BOND INVESTMENTS and BONDS PAYABLE © bonds.doc Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM Please observe all copyright laws Bonds are issued by businesses as a means of borrowing money. They are, in essence, a note payable where the repayment terms are determined before the amount borrowed is determined. Other businesses or individuals purchase bonds as a means of investing money. The borrower (aka. bond seller or issuer) pays interest for the privilege of having the use of someone else's money. The bond buyer (aka. lender or investor) earns interest because they are loaning their money to someone else to use. Bonds are sold/purchased at the present value of their future cash flows. I.e., the bonds are sold/purchased so that the cash paid and received later will pay back the money borrowed/loaned PLUS interest. The cash paid and received later consist of several semiannual payments/receipts and one lump sum payment/receipt. The semiannual interest payments/receipts are the same amount each six months and therefore are also an annuity. (Annuity: cash flow where the same amount is paid/received more that once AND is paid/received at equal intervals of time AND bear the same interest rate each period.) Sometimes the semiannual payments/receipts are referred to as "rents". The one time lump sum payment/receipt at the end of the contract term is equal to the Face Value; this is also referred to as the Maturity Value because it is the final amount paid/received when the bond matures. TERMS AND SYMBOLS: Maturity date: The due date on the bond. Face value: The amount of money that will be paid or received at the maturity date. Stated rate of interest: The interest rate stated (printed) on the Bond, which is used to determine the amount of periodic (semiannual) payment of cash to the bond investor from the bond seller. E.g., Bond face times stated rate times ½ = cash each six months. This is the annuity portion of the bond. Effective interest rate: The interest rate that the bond investor and seller agrees upon at the date the bonds are sold/purchased. I.e., the actual rate of interest earned or paid. This is the interest rate used to determine the present value of the bond (the rate that is used in the Tables). Par: The same as the Face value. Also means 100%. This is when the stated interest rate is equal to the effective interest rate. E.g., if a bond sells for par, it is selling for face value or 100%. If a bond sells for 103, it is selling for 103% of par or face value. Discount: When the bond sells for less than Face value or Par. Also means that the stated interest rate is less than the effective interest rate. E.g., a bond selling at less than 100. Premium: When the bond sells for more than Face value or Par. Also means that the stated interest rate is more than the effective interest rate. E.g., a bond selling at more than 100. Accrued interest: The amount of interest that would be received or paid since the last interest date to the current date. Only applicable when bonds are sold/purchased between interest dates. n = number of time periods from the purchase/sales date until the maturity date. r = rent or cash received/paid each six months (face value x stated interest rate x ½). i = effective interest rate adjusted for portion of year. E.g., 8% per year with two interest periods per year (semiannual payments) would be one-half or 4% per interest period. PvAmt = Present value of an amount. Present value of the Face value. PvAo = Present value of an ordinary annuity. Present value of the cash paid/received each 6 months.

EXAMPLE: Assume a $1000 bond is being sold today to yield 12% annual interest and the maturity date is one and one-half years from today. The bond pays interest semiannually. The stated rate of interest is 10%. This means the following: Face value, maturity value or Par = $1000 The number of time periods, n = 3 (1 ½ years time 2 time periods per year). Interest rate to use in tables is 6%. (12% / 2 = 6%) Annuity payment/receipt each six months = cash paid/received = Face value times stated rate times ½ = $1000 x 10% x ½ = $50 Sales/Purchase price of bond is: PvAmt = $1000 x .83962 = 839.62 (.83962 is the table factor from using a present value of amount table where n = 3, I = 6%) PvAo = $50 x 2.67301 =133.65 (2.67301 is the table factor from using a present value of an annuity table where n = 3, I = 6%) Purchase/sales Price will equal the sum of the above two amounts = 839.62 + 133.65 = 973.27

This bond is sold/purchased at a discount as a result of the stated interest rate of 10% being less that the effective interest rate of 12% annually. The bond is being sold/purchased at 97.327 or 97.327% of par. A bond that sells at a discount also means the true amount of interest agreed upon by the issurer/buyer is more than the $150.00 over the life of the bond. ($50.00 paid/received every six months for 1 ½ years, or a total of $150.00). The true amount of interest over a life of a bond can be determined by comparing the sum of the maturity value plus all interest payments to the issue/purchase price. In this case [$1000.00 + 3($50.00)] compared to $973.27; which equals a difference of $176.73. Therefore, the true amount of interest over the life of the bond is $176.73. This will be recognized in the books of the issuer/buyer over the three six-month periods using the Revenue Recognition Principle. There are two different ways the interest may be recognized over the life of the bond. One is the Straight-line method the other is the Effective Interest method.

