Valuing Zero-Coupon Bonds

The value of a zero-coupon bond equals the present value of its face value discounted by the bond's contract rate.

Learning Objective

Explain how to value a zero coupon bond

Key Points

A zero-coupon bond is one that does not make ongoing interest payment to the bondholder over the term of the bond.
$\quad \frac { Face\quad Value\quad of\quad Bond }{ { (1+\quad interest\quad rate\quad of\quad bond) }^{ Term\quad of\quad Bond } } = Present Value of Zero-Coupon Bond.$
The issuing entity will sell the zero-coupon bond at lower than face value. When the bond's term is over, the issuing business will repay the bond at its face value.

Term

zero-coupon bond
A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity.

Example

A zero-coupon bond with requires repayment of $100,000 in 3 years. If the effective interest rate is 7%, what are the proceeds? How much interest expense is recognized? The proceeds will be the present value of $100,000 at 7% for 3 years: $\frac { 100,000 }{ { 1.07 }^{ 3 } }$ which is equal to $81,629.79. The journal entry for the firm issuing the bond is: Cash 81,629.79 Discount 18,370.21 Bond Payable 100,000.00 The discount is the difference between the bond payable (how much will be repaid at maturity) and the proceeds (the cash initially received); zero-coupon bonds will always be issued at a discount. The discount is a contra-liability linked to the bond payable; this yields a net bond payable of 81,629.79, the bond payable less the discount. Note: this is also the initial proceeds. The effective interest rate method indicates that interest expense must be recognized each period the bond is outstanding, even if no cash interest is being paid. The interest expense is the net payable times the effective rate, in this example: $81,629.79\times 7%$ %Which is 5,714.09. The journal entry to recognized the interest expense is: Interest Expense 5,714.09 Discount 5,714.09 The bond discount is reduced by 5,714.09 to 12,656.12, yielding a net bond payable of 87,343.88. Using the same calculation, the second and third years' interest expenses of 6,114.07 and 6,542.06 can be calculated. The total interest expense recognized at the end of the third year is 18,370.21, the total of the original discount, which is fully amortized at maturity.

Full Text

"Beat Back the Hun with Liberty Bonds"

After war was declared, the moral imperative of liberty and the Allied cause was touted in official, government-sponsored propaganda.

A zero-coupon bond is one that does not pay interest over the term of the bond. Instead, the entity will sell the bond at lower than face value. When the bond's term is over, the issuing business will repay the bond at its face value. The bondholder generates a return paying less than what he receives in payment at the end of the bond's term.

While the business may not make periodic interest payments, interest income is still generated. The interest income is merely accumulated and paid at the end of the bond's term.

Formula for Calculating Value of Zero-Coupon Bond

Zero-Coupon Bond Value = Face Value of Bond / (1+ interest Rate)

Generally, the price of a zero-coupon bond is based on the present value of the amount the issuing business will pay the bondholder when the bond matures. The amount the company pays at the end of the term equals the bond's face value. The present value is determined using the interest rate stated on the bond. The bond's term is used as the time period in the present value calculation.

It is important when completing the zero-coupon bond calculation to ensure the time period and term of the bond are expressed in similar terms. If the interest rate of the bond is expressed as a monthly rate and the term of the bond is 10 years, the bond term should be expressed as 120 months when making the calculation.

Example Calculation

Assume a business issues a 2 year note, paying 5% interest with a face value of $100,000. To calculate its present value, you would raise 1.05 to the tenth power. This equals 1.1025. You then divide $100,000 by 1.1025. The result is that the bond would have a present value of $90,702.95.

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