## Zero Coupon Bonds

A bond that pays no coupons at all must be offered at a price that is much lower than its stated value. Such bonds are called zero coupon bonds, or just zeroes.5

Suppose the Eight-Inch Nails (EIN) Company issues a \$1,000-face value, five-year zero coupon bond. The initial price is set at \$497. It is straightforward to verify that, at this price, the bond yields 15 percent to maturity. The total interest paid over the life of the bond is \$1,000 - 497 = \$503.

For tax purposes, the issuer of a zero coupon bond deducts interest every year even though no interest is actually paid. Similarly, the owner must pay taxes on interest accrued every year, even though no interest is actually received.

The way in which the yearly interest on a zero coupon bond is calculated is governed by tax law. Before 1982, corporations could calculate the interest deduction on a straight-line basis. For EIN, the annual interest deduction would have been \$503/5 = \$100.60 per year.

Under current tax law, the implicit interest is determined by amortizing the loan. We do this by first calculating the bond's value at the beginning of each year. For example, after one year, the bond will have four years until maturity, so it will be worth \$1,000/1.154 = \$572; the value in two years will be \$1,000/1.153 = \$658; and so on. The implicit interest each year is simply the change in the bond's value for the year. The values and interest expenses for the EIN bond are listed in Table 7.2.

zero coupon bond

A bond that makes no coupon payments, thus initially priced at a deep discount.

5A bond issued with a very low coupon rate (as opposed to a zero coupon rate) is an original-issue discount (OID) bond.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

7. Interest Rates and Bond Valuation

© The McGraw-Hill Companies, 2002

PART THREE Valuation of Future Cash Flows

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