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A zero-coupon bond is treated quite differently than a standard coupon bond in terms of timing but not character. In particular, zeros fall under the rules for original issue discount (OID) securities. A bond is designated OID if the issuance price is lower than the de minimis threshold. Therefore, a bond is deemed to be OID if the discount is more than 0.25 times the number of years to maturity. A 10-year corporate zero priced at 60 (percent of par value) easily passes that test – as would any 10-year, low-coupon bond, issued at a price below 97.5.

The key tax aspect of an OID bond is that the yearly movement along the constant-yield price trajectory is the reported ordinary interest income to the investor and interest expense to the issuer. These tax rules have been in effect since 1982; before that, straight-line amortization of the discount was allowed. That gave significant benefit to corporate issuers of zero-coupon bonds because the deductible interest expense was much more front-loaded than when the constant-yield trajectory is used.

An investor who buys and holds to maturity an OID bond will not have a capital gain because the discount will be taxed as ordinary income over the lifetime of the bond. The problem is that this is “phantom” income in that there is a tax liability each year despite the absence of a cash receipt to pay the tax. That creates a market segmentation effect – most zero-coupon bonds such as Treasury STRIPS are owned by defined benefit pension funds or by individuals in their retirement savings accounts, for example, 401(k)s. The other significant aspect to OID taxation is that capital gains and losses are measured from the constant-yield price trajectory if the bond is sold prior to maturity.

These tax rules for OID bonds match the economic fundamentals in that interest income is the price change caused purely by the passage of time. A capital gain or loss is the price movement caused by the change in value, meaning a change in the bond yield. We can see this in the 10-year zero-coupon bond issued at 60 (percent of par value) that we studied in Chapter 2. Its pretax cash flows are laid out in Figure 2.2, which shows year-by-year prices along the constant-yield trajectory. If the investor holds the bond to maturity (and there is no default), there is no capital gain for tax purposes despite buying at 60 and getting back 100. The full original issue discount of 40 is taxable ordinary interest income spread out over the 10-year life of the bond.

The investor's after-tax rate of return depends on the ordinary tax rates that prevail in each year and on the capital gains rate if the zero-coupon bond is sold prior to maturity. Let's suppose that the 10-year bond is purchased at 60 and sold two years later at 68. We calculate in Chapter 2 that this trade generates a horizon yield of 6.357% (s.a.) – but that is before OID tax consideration. Let's suppose that this investor's tax rate is 25% on ordinary income and 15% on capital gains. The OID ordinary interest incomes are 3.145 for the first year (= 63.145 – 60) and 3.309 for the second year (= 66.454 – 63.145). The annual income tax liabilities are 0.786 (= 3.145 * 0.25) and 0.827 (= 3.309 * 0.25), respectively.

When the bond is sold at 68, the taxable capital gain is 1.546 (= 68 – 66.454). If you remember your first financial accounting course, you'll note that the investor credits interest income and debits the bond investment by 3.145 after the first year and by 3.309 after the second year. Those entries raise the carrying book value (and the basis for taxation) of the zero-coupon bond up from 60 to 66.454. The capital gain represents the profit from selling at a price above that amount. The capital gains tax payment payable in year 2 is 0.232 (= 1.546 * 0.15).

The investor's after-tax horizon yield is the internal rate of return on the after-tax cash flows. These cash flows, year by year, are -60, -0.786, +66.941, using – to indicate outflows and + for inflows. The year-0 cash flow is negative because we are taking the perspective of the buyer of the bond. The year-1 cash flow is negative because of the phantom income problem and the tax liability. The year-2 after-tax inflow of 66.941 is the sale price of 68, less the ordinary income tax of 0.827 and the capital gains tax of 0.232. The after-tax rate of return, calculated on an effective annual rate basis, is the solution for aty in this expression:

Solving this equation requires trial-and-error search; 4.973% turns out to be the interest rate such that the net present value of all cash flows is zero. This is easily handled by a financial calculator that allows for variable cash flows or a spreadsheet program. To compare the after-tax rate of return to yields to maturity on standard bonds paying coupon interest twice a year, convert this effective annual rate to a semiannual bond basis. Using equation 1.10, it is the solution for APR2:

The investor's after-tax holding period rate of return is 4.913% (s.a.).

Given these OID tax rules, we now can see what a prodigious task it was to create synthetic zero-coupon Treasury bonds such as TIGRS, CATS, and LIONS in the 1980s. The Treasury bonds that went into the special-purpose entities were taxed as traditional coupon bonds issued at par value (or de minimis OID). By the way, these are called non-OID bonds. So, the financial engineering involved the transformation of non-OID Treasury bonds into OID Treasury zeros. That's why the IRS back then had to approve the SPE structures and issue statements clarifying how the TIGRS, CATS, and LIONS would be taxed.

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