# Bond Premium Amortization

When a bond is issued at a price higher than its par value, the difference is called bond premium. The bond premium must be amortized over the life of the bond using the effective interest method or straight-line method.

A bond has a stated interest rate which is also called coupon rate. It pays periodic interest payments i.e. coupon payments based on the stated interest rate. If the market interest rate is lower than the coupon rate, the bond must trade at a price higher than its par value. It is because the bond is overcompensating the bond-holder in terms of interest payments and the bond must fetch a premium. This is based on the most fundamental time value of money relationship in that the present value decreases with an increase in the interest rate. A bond is valued at the present value of its future cash flows (i.e. coupon payments and the par value) determined based on the market interest rate.

## Issuance of Bond at Premium

Let’s consider a conventional bond with the following features:

Face value of bond | $1,000 |

Annual stated interest rate (coupon rate) | 5% |

Maturity in years | 5 |

Coupon payments per year | 2 |

Market interest rate | 4.8% |

By just comparing the market interest rate with the annual coupon rate, you can tell if the bond will trade a discount or premium. In this case, the bond will trade at a premium, hence it can be called a premium bond. It is because the bond pay interest at 5% which is higher than the prevailing interest rate in the market. The bond premium equals bond value determined at market interest rate minus the par value. The bond value is determined based on the market interest rate using the bond price formula:

$$ Bond\ Price\ (P)\\=$1,000\times2.5\%\times\frac{1-{(1+2.4\%)}^{-2\times5}}{2.4\%}+\frac{$1,000}{{(1+2.4\%)}^{2\times5}}\\=$1,008.80 $$

The bond will be issued at a premium of $8.80 per bond. If 100,000 bonds are issued, it must be recorded using the following journal entry:

Account | Dr | Cr |
---|---|---|

Cash | 100,879,746 | |

Bond payable | 100,000,000 | |

Bond premium | 100,879,746 |

## Payment of Interest and Amortization of Premium

After the first six-month period, you will pay interest on the bond based on the coupon rate. Your interest payment will be $2,500,000 (=100,000 × $1,000 × 5%/2).

At the time of issue of bonds, you received a cash of $100.9 million but your liability is $100 million. The difference of $0.9 million will be used over the life of the bond to reduce your interest expense. There are two methods to work out periodic amortization of bond premium: the effective interest method and the straight-line method.

Under the effective interest method, bond premium amortized each period is calculated using the following formula:

$$ Bond\ Premium\ Amortized=P\times m\ -\ F\ \times\ c $$

Where P is the bond issue price, m is the periodic market interest rate, F is the face value of the bond and c is the periodic coupon rate.

Under the straight-line method, bond premium is amortized equally in each period.

The journal entry for payment of interest and bond premium amortization is the same regardless of the method used. Let’s say you use the straight-line amortization method. The bond interest payment and amortization journal entry would be:

Account | Dr | Cr |
---|---|---|

Interest expense | $2,587,975 | |

Bond premium (879,746/10) | $87,975 | |

Cash | $2,500,000 |

## Bond Premium Amortization Schedule

Under the effective interest method, bond premium amortization in each period is different. It is useful to create an amortization schedule in such a situation. An amortization schedule lists each interest payment and reconciles it with interest expense showing period-wise amortization of bond premium. Following is the amortization schedule relevant to the bond payable discussed above:

Period | Interest Payment | Interest Expense | Amortization of Bond Premium |
Bond Premium | Carrying Value of Bond Payable |
---|---|---|---|---|---|

0 | 879,746 | 100,879,746 | |||

1 | 2,500,000 | 2,421,114 | 78,886 | 800,860 | 100,800,860 |

2 | 2,500,000 | 2,419,221 | 80,779 | 720,081 | 100,720,081 |

3 | 2,500,000 | 2,417,282 | 82,718 | 637,363 | 100,637,363 |

4 | 2,500,000 | 2,415,297 | 84,703 | 552,659 | 100,552,659 |

5 | 2,500,000 | 2,413,264 | 86,736 | 465,923 | 100,465,923 |

6 | 2,500,000 | 2,411,182 | 88,818 | 377,105 | 100,377,105 |

7 | 2,500,000 | 2,409,051 | 90,949 | 286,156 | 100,286,156 |

8 | 2,500,000 | 2,406,868 | 93,132 | 193,024 | 100,193,024 |

9 | 2,500,000 | 2,404,633 | 95,367 | 97,656 | 100,097,656 |

10 | 2,500,000 | 2,402,344 | 97,656 | 0 | 100,000,000 |

Written by Obaidullah Jan, ACA, CFA and last modified on