# Bond Discount Amortization

Bond discount amortization is the process through which bond discount written off over the life of the bond. There are two primary methods of bond amortization: straight-line method and effective interest rate method. An amortization schedule lists bond payments, bond discount amortization and interest expense for each period.

Bond discount arises when the rate of return expected in the market on a bond is higher than the bond’s coupon rate. This causes the bond to sell at a price lower than the face value of the bond and the difference is attributable to bond discount. Similarly, bond premium occurs when the coupon rate is higher than the market expectation of required return. Due to higher coupon rate, there is high demand for the bond and it sells for a price higher than the face value of the bond. The difference between the face value of the bond and the bond price is called bond premium.

## Issue of bond at discount

Let’s consider a $1,000 bond due to mature in 10 years paying 6% semi-annual coupon rate when the market interest rate is 6.2%. You can verify that this bond will sell at$985.26. If the 10,000 bonds are issued, total bond proceeds will be $9,852,591. You will need to pass the following journal entry to record the issue of this bond:  Bank$9,852,591 Bond discount $147,409 Bond payable$10,000,000

Total bond liability equals $10 million i.e. the product of 10,000 number of bond and the bond face value of$1,000. Because actual cash proceeds are $9,852,591, the bank is debited by this amount and the balancing figure is attributable to bond discount. Bond discount is a contra-account to the bond payable account on the balance sheet. Bond carrying value i.e. book value on the balance sheet equals the bond face value minus the bond discount i.e.$9,852,591.

 Bond payable $10,000,000 Bond discount ($147,409) Net bond payable $9,852,591 ## Interest payment and bond discount amortization After six months, the issuer will make interest payments amounting to$300,000 (10,000 × $1,000 × 6%/2). However, the interest expense will be higher than the coupon payments due to amortization of bond discount. ### Straight-line method Under the straight-line method, bond discount amortized in each period will equal total bond discount divided by total number of periods. In this case, it works out to$7,370 (=$147,409/20). $$\text{Bond Amortization}\ (\text{Straight Line Method})=\frac{\text{BD}}{\text{n}\times \text{m}}$$ Where BD is the total bond discount, n is the bond life in year and m is the total coupon periods per year. ### Effective interest method Under the effective interest method, bond discount amortization each period equals the difference between the product of bond carrying value and market interest rate and the product of bond face value and the coupon rate. Following is the formula for bond amortization: $$\text{Bond Amortization}\ (\text{Effective Interest Method})\\=\text{BV}\times \text{r}/\text{m}\ -\ \text{FV}\times \text{c}/\text{m}$$ Where FV is the face value of the bond, c is the periodic coupon rate, BV is the book value of the bond and r is the market or effective interest rate i.e. the interest rate that causes the bond cash flows to equal its issue price. In case of the example above, bond discount amortization in the first period is$5,430 (=$9,852,591×6.2%/2 -$10,000,000×6%/2) and it increases as the bond nears its maturity.

The journal entry for the bond discount amortization under the straight-line method for the first interest period will be as follows:

 Interest expense $307,370 Bond discount$7,370 Bank $300,000 Because the bond discount has a debit balance, a credit to it reduces it balance and because the bond discount is a contra-account to the bond payables account, the carrying value of bond issued at discount increased after bond discount amortization. Bond carrying value after the first payment and amortization equals$9,859,962:

 Bond payable $10,000,000 Bond discount (147,409-7,370) ($140,039) Net bond payable $9,852,591 Similarly, the journal entry for interest payment and bond amortization under the effective interest method is as follows:  Interest expense$305,430 Bond discount $5,430 Bank$300,000

Bond carrying amount after first payment shall be $9,858,022 ## Bond discount amortization schedule A bond discount amortization table is a useful tool that lists all the expected bond payments, bond discount amortization to be charged each period, the consequent bond interest expense the relevant bond carrying value. Using the example above, following is a bond amortization schedule based on the straight-line method of bond discount amortization: Period Interest Payment Bond Discount Amortization Interest Expense Book Value IP=$FV × c/m BDi=$147,409/20 IE = IP+BD BV=BVi-1 + BDi 0$9,852,591
1 $300,000$ 7,370 $307,370$ 9,859,962
2 $300,000$ 7,370 $307,370$ 9,867,332
3 $300,000$ 7,370 $307,370$ 9,874,703
4 $300,000$ 7,370 $307,370$ 9,882,073
5 $300,000$ 7,370 $307,370$ 9,889,444
6 $300,000$ 7,370 $307,370$ 9,896,814
7 $300,000$ 7,370 $307,370$ 9,904,185
8 $300,000$ 7,370 $307,370$ 9,911,555
9 $300,000$ 7,370 $307,370$ 9,918,926
10 $300,000$ 7,370 $307,370$ 9,926,296
11 $300,000$ 7,370 $307,370$ 9,933,666
12 $300,000$ 7,370 $307,370$ 9,941,037
13 $300,000$ 7,370 $307,370$ 9,948,407
14 $300,000$ 7,370 $307,370$ 9,955,778
15 $300,000$ 7,370 $307,370$ 9,963,148
16 $300,000$ 7,370 $307,370$ 9,970,519
17 $300,000$ 7,370 $307,370$ 9,977,889
18 $300,000$ 7,370 $307,370$ 9,985,260
19 $300,000$ 7,370 $307,370$ 9,992,630
20 $300,000$ 7,370 $307,370$ 10,000,000

Here’s the bond discount amortization schedule based on the effective interest method:

Period Interest Payment Bond Discount Amortization Interest Expense Book Value
FV× c/m BDi=BVi-1 × r/m - FV× c/m BVi-1 × r/m BV=BVi-1 + Bdi
0 $9,852,591 1$ 300,000 $5,430$ 305,430 $9,858,022 2$ 300,000 $5,599$ 305,599 $9,863,620 3$ 300,000 $5,772$ 305,772 $9,869,393 4$ 300,000 $5,951$ 305,951 $9,875,344 5$ 300,000 $6,136$ 306,136 $9,881,480 6$ 300,000 $6,326$ 306,326 $9,887,805 7$ 300,000 $6,522$ 306,522 $9,894,327 8$ 300,000 $6,724$ 306,724 $9,901,052 9$ 300,000 $6,933$ 306,933 $9,907,984 10$ 300,000 $7,148$ 307,148 $9,915,132 11$ 300,000 $7,369$ 307,369 $9,922,501 12$ 300,000 $7,598$ 307,598 $9,930,098 13$ 300,000 $7,833$ 307,833 $9,937,931 14$ 300,000 $8,076$ 308,076 $9,946,007 15$ 300,000 $8,326$ 308,326 $9,954,333 16$ 300,000 $8,584$ 308,584 $9,962,918 17$ 300,000 $8,850$ 308,850 $9,971,768 18$ 300,000 $9,125$ 309,125 $9,980,893 19$ 300,000 $9,408$ 309,408 $9,990,301 20$ 300,000 $9,699$ 309,699 \$ 10,000,000