## Wednesday, November 21, 2018

### Taxes and the viability of zero coupon bonds

Taxes and the viability of zero coupon bonds

The questions presented here were motivated by this short article on zero coupon bonds.

Questions:

What is the pre-tax yield on a zero-coupon bond when you pay \$3,500 for a bond that returns \$10,000 in twenty years?

You purchase this bond outside a tax-preferred account.   The IRS requires you to impute interest on the bond and pay tax on the bond each year.   How much tax do you pay for interest earned on the bond each year?

Calculate the after-tax yield on the bond assuming the bond was purchased on January 1 of a given year, matures 20 years hence and that taxes are paid each year on April 1.

Briefly, discuss why zero-coupon bonds might be a great asset to hold in a retirement account.

Analysis:

The yield on the zero-coupon bond prior to tax or without tax is calculate two ways.   Calculations are laid out below.

 Calculation of Zero Coupon Bond Yields Method One Bond Purchase I 3500 Face Value in 20 years F 10000 Yield (F/i)(1/20)-1 5.4% Method Two 1/1/19 -3500 1/1/39 10000 XIRR function 5.4%

The imputed interest and the imputed tax due assuming a 30 percent tax rate is laid out in the table below

(I have added interest to the value of the bond after each additional year of ownership.)

 Imputed Tax Estimates @ Tax Rate of 0.30 Value of Bond Interest Earned Tax 2019 \$3,500 2020 \$3,688.49 \$188.49 \$56.55 2021 \$3,887.14 \$198.65 \$59.59 2022 \$4,096.48 \$209.34 \$62.80 2023 \$4,317.10 \$220.62 \$66.19 2024 \$4,549.60 \$232.50 \$69.75 2025 \$4,794.62 \$245.02 \$73.51 2026 \$5,052.83 \$258.22 \$77.46 2027 \$5,324.96 \$272.12 \$81.64 2028 \$5,611.73 \$286.78 \$86.03 2029 \$5,913.95 \$302.22 \$90.67 2030 \$6,232.45 \$318.50 \$95.55 2031 \$6,568.10 \$335.65 \$100.70 2032 \$6,921.83 \$353.73 \$106.12 2033 \$7,294.61 \$372.78 \$111.83 2034 \$7,687.46 \$392.85 \$117.86 2035 \$8,101.47 \$414.01 \$124.20 2036 \$8,537.78 \$436.31 \$130.89 2037 \$8,997.58 \$459.80 \$137.94 2038 \$9,482.15 \$484.57 \$145.37 2039 \$10,000.00 \$517.85 \$155.35

The after-tax yield was calculated with the XIRR function and is laid out below.

 Yield of Zero Coupon Bond After Taxes 1/1/19 (\$3,500) 4/15/20 (\$56.55) 4/15/21 (\$59.59) 4/15/22 (\$62.80) 4/15/23 (\$66.19) 4/15/24 (\$69.75) 4/15/25 (\$73.51) 4/15/26 (\$77.46) 4/15/27 (\$81.64) 4/15/28 (\$86.03) 4/15/29 (\$90.67) 4/15/30 (\$95.55) 4/15/31 (\$100.70) 4/15/32 (\$106.12) 4/15/33 (\$111.83) 4/15/34 (\$117.86) 4/15/35 (\$124.20) 4/15/36 (\$130.89) 4/15/37 (\$137.94) 4/15/38 (\$145.37) 1/1/39 \$10,000 4/15/39 (\$155.35) xirr 3.8%

Taxes reduce the yield from 5.4 percent to 3.8 percent.

Discussion of use of zero coupon bonds in retirement accounts:

Interest earned on assets is retirement accounts is not taxed.  Most retirement accounts tax all disbursements but all assets even interest and accumulated gains are never taxed inside a Roth account.

Having to pay tax on interest which is rolled over and not received until maturity can be very frustrating.  Also, zero coupon bonds issued by corporations may end up in default.

You should consider holding government backed zero coupons bonds in a tax deferred account.

Typically, 401(k) investors hold bond funds and the share of their investments in bonds funds increase as they get hold under many life cycle portfolios.  Around half of funds saved in ETFs for retirement are in target date funds.   These target date funds expose investors to substantial interest rate risk.

The government guaranteed zero coupon bond is better than a bond fund.

Bond funds have no maturity date.  The value of the bond fund is always tied to interest rates.

The value of the zero-coupon is also generally linked to interest rates.   However, on the maturity date the holder of the bond fund get full face value.

The use of staggered zero coupon bonds in a retirement fund is a more effective way to minimize risk than the more common approach of switching from equity funds to debt funds as the investor ages.

Unfortunately, most 401(k) plans do not include a zero-coupon government bond option.    The reason:   Investment companies get fee income from their own bond funds.