Consider a company that issues bonds with a face value of $100,000 and a coupon rate of 6% payable annually for a fixed term of three years. Face value refers to the amount that the company promises to return to lenders at the end of the term. Coupon rate is the contracted rate at which the company agrees to pay interest and the dollar amount of such payment is called the coupon payment. In our example, the coupon payment is $6,000 per year.
The effective interest rate is the rate that the market assigns to the bond at the time of its issuance. This rate determines the present value of the bond at the time of issuance, whichequals the cash proceeds that the company receives from the bond issue. The effective interest rate is determined by the market after considering factors such as the prevailing risk-free interest rate and the bond’s term and riskiness. There needs to be no relation between the coupon rate and the effective interest rate. For example, companies issue zero coupon bonds, where the only payment to the investors is the face value at the end of the term. Such bonds are also present valued by the market at some effective interest rate.
To understand the mechanics of bonds and their accounting, we consider three different effective interest-rate scenarios: 6%, 3%, and 10%. Exhibit 3.1 illustrates these scenarios. First, consider the 6% interest-rate scenario. In this case, the present value of thebond at issue which is represented by Year 0 exactly equals $100,000.1 Because the company gets to raise exactly the face value, we say that the bonds were issued at par. In this scenario, interest expense (Effective interest rate Beginning of period present value) also exactly equals the coupon payment of $6,000 (6% $100,000) in each year.
Now consider the case where the effective interest rate is 3%. The present value at the time of issue is now $108,486. Because the market values the bonds at their present value, the company gets to issue the bonds above the face value of $100,000, or at a premium of $8,486. Interest expense is now much lower than the coupon payment. For example, in Year 1 it is $3,255 (3% $108,486). Therefore, when the company pays the $6,000 coupon to the lenders, it is as if the company is also returning principal to the tune of $2,745 ($6,000 $3,255), which reduces the present value of the bond. We refer to this $2,745 as amortization of bond premium. Note that the interest expense and the amortization are not the same every year, but the two will always add up to the coupon payment.
When the interest rate is much higher than the coupon rate, then the mirror image of the “premium” scenario unfolds. The present value at issue is $90,053. Therefore, the company issues the bonds below face value or at a discount of $9,947. Every year, interest expense is higher than the coupon payment, and so it is as if the company is borrowing more every year, therefore increasing the present value of the bond. For example, in Year 1 this notional borrowing which we call amortization of bond discount is $3,005 ($9,005 $6,000).
The effective interest rate is the rate that the market assigns to the bond at the time of its issuance. This rate determines the present value of the bond at the time of issuance, whichequals the cash proceeds that the company receives from the bond issue. The effective interest rate is determined by the market after considering factors such as the prevailing risk-free interest rate and the bond’s term and riskiness. There needs to be no relation between the coupon rate and the effective interest rate. For example, companies issue zero coupon bonds, where the only payment to the investors is the face value at the end of the term. Such bonds are also present valued by the market at some effective interest rate.
To understand the mechanics of bonds and their accounting, we consider three different effective interest-rate scenarios: 6%, 3%, and 10%. Exhibit 3.1 illustrates these scenarios. First, consider the 6% interest-rate scenario. In this case, the present value of thebond at issue which is represented by Year 0 exactly equals $100,000.1 Because the company gets to raise exactly the face value, we say that the bonds were issued at par. In this scenario, interest expense (Effective interest rate Beginning of period present value) also exactly equals the coupon payment of $6,000 (6% $100,000) in each year.
Now consider the case where the effective interest rate is 3%. The present value at the time of issue is now $108,486. Because the market values the bonds at their present value, the company gets to issue the bonds above the face value of $100,000, or at a premium of $8,486. Interest expense is now much lower than the coupon payment. For example, in Year 1 it is $3,255 (3% $108,486). Therefore, when the company pays the $6,000 coupon to the lenders, it is as if the company is also returning principal to the tune of $2,745 ($6,000 $3,255), which reduces the present value of the bond. We refer to this $2,745 as amortization of bond premium. Note that the interest expense and the amortization are not the same every year, but the two will always add up to the coupon payment.
When the interest rate is much higher than the coupon rate, then the mirror image of the “premium” scenario unfolds. The present value at issue is $90,053. Therefore, the company issues the bonds below face value or at a discount of $9,947. Every year, interest expense is higher than the coupon payment, and so it is as if the company is borrowing more every year, therefore increasing the present value of the bond. For example, in Year 1 this notional borrowing which we call amortization of bond discount is $3,005 ($9,005 $6,000).
Thus far, we have estimated present value using the market interest rate at the time of issue. In reality, however, bond prices fluctuate as interest rates change over time. The fair value of the bond is the present value of the bond discounted at the current interest rate, rather than the rate at the time of issue. It happens to also equal the current market value of the bond. For example, in our “discount” scenario, if the interest rate drops from 10% to 7% at the end of Year 1, the fair value of the bond at Year 1 end would be $98,192(present value of the remaining two coupon payments and face value discounted at 7%). If the interest subsequently dropped to 3% by the end of Year 2, the fair value at Year 2 end would be $102,913 (present value of one remaining coupon payment and face value discounted at 3%).
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