Bonds are often acquired at a discount from, or premium over, their face value.
Discount bonds are bonds acquired at an amount less than their face value and premium bonds are acquired at an amount greater than their face value. Discount or premium results when the bonds are purchased at an effective yield (market interest rate) that differs from the stated coupon rate on the bonds. If the effective yield is greater than the coupon rate, the bonds will be acquired at a discount. If the effective yield is less than the coupon rate on the bonds, the bonds will be purchased at a premium. The discount or premium on the bonds is an adjustment to the stated or coupon rate of interest on the bonds and must be amortized as an adjustment to interest revenue over the remaining term of the bonds. There are two methods of amortizing bond premium or discount. They are the straight line method and the effective interest method.
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a. Straight Line Amortization of Bond Discount or Premium
For purposes of illustrating the treatment of bond discount or premium, assume that a
$1,000,000 bond issue is acquired on July 1, 201x, with a 9% stated interest rate payable semi-annually on June 30 and December 31. The bonds are ten-year bonds and mature on June 30, 201x. The bonds are acquired at a discount of $119,500 from face value.
That means that the bonds are acquired at a price of $880,500. This price reflects an actual yield on the bonds over their term to maturity of 11% rather than the stated or coupon rate of 9%. (The price of the bonds is the discounted present value of the scheduled payments of interest and principal on the bonds using the market rate as the discount rate. See Appendix A for a review of present value calculations.)
The acquisition of the bonds would be recorded as follows:
Investment in Bonds $1,000,000
Bond Discount $119,500
Cash $880,500
The bonds are recorded at their face value and the discount is recorded in a separate account in order to assist in keeping track of the remaining discount on the bonds. If a balance sheet were prepared immediately after the acquisition of these bonds, they would be reported in the balance sheet
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at $880,500, the net of the face amount minus the bond discount.
The $119,500 of bond discount will be amortized and recognized as additional interest income over the term of the bonds. As the discount is amortized, the bond discount account will be reduced until the maturity date of the bonds, at which point the bond discount will be zero and the carrying amount of the bonds will be their face value of
$1,000,000. Under the straight line method of amortization, the bond discount is amortized in equal amounts over the term of the bonds. For each six-month interest period during the term of the bonds, 1/20th of the total discount, or $5,975, will be amortized.
On December 31, 201x, the receipt of the first interest payment and the amortization of bond discount would be recorded as follows:
Cash $45,000
Bond Discount $ 5,975
Interest Income $50,975
The total interest income of $50,975 includes the cash interest of $45,000 plus the amortized bond discount of $5,975. The interest income attributable to bond discount will not actually be received in the form of cash until the bonds are repaid at their full face amount on the date of maturity.
If the bonds are acquired at a premium, a similar amortization process is followed. The premium on
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the bonds represents a reduction in the effective interest rate on the bonds since the purchaser is paying more for the bonds than will be received at the maturity date of the bonds. To illustrate, assume that the 9% bond issue described above is acquired at a premium over the face value of the bonds of $142,120, or a total price of $1,142,120. The effective yield on these bonds would be 7% rather than the coupon rate of 9%. The entry
to record the acquisition of the bonds would be:
Investment in Bonds $1,000,000
Bond Premium $ 142,120
Cash $1,142,120
Using the straight line method of amortization, the interest income on December 31, 201x, would be recorded as follows:
Cash $45,000
Bond Premium $ 7,106
Interest Income $37,894
In effect, a portion of the stated interest payment represents a return of the bond premium paid at the time of acquisition since the holder of the bonds will only receive the face value of $1,000,000 at the maturity date. The same entry would be made for each of the twenty semi-annual interest payments over the life of the bonds. At the end of the term of the bonds, the entire bond premium will have been amortized and the carrying value of the bonds will be their face value of $1,000,000.
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b. Effective Interest Method of Amortizing Bond Discount and Premium
If the effective interest method is used for amortizing bond discount or premium, the format of all the entries remains the same as illustrated above but the method of computing each period’s amortization of bond discount or premium is different. The effective interest method of computing the amortization results in the same effective yield (rate of return) being reported on the bonds for each interest payment period. The amount of amortization in each period is computing by multiplying the carrying value of the bonds (face value of the bonds less any discount or plus any premium) at the beginning of the period by the effective interest rate or yield to maturity implied by the initial purchase price of the bonds. This produces the interest income to be reported for the period. The difference between the interest income computed in this manner and the stated or coupon interest payment for the period is the amount of bond discount or premium to be recognized for that period.
In the illustration above in Section A.2.a., the bonds purchased at a discount provide a yield to maturity of 11% compounded semi-annually. To compute the bond discount for the first interest period under the effective interest method, the carrying value of
$880,500 is multiplied by the effective yield for half a year of 5.5%. The resulting amount of $48,427.50 is the total interest income for the period. Since the actual interest payment on the bonds
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is only $45,000, the bond discount to be amortized is the difference between these two amounts, or $3,427.50. The entry to record interest revenue would be:
Cash $45,000.00
Bond Discount $ 3,427.50
Interest Income $48,427.50
At the time of the second interest payment, the new carrying value of the bonds is
$883,927.50 (the initial carrying value of $880,500 plus the bond discount amortized in the first period of $3,427.50). For the second interest period ending on June 30 of the following year, the interest income will be $48,616.01 ($883,927.50 × 5.5%). The bond discount amortized in the second period would be $3,616.01. Note that the bond discount amortized using the effective interest method increases each period because the carrying value of the bonds increases each period. While the semi-annual amortization is initially less than that under the straight line method ($5,975), the semi-annual bond discount amortization will eventually be greater under the effective interest method as the bonds approach maturity.
The procedure for amortization under the effective interest method is the same in the case of bond premium. In the bond premium example above, bonds were purchased at a premium of $142,124 to yield 7% effective interest, compounded semi-annually. To compute the bond premium for the first interest period, the initial carrying value of
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$1,142,124 would be multiplied by 3.5% to calculate the total interest income for the first semi-annual period of $39,974.34. Since the stated interest is $45,000, the amount of bond premium to be amortized would be $5,025.66. In the second interest period ending June 30 of the following year, the carrying value at the beginning of the period would be $1,137,098.34 ($1,142,124 minus $5,025.66). The interest income for the second period using the effective interest method would be $39,798.44 (3.5% of
$1,137,098.34). The bond premium amortized in the second period would therefore be
$5,201.56 ($45,000 minus $39,798.44). The amount of bond premium amortized in each period will continue to decrease as the bonds approach maturity and the carrying value approaches the face amount of $1,000,000.