The Straight-line method will take the total amount of interest over the life of the bond and divide by the number of periods to arrive at an equal amount then recognize this amount each period. The Effective Interest method will use the true interest rate (in this case 12%) and multiply it times the Carrying Value of the bond (Bond payable minus Discount amount, or Bond payable plus Premium amount). In this case it would be $1000.00 – $26.73 = $973.27, which you can see is the sales/purchase price to start with. The Carrying Value changes each period, and therefore, the Effective Interest method results in a slightly different amount of interest being recognized each period. The Effective Interest method is required under GAAP. The Straight-line method can be used if it is “not materially different” than the Effective Interest method. JOURNAL ENTRIES: Entry at date of sale/purchase: Seller/Issuer/Borrower: Cash 973.27 Discount on bond payable 26.73

Bond payable 1000.00

Buyer/Lender/Investor: Bond investment 973.27

Cash 973.27 OR Bond investment 1000.00

Discount on bond investment 26.73 Cash 973.27

Entry On Interest Payment Dates – Seller/Issuer/Borrower Only: Straight-Line Method: Bond Discount amortization each period would be equal to (1000.00 - 973.27) / 3 = 8.91 First Payment: Second Payment: Third Payment: Interest expense 58.91 58.91 58.91 Discount on B/P 8.91 8.91 8.91 Cash 50.00 50.00 50.00 Effective Interest Method: See below for amortization calculations.

First Payment: Second Payment: Third Payment:

Interest expense 58.40 58.90 59.43 Discount on B/P 8.40 8.90 9.43 Cash 50.00 50.00 50.00

Calculation of interest expense and amortization using the Effective Interest method follows: Carrying value times annual interest rate times time in relation one year equals the interest amount. Also remember that carrying value changes each period by the amount of discount amortization. 973.27 x 12% x 6/12 = 58.40 981.67 x 12% x 6/12 = 58.90 981.67 = 973.27 + (58.40 - 50.00) 990.57 x 12% x 6/12 = 59.43 990.57 = 981.67 + (58.90 - 50.00) After the third payment (at the maturity date) the carrying value would be equal to 1,000.00. (990.57 + 8.91 + 8.91 + 8.91) or (990.57 + 8.40 + 8.90 + 8.93) which means the bond is due to be paid off/collected. The following entry would be made on the maturity date: Entry on Maturity Date: Seller/Issuer/Borrower: Bond payable 1000.00

Cash 1000.00 Buyer/Lender/Investor: Cash 1000.00

Bond investment 1000.00

If instead of being issued on the interest date the bond was sold/purchased one month after the first interest date, there would be accrued interest and the entry for buying/selling would be a little different. Accrued interest = 1000.00 x 12% x 1/12 = 10.00. Entry at date of sale/purchase: Seller/Issuer/Borrower: Cash 983.27 Discount on B/P 26.73

Bond payable 1000.00 Interest payable 10.00

Buyer/Lender/Investor: Bond investment 973.27 Interest receivable 10.00

Cash 983.27 OR Bond investment 1000.00 Interest receivable 10.00

Discount on bond 26.73 Cash 983.27

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Recall from page one, when the stated rate of interest is more than the market rate of interest a bond would sell for a premium. As a result the interest expense of the seller and the interest revenue of the buyer would be less than the interest payment - just the opposite of a discount situation. An entry for a $1,000.00 bond selling at a premium of 5% (i.e., at 105) would be as follows: Seller/Issuer/Borrower: Cash 1050.00

Bonds payable 1000.00 Premium on bonds payable 50.00

Buyer/Lender/Investor: Bond investment 1050.00

Cash 1050.00 OR Bond investment 1000.00 Premium on bond investment 50.00

Cash 1050.00 Helpful Hint: Use T accounts for all entries to visualize the effects of each entry on the accounts.