# Accounting for Zero-Coupon Bonds

A zero-coupon bond is a bond which does not pay any periodic interest but whose total return results from the difference between its issuance price and maturity value.

For example, if Company Z issues 1 million bonds of $1000 face value bonds due to maturity in 5 years but which do not pay any interest, it is a zero-coupon bond. The company must price the bond significantly below par to be able to sell it. ## Issuance of a zero-coupon bond In order to determine the amount at which to recognize the issuance of a zero-coupon bond, we need to be able to value it. The value of a zero-coupon bond equals the present value of its maturity value determined as follows: $$\text{PV} = \frac{\text{FV}}{(\text{1}+\text{r})^{\text{n}}}$$ Where PV is the present value of the bond, FV is the maturity value, r is the periodic discount rate and FV is the maturity value. Considering the example above, if the required return is 10%, the present value of a$1,000 bond due in 5 years would be $680.58. $$\text{PV} = \frac{\text{\1,000}}{(\text{1}+\text{8%})^{\text{5}}}=\text{\680.58}$$ This would result in total proceeds of$680.58 million which are recognized as follows:

 Bank $680.58 M Bond discount$319.42 M Bonds payable $1,000 M On the statement of financial position, the bonds are presented at an amount equal to the face value of the bonds minus the discount:  Bonds payable$1,000 M Bond discount ($319.42 M) Carrying amount$680.58 M

## Recognition of interest expense

Under the effective interest method, interest expense equals the product of carrying amount of the bonds and the effective interest rate:

Interest Expense = (Bonds Payable - Discount) × Effective Interest Rate

In the example above, interest expense equals $54.45 million (=$680.58 million × 8%). This is recognized using the following journal entry:

 Interest Expense $54.45 M Bond discount$54.45 M

The carrying amount of the bonds after the first interest payment is as follows:

 Bonds payable $1,000 M Bond discount ($319.42 million - $54.45 million) ($264.97 M) Carrying amount \$735.03 M