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LINKER TAXATIONThis discussion of the taxation of inflationindexed bonds is going to be simplistic, especially after the detail of Chapter 4. The stylized PLinker and CLinker are assumed to be purchased at par value and held to maturity. There are no capital gains or losses and no de minimis OID, just ordinary income tax. My objective is to demonstrate that these two designs offering inflation protection generate very different aftertax cash flows. Moreover, when the inflation rate is high, the aftertax real rates of return become negative. That explains why linkers usually are held in taxdeferred, retirement portfolios like definedbenefit and definedcontribution pension funds. Table 7.5 shows the aftertax cash flows on the 2.50%, annual payment, 10year PLinker assuming a 30% tax rate on ordinary income and the highinflation scenario. On date 6, the inflation rate for the year reaches double digits, 15.626%, raising the accrued principal up to $1,613.63 from $1,395.56. The interest payment is $40.34 (= 0.0250 * $1,613.63). The tax obligation on the interest income is $12.10 (= 0.30 * $40.34). But PLinker taxation does not stop there – the increase in the accrued principal is taxed as ordinary income in the current year even though that compensation for inflation is not received until maturity. This is another example of phantom income. The tax liability on the increase in the accrued principal is $65.42 [= 0.30 * ($1,613.63 – $1,395.56)]. The total tax obligation is $77.52 (= $12.10 + $65.42), resulting in an aftertax cash flow of$37.18 (= $40.34 – $77.52). Negative aftertax cash flows for the PLinker start in the third year and last until maturity in this highinflation scenario. A useful calculation for the investor is the threshold inflation rate, shown in equation 7.11, which indicates the point at which negative aftertax cash flows arise. It's derived in the Technical Appendix. TABLE 7.5 AfterTax Cash Flows on the 2.50%, 10Year, Annual Payment PLinker, HighInflation Scenario, 30% Tax Rate
(7.11) Fixed Rate is the coupon rate on the PLinker, here 2.50%, and Tax Rate is the applicable rate on ordinary income, here 30%. Substituting those into equation 7.11 gives a threshold rate of 6.195%. In general, the lower the fixed coupon rate and the higher the tax rate, the lower is the threshold inflation rate that results in negative aftertax cash flow. The aftertax cash flows for the 2.50%, annual payment, 10year CLinker are shown in Table 7.6 for the same highinflation scenario. For the sixth year when the inflation rate is 15.626%, the coupon rate is set at 18.126% (= 2.50% + 15.626%) and the interest payment is $181.26 per $1,000 in par value. The tax obligation is $54.38 (=0.30 * $181.26), leaving TABLE 7.6 AfterTax Cash Flows on the 2.50%, 10Yeag Annual Payment CLinker, HighInflation Scenario, 30% Tax Rate
an aftertax cash flow of $126.88 (= $181.26 – $54.38). This is much more straightforward than the PLinker – there is no taxable phantom income or negative aftertax cash flow. The sad news is that both of these linkers are projected to deliver negative aftertax real IRRs. To be sure, the realized real rates of return will depend on actual real rates when the coupons are reinvested. These results ultimately depend on the particular price and rate assumptions. It's easy to put these stylized linkers onto a spreadsheet to see the impact of lowering the purchase price, raising the fixed coupon rate, lowering the tax rate, and lowering the average inflation rate. Those changes raise the aftertax real IRR and can make it a positive outcome. For instance, other things being equal, if the tax rate is less than 23.04% on this 2.50%, 10year PLinker, and less than 22.21% on the CLinker, the aftertax IRRs are above zero. An individual investor can manage the tax problem by holding the linker in a taxdeferred, retirement savings account like a 401(k) or 403(b). Doing so won't make the tax obligation go away, but will allow the investment to compound at the beforetax real yield. Yield duration in Chapter 6 is defined as the sensitivity of the fixedincome bond price to a change in the nominal yield to maturity. Inflationindexed bonds require that we focus on why the nominal rate changes and distinguish between a change in the real rate and a change in the inflation rate. Let's start by formalizing the stylized linkers, keeping close to the notation of Chapter 3. Let the nominal rate be y, the real rate r, and the inflation rate i. Also, let the number of periods to maturity be N, the fixed coupon rate c, the par (or face) value of the linker FV, and the current price PV. For these stylized linkers, we are on a coupon payment date so there is no accrued interest to sully the equations. PLinker valuation is based on the assumed path for the accrued principal. Given a constant inflation rate, this path will be (1 + i) * FV, (1 + i)2 * PV, ..., (1 + i)N * PV. Then the price of the PLinker, denoted PVPLINK, is the present value of the cash flows, discounted at the nominal rate. 
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