discount amortized for the period is the difference between the two amounts.

After the preceding entry, the carrying value of the bonds is USD 95,899, or USD 95,233 + USD 666. Carr reduced the balance in the Discount on Bonds Payable account by USD 666 to USD 4,101, or USD 4,767 - USD 666. Assuming the accounting year ends on December 31, the entry to record the payment of interest for the second semiannual period on 2011 June 30 is:

2011 June 30	Bond interest expense ($95,899 x 0.14 x ½) (-SE)	6,713
	Cash ($100,000 x 0.12 x ½) (-A)	6,000
	Discount on bonds payable (+L)	713
	To record discount amortization and interest payment.

Carr can also apply the effective interest rate method to premium amortization. If the Carr bonds had been issued at USD 105,076 to yield 10 percent, the premium would be USD 5,076. The firm calculates interest expense in the same manner as for bonds sold at a discount. However, the entry would differ somewhat, showing a debit to the premium account. The entry for the first interest period is:

2010 Dec. 31	Bond Interest Expense ($105,076 x 0.10 x ½) (-SE)	5,254
	Premium on bonds payable (-L)	746
	Cash ($100,000 x 0.12 x ½) (-A)	6,000
	To record interest payment and premium amortization.

After the first entry, the carrying value of the bonds is USD 104,330, or USD 105,076 - USD 746. The premium account now carries a balance of USD 4,330, or USD 5,076 - USD 746. The entry for the second interest period is:

2011 June 30	Bond interest expense ($104,330 x 0.10 x ½) (-SE)	5,216*
	Premium on bonds payable (-L)	784
	Cash ($100,000 x 0.12 x ½) (-A)	6,000
	To record interest payment and premium amortization

*rounded down

An accounting perspective:

Business Insight The difference between the single-line method and effective interest method for amortizing a bond discount can be seen in the following graphic. The carrying values (CV) start at the same point and end at the same point under both methods.The total interest expense is the same under both methods. However, the interest expense and amortization of bond discount are at a constant amount each period under the straight-line method,and they are at a concentrate under the effective interest rate matched.

Discount and premium amortization schedules A discount amortization schedule (Exhibit 44) and a premium amortization schedule (Exhibit 45) aid in preparing entries for interest expense. Usually, companies prepare such schedules when they first issue bonds, often using computer programs designed for this purpose. The companies then refer to the schedules whenever they make journal entries to record interest. Note that in each period the amount of interest expense changes; interest expense gets larger when a discount is involved and smaller when a premium is involved. This fluctuation occurs because the carrying value to which a constant interest rate is applied changes each interest payment date. With a discount, carrying value increases; with a premium, it decreases. However, the actual cash paid as interest is always a constant amount determined by multiplying the bond's face value by the contract rate.

Recall that the issue price was USD 95,233 for the discount situation and USD 105,076 for the premium situation. The total interest expense of USD 40,767 for the discount situation in Exhibit 44 is equal to USD 36,000 (which is six USD 6,000 payments) plus the USD 4,767 discount. This amount agrees with the earlier computation of total interest expense. In Exhibit 45, total interest expense in the premium situation is USD 30,924, or USD 36,000 (which is six USD 6,000 payments) less the USD 5,076 premium. In both illustrations, at the maturity date the carrying value of the bonds is equal to the face value because the discount or premium has been fully amortized.

Adjusting entry for partial period Exhibit 44 and Exhibit 45 also would be helpful if Carr must accrue interest for a partial period. Instead of a calendar-year accounting period, assume the fiscal year of the bond issuer ends on August 31. Using the information provided in the premium amortization schedule (Exhibit 45), the adjusting entry needed on 2010 August 31 is:

2010 Aug. 31	Bond interest expense ($5,254 x (2/6))	1,751
	Premium on bonds payable ($746 x (2/6))	249
	Bond interest payable ($6,000 x (2/6))	2,000
	To record two months' accrued interest.

(A) Interest Payment Date	(B) Bond Interest Expense Debit (E x 0.14 x ½)	(C) Cash credit ($100,000 x 0.12 x ½)	(D) Discount on Bonds Payable Credit (B-C)	(E) Carrying value of Bonds Payable (previous balance in E+D)
Issued Price				$ 95,233
2010/12/31	$6,666	$6,000	$666	95,899
2011/6/30	6,713	6,000	713	96,612
2011/12/31	6,763	6,000	763	97,375
2012/6/30	6,816	6,000	816	98,191
2012/12/31	6,873	6,000	873	99,064
2013/6/30	6,936*	6,000	936	100,000
	$40,767	$36,000	$4,767

Exhibit 44: Discount amortization schedule for bonds payable

This entry records interest for two months, July and August, of the six-month interest period ending on 2010 December 31. The first line of Exhibit 45 shows the interest expense and premium amortization for the six months. Thus, the previous entry records two-sixths (or one-third) of the amounts for this six-month period. Carr would record the remaining four months' interest when making the first payment on 2010 December 31. That entry reads:

2010 Dec. 31	Bond interest payable (-L)	2,000
	Bond interest expense ($5,254 x (4/6)) (-SE)	3,503
	Premium on bonds payable ($746 x 4/6) (-L)	497
	Cash (-A)	6,000
	To record four months' interest expense and semiannual interest payment.

During the remaining life of the bonds, Carr would make similar entries for August 31 and December 31. The amounts would differ, however, because Carr uses the interest method of accounting for bond interest. The entry for each June 30 would be as indicated in Exhibit 45.