As we know, **bonds** are also issued at **other than face value**, i.e. above or below their face value. If the prevailing market interest rate is above the stated rate, the bonds will be **issued at a discount**. conversely, if the prevailing interest rate is below the stated rate, the bonds will be issued at a premium.

## Accounting for Bonds Issued at a Discount

To illustrate the issuance of bonds at a discount, assume that on January 2, 2020, the Valenzuela Corporation issues $100,000, 5-year, 12% term bonds. The interest of 6% is payable semiannually on January 2 and July 1. The bonds were issued when the prevailing market interest rate for such investments was 14%. Thus the bonds were issued at a discount to yield 14%. This rate is also called the effective interest rate. Based on this effective rate, the bonds would be issued at a price of 92.976, or $92,976.

The journal entry to record the Valenzuela bonds shown as:

As this entry illustrates, Cash is debited for the actual proceeds received, and Bonds Payable is credited for the face value of the bonds. The difference of $7,024 is debited to an account called Discount on Bonds Payable.

This Discount on Bonds Payable account is a contra-liability account in that it is offset against the Bonds Payable account on the balance sheet in order to arrive at the bonds’ net carrying value. To illustrate, a balance sheet prepared on January 2, 2020, immediately after the bonds were issued, would show the following under the long-term liability section:

### Using Present Value to determine Bond Prices

This section explains how to use present-value techniques to determine bond prices. If you have not covered present-value concepts or your professor instructs you to do so, this section may be omitted with no loss of continuity.

Given the prevailing market interest rate, the stated or coupon interest rate, and the maturity date, bond prices can be calculated using present-value techniques. When bonds are issued, the borrower agrees to make two different types of payments: an annuity made up of the future cash interest payments and a single future amount constituting the bond’s maturity value. Rational investors would not pay any more than the present value of these two future cash flows, discounted at the desired yield rate.

**Exhibit ‘A’**

The issue price of $92,976 is calculated in the above Exhibit. As this exhibit indicates, the issue price is composed of the present value of the maturity payment of $100,000 discounted at 7% for 10 periods, and the present value of semiannual cash interest payments of $6,000 ($100,000 x .06) also discounted at 7%. The periods are used because the 5-year bonds pay interest semiannually.

The discount rate is the semiannual yield, or an effective rate of 7%. You should remember that the $6,000 annuity; which is the cash interest payment, is calculated on the actual semiannual coupon rate of 6%. Borrowers and investors need not make these calculations. Various bond tables are available that determine the correct prices at different yield rates and maturity dates.

### The Nature of the Discount Account

It is important to understand the nature of the Discount on Bonds Payable account. In effect, the discount should be thought of as an additional interest expense that should be amortized over the life of the bond. Remember that the bond was issued at a discount because the stated rate was below the market rate. The bondholders are receiving only $6,000 every 6 months, whereas comparable investments yielding 14% are paying $7,000 every 6 months ($100,000 x .07).

The discount of $7,024 represents the present value of that $1,000 difference that the bondholders are not receiving over each of the next 10 interest periods (5 years’ interest paid semiannually). Essentially the company incurs that additional interest of $7,024 at the time of issuance by receiving only $92,976 rather than $100,000. But, because of the-matching concept, this cost of $7,024 cannot be expensed when the bonds are issued but must be written off over the life of the bond.

As a result of issuing the bonds at a discount, the total interest expense incurred by the Valenzuela Corporation over the 5-year life of the bond is $67,024, calculated as follows:

Another way to view this is to look at the difference between the cash that the company will eventually repay the bondholders versus what it received at the time of issuance. This calculation is:

## Amortizing the Discount

The discount of $7,024 must bc written off or amortized over the life of the bond. There are two methods used to do this; the straight-line method and the effective-interest method. The effective-interest method is conceptually preferable, and accounting pronouncements require its use unless there is no material difference in the periodic amortization between it and the straight-line method.

However, the straight-line method is easy to compute and understand and so it is examined first in order to aid in your understanding of the concepts.

### The Straight-tine Method

The straight-line method simply allocates the discount evenly over the life of the bond. There is a constant interest charge each period. An entry is usually made on every interest date, and if necessary, an adjusting journal entry is made at the end of each period to record the discount amortization.

To demonstrate the application of the straight-line method, we will return to the Valenzuela Corporation example. In this case, the discount of $7,024 will be amortized over 10 interest periods at a rate of $702 per interest period ($7,024 / 10). The total interest expense for each period is $6,702, consisting of the $6,000 cash interest and the $702 amortized discount. Another way to calculate the $6,702 is to divide the total interest cost, $67,024, as shown above into the 10 interest periods of the bond’s life, journal entry at July 1, 2020, and each interest payment date thereafter is:

As the bonds approach maturity, their carrying value increases, and the result of this and subsequent entries is to reflect this increase in the carrying value of the bonds. This is because of the discount account, which is offset against bonds payable in arriving at the bonds’ carrying value, is decreased each time a credit entry is made to that account. To Illustrate, the relevant T accounts and a partial balance sheet as of July 1, 2020, are presented next:

In each interest period, the bond’s carrying value will be increased by $702, so that by the time the bond matures, the balance in the Discount on Bonds Payable account will be zero, and the bond’s carrying value will be $100,000. The below Exhibit ‘B’ presents an amortization schedule for this bond on the straight-line method. Thus, when the company repays the principal it makes the following entry:

**Exhibit ‘A’**