FIXED INCOME SECURITIES - University of Florida
FIXED INCOME SECURITIES
LECTURE NOTE: TAXES ONE
PROFESSOR DAVID T. BROWN
UNIVERSITY OF FLORIDA
WARRINGTON COLLEGE OF BUSINESS
Overview.
There are two class periods dedicated to taxes and fixed income securities. The first lecture is largely focused on the municipal bond market. The municipal bond interest is exempt from Federal and in many cases state taxes. We will discuss the kinds of investors that are attracted to municipal bonds and how this effects the municipal bond yield curve. In the next lecture (TAXES TWO) we look at tax timing options.
Marginal Tax Rate and Municipal Bond Market.
Marginal Tax Rate.
Suppose an investor is comparing two securities that are identical other than the fact that one security is taxable and the other is non-taxable, i.e. a muni bond. The investors tax rate is τ. The after-tax rate of return on a non-taxable bond with a yield of rnt is rnt and the after-tax rate of return on an other wise identical bond taxable bond with a yield of rt is rt(1-τ). Therefore, an investor buys a muni bond only if
rnt > rt(1-τ), or
τ > (1 – rnt/rt). (1)
Clearly, municipal bonds are more attractive to high tax bracket investors: Equation (1) is more likely to hold if your tax rate is high or rnt is just a little below rt.
The marginal tax rate is the tax rate that makes an investor indifferent between investing in municipal bonds and taxable bonds. The marginal tax rate, τm solves
rnt = rt(1-τm), or
τm = (1 – rnt/rt). (2)
If your tax rate is greater than the marginal tax rate, then it makes sense to consider municipal bonds. Municipal bond market conditions are usually expressed in terms of the marginal tax rate.
Example: If the muni-bond rate is 5% and the taxable bond rate is 6%, then the marginal tax rate is 16.67%.
Industry Convention: The municipal yield curve is usually presented as a percentage of the Treasury yield curve: see for example exhibit 8-2 in Fabozzi. If the AAA municipal bond yield is 80% of the Treasury yield curve then the marginal tax rate is 20%.
Note: In this case, the marginal tax rate is really not 20% because AAA munis and Treasuries is not an apples to apples comparison. Suppose that the treasury yield is 10% and the muni yield is 8% so that the yield ratio is 80%. An investor would lower the yield on the muni to account for the fact that it has less liquidity and some default risk.
Investors in Municipal Bonds.
Pension funds and individual retirement products are non-taxable or tax deferred. Thus, large institutional investors (pension plans) do not invest in muni-bonds. The big investors are (1) individuals and (2) property and casualty insurance companies. The demand for muni bonds can change dramatically over time with changes in the profitability of the P&C industry.
Maturity Spreads.
There is some interesting economics in the term structure of marginal tax rates. For the last several years the marginal tax has declined dramatically with maturity. This leads to two questions:
1) Why do investors buy short term muni bonds?
(2) Why do municipalities issue long term muni bonds?
Types of Muni-Bonds.
Municipal bonds are largely either (1) general obligation bonds or (2) revenue bonds. Revenue bonds are basically “project finance” and thus have sinking fund features.
Taxation of Fixed Income Securitites.
Quick Look at Tax Timing Options.
Investors chose when they “recognize” capital gains and losses by deciding when to sell a security that they hold. The investor’s choice is often referred to as “tax timing options.” In general you want to postpone the realization of capital gains and realize capital losses as soon as possible.
Premium Bonds.
Bonds selling above their face value will incur a loss with certainty. The tax code allows you to amortize the loss according to the following schedule with out selling the bond. You deduct an equal amount of the premium each year. Thus, if the bond has ten years to maturity and you purchase it for $1080, then you recognize a loss of $8 per year.
The “basis” changes over time: the taxable gain or loss at the time of sale depends on the sale price and how much of the premium has been amortized.
Discount Bonds.
Coupon bearing bonds purchased at a discount will incur a capital gain with certainty (unless the bond defaults). The tax code gives you a choice as to whether to amortize this gain (pay part of it every year) or pay the gain at maturity. In almost every conceivable situation you would chose to pay the capital gain at maturity. Thus, the “basis” is the purchase price.
Zero Coupon Bonds.
The IRS wasn’t born yesterday. You have to pay gains each year according to a “constant yield” amortization schedule. This schedule becomes your basis.
Suppose you purchase a ten-year bond with a price of $266.68 (this has a yield of 10%).
a. What taxes must you realize the first year you own the bond?
b. What taxes must you realize the second year you own the bond?
c. If you sell the bond for $312.67 at the end of two years, what is your taxable capital gain or loss?
Pricing Bonds.
Example: Assume that the marginal tax rate on ordinary income and capital gains is 30%. The term structure of municipal bond interest rates is flat at 10%. What are the prices and yields of the following three securities, each having three years until maturity: (1) a coupon bond that pays annual coupons of $20 and has a face value of $100, (2) a coupon bond that pays annual coupons and has a face value of $100, and (3) a zero coupon bond that has a face value of $100. All of these bonds are taxable.
20% Coupon Bond.
The first thing to recognize is that the after-tax coupon payments on this bond are (1-30%)*(20%) or 14%. Thus, this bond will clearly sell for a premium.
The price of this bond is determined by solving the following equation (the present value of the after-tax cash flows at the municipal bond rate):
P = [(P-100)/3(.3) + (20)(.7)]/(1.10) + (P-100)/3(.3) + (20)(.7)]/(1.10)2 + [(P-100)/3(.3) + (20)(.7) + 100]/(1.10)3.
The price of this bond is $113.19. The yield to maturity on this bond is 14.29% which is exactly what you would expect: 14.29%*70% = 10%.
Result. The yield on all premium bonds in this case will be 14.29%. All premium bonds have the same tax treatment: all income is taxed in the year it occurs. This result would not hold if the ordinary income and capital gains rates were different.
Zero Coupon Bond.
You would need to write a computer program to solve for the amortization schedule. However, there is a trick. As with the premium bond, all income is taxed in the year it occurs. Therefore, it must have the same yield as the premium bond and must have a yield of 14.29%. Therefore, the price of this bond is $66.98.
Check. Go back and figure out all of the tax outflows and discount the resulting stream at 10% and you will get a price of $66.98.
10% Coupon Bond.
The first thing to recognize is that the after-tax coupon rate on this bond is 7%, and thus this bond sells for a discount. The price of the bond is
P = (10)*(.7)/(1.10) + (10)*(.7)/(1.10)2 + [(10)*(.7) – (100-P)(.3) + 100]/(1.10)3 .
In this case, the bond sells for $90.37. The yield on this bond is 14.16%. The discount bond has a slightly lower yield than the premium and zero coupon bonds because this bond has preferential tax treatment: the gains can be postponed.
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