Issuing a bond is a way for a company to raise funds. When the bond is issued, the firm receives money from the investors which in turn become bondholders who will receive interest payments (‘the coupon’), and at maturity, receive the repayment of the principal.

When the firm is issuing a bond, the firm is offering to pay the nominal interest and the nominal amount of the bond. Because of legal proceedings, there is some time lag between deciding on the terms of the bond (which is a binding contract), and the actual bond issue. As market interest rates are changing continuously, it is not possible for the firm to ‘match’ the nominal interest rate with the rate that the market requires. Instead, changes in the market interest rates result in an issue price for the bond that is potentially different than the face value.

When the market requires a higher rate of return than the firm offers, investors will still be interested in buying the bond. However, they will require a discount. Similarly, when the market interest rate is below the nominal interest rate, investors will bid up, and pay a premium. Investors will bid a price where they will make their required return, regardless the terms of the bond.

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## Bond Example

The firm is issuing a 100 bonds, each with a 1,000 face value with a maturity of 5 years and nominal interest of 8%. At the day the bond issue is settled, investors are willing to pay 102% of the face value, i.e. 1,020 for each bond. The value of 1,020 corresponds with an effective interest rate of 7.5%.

Important: even though the interest payments are based on the nominal interest rate, the interest expense will equal the effective interest rate. When the investor earns the effective interest rate on its investment, the firm – as the party on the other side of the same deal – must have the same percentage as the effective interest expense.

In summary: when dealing with bonds, there are two percentages. The nominal interest rate which determines the interest payments and the effective interest rate, which is the interest expense. These are not the same because although the repayment at maturity is fixed by contract, the money received at time of issue determines the effective interest rate. Thus, a bond can be issued at the nominal value (at ‘par’), at a premium, or at a discount. The discount/premium is recorded on a contra T-account.

**Bond Premium/Discount Example**

The firm is issuing a 100 bonds, each with a 1,000 face value with a maturity of 5 years and nominal interest of 8%. At the day the bond issue is settled, investors are willing to pay 102% of the face value, i.e. 1,020 for each bond. The value of 1,020 corresponds with an effective interest rate of 7.5%.

At the day the issue is finalized, the market interest rate that is used to price this bond is 7.5%. Therefore, the bond is issued at a premium.

The value of a single bond is computed by discounting the cash flows (interest payment and repayment at maturity):

Period | Amount | Discount factor | Present value | |

1 | 80 | 1/1.075 | 74.42 | |

2 | 80 | 1/1.075^2 | 69.23 | |

3 | 80 | 1/1.075^3 | 64.40 | |

4 | 80 | 1/1.075^4 | 59.90 | |

5 | 1,080 | 1/1.075^5 | 752.28 | |

_____ | _____ | |||

1,400 | 1,020.23 |

Thus, for an investor that is using 7.5% as the interest rate, 74.42 today is equivalent to 80 one year later. Similarly, an investor (using 7.5%) is indifferent between buying the bond for 1,020.23 or not buying the bond.

The total interest expense equals the total interest payments minus a premium or plus a discount. In other words, when a bond is issued at a premium, the premium is a gain for the company, because it will only need to repay the nominal value. Similarly, when it is issued at a discount, the discount is an additional expense on top of the interest payments, because the firm will need to repay the nominal value (as this is determined by the bond contract). The matching principle requires that the discount/premium needs to be allocated over the lifetime of the bond.

There are two methods to allocate the premium/discount to the duration of the bond: the straight line method, and the effective interest method.

With the straight line method the premium/discount is amortized linearly over the duration of the bond.

**Bond Journal Entry Example**

The firm is issuing a 100 bonds, each with a 1,000 face value with a maturity of 5 years and nominal interest of 8%. At the day the bond issue is settled, investors are willing to pay 102% of the face value, i.e. 1,020 for each bond. The value of 1,020 corresponds with an effective interest rate of 7.5%.

The journal entry of issuing the bond (numbers are rounded):

T-account | Debit | Credit | |

Cash | 102,000 | ||

Bond payable | 100,000 | ||

Bond premium | 2,000 |

The yearly journal entry for the interest payment:

T-account | Debit | Credit | |

Interest expense | 7,600 | ||

Bond premium | 400 | ||

Cash | 8,000 |

*400 = 2,000 / 5 years

When the effective interest method is used, the bond remains valued over the duration of the bond at the present value of the interest payments and repayment at maturity.

It is helpful to make a repayment schedule, to highlight the difference between the interest payment and interest expense over time. The repayment schedule will show for each year the beginning of year present value of the bond, the interest expense (= effective interest rate x beginning of year present value), the interest payment (=nominal interest rate x nominal value) and the end of the period present value of the bond(=beginning value + interest expense – interest payment).

In case of a premium, in each period, the interest expense will be less than the interest payment. Similarly, in case of a discount, the interest expense will be greater than the interest payment. Regardless whether there is a premium or discount, at maturity, all of the premium/discount will have been allocated.

**Present Value Bond Example**

The expense is computed as the beginning of year present value multiplied by the effective interest rate. The interest payments and repayment are dictated by the terms of the bond.

The journal entry of the first year’s interest payment (for the 100 bonds in total):

T-account | Debit | Credit | |

Interest expense | 7,652 | ||

Bond premium | 348 | ||

Cash | 8,000 |

The journal entry of the last year’s interest payment and repayment of the nominal value:

T-account | Debit | Credit | |

Bond | 100,000 | ||

Interest expense | 7,535 | ||

Bond premium | 465 | ||

Cash | 108,000 |

Note that the sum of the total interest expense (379,77) equals the total interest payments (400) minus the premium (20.23), which is received at time of issue, but does not have to be repaid.

When a bond is callable, the firm has the right (not the obligation) to repay the bond at an earlier point in time than the maturity date. This option has value for the firm when interest rates have declined. In this case, the firm can lower its interest expenses by repaying the bond with the proceeds of a new bond. Bondholders, however, will require to be compensated for allowing the firm to have such an option. The terms of the bond will therefore include a penalty to be paid by the firm to the bondholders when the firm calls the bond.

## Bonds Explained

**Key points:**

– the firm can issue a bond to fund their operations; bondholders pay for the bond in return for interest payments and repayment of the principal at maturity

– the nominal interest rate is used to compute the interest payments

– investors use the market interest rate to price the bond at issue, the resulting issue price implies an effective interest rate on the bond

– the effective interest rate is only equal to the nominal interest rate if the issue price equals the nominal value

– the effective interest rate is the return that bondholders will make if they hold until maturity (and the firm does not default); it is also the interest expense for the firm

– if the effective interest rate is lower than the nominal interest rate (used to compute the interest payments), investors are willing to pay a premium for the bond at time of issue

– if the effective interest rate is higher than the nominal interest rate (used to compute the interest payments), investors are demanding a discount in order to buy the bond at time of issue

– the premium/discount are recorded at a contra T-account to bond payable and are amortized over the term of the bond

– the straight line method amortizes the premium/discount in yearly equal amounts

– the effective interest method amortizes the premium/discount so that the carrying value of the bond equals the present value of the remaining interest payments and repayment at maturity