Pricing of Municipal Securities and Mathematical Calculations

This unit covers how municipal bonds are priced, how accrued interest is calculated, and how yields are computed. The taxable equivalent yield (TEY) formula is one of the most frequently tested concepts on the Series 7.

Dollar Price

• Quoted as a percentage of par; a price of 102 means the bond trades at $1,020 per $1,000 par
• Premium bond: Dollar price above 100 (above par)
• Discount bond: Dollar price below 100 (below par)
• Inverse relationship: When yields rise, bond prices fall; when yields fall, bond prices rise

Accrued Interest (30/360 Day Count Convention)

Municipal bonds use the 30/360 day count basis (Municipal Securities Rulemaking Board (MSRB) Rule G-33):

• Each month is treated as 30 days; each year is 360 days
• Accrued interest is calculated from the last interest payment date up to (but not including) the settlement date

Accrued Interest Formula:

• Buyer pays accrued interest to the seller on settlement
• The buyer will then receive the full next coupon payment (recovering the accrued interest paid)

Odd first coupon:

• If the first coupon period is longer or shorter than 6 months, accrued interest is adjusted accordingly
• A long first coupon (more than 6 months) accrues more interest
• A short first coupon (less than 6 months) accrues less

Example: A $5,000 par, 4% municipal bond with a January 1 and July 1 payment schedule. Trade settles April 1.

• Days accrued: January (30) + February (30) + March (30) = 90 days
• Annual coupon: $5,000 x 4% = $200
• Accrued interest: (90 / 360) x $200 = $50
• Buyer pays the seller $50 in accrued interest at settlement

Exam Tip: Gotchas

• Municipal and corporate bonds both use 30/360 day count (every month = 30 days). U.S. government bonds use actual/actual (actual days in month, 365-day year). This distinction is a common exam trap.
• The buyer pays accrued interest to the seller, then recoups it when the next full coupon payment arrives. The seller does not "keep" interest earned during their holding period.

Amortization of Premium

When a municipal bond is purchased at a premium in the secondary market:

• The premium must be amortized (reduced) over the remaining life of the bond
• Amortization reduces the bondholder's cost basis each year
• For tax-exempt municipal bonds, the amortized premium cannot be deducted as a loss (because the interest income is already tax-free)
• At maturity, the adjusted basis equals par, so there is no capital loss

Exam Tip: Gotchas

• Premium amortization on tax-exempt munis is NOT deductible. Since the interest income is tax-free, you cannot also deduct the premium. The amortization only adjusts your cost basis downward.

Accretion of Discount

Two different types of discount receive different tax treatment:

• OID accretion is tax-free for municipal bonds, which is a significant advantage
• Market discount is NOT tax-free; this is a frequent exam trap

Exam Tip: Gotchas

• OID on munis accretes as tax-exempt income; market discount accretes as taxable ordinary income. The difference depends on whether the discount existed at issuance (OID) or was created by market price changes after issuance (market discount).

Relationship of Bond Prices to Maturity and Coupon

Think of it this way: A bond with a long maturity and low coupon gives you very little cash flow early on, so most of your return depends on what happens far in the future. That makes it highly sensitive to interest rate changes. Long maturity + low coupon = maximum price volatility.

Yield Calculations

Which yield to quote for callable bonds:

• For premium callable bonds: YTC < YTM, so quote the lower yield (YTC is the worst case)
• For discount callable bonds: YTM < YTC, so quote the lower yield (YTM is the worst case)
• Always quote the yield that represents the worst case for the investor

Basis point: 1/100th of 1% (0.01%). A move from 3.50% to 3.55% is 5 basis points.

Exam Tip: Gotchas

• For callable bonds, always quote the LOWER yield (worst case for the investor). Premium callable bonds: quote yield to call (YTC). Discount callable bonds: quote yield to maturity (YTM).
• TEY formula divides by (1 - tax rate). A common wrong answer multiplies tax-exempt yield by the tax rate instead.

Taxable Equivalent Yield (TEY)

TEY Formula:

This converts a municipal bond's tax-free yield to the equivalent yield a taxable bond would need to offer.

Example: An investor in the 32% federal tax bracket is considering a municipal bond yielding 4%.

• TEY = 4% / (1 - 0.32) = 4% / 0.68 = 5.88%
• The investor would need a taxable bond yielding at least 5.88% to match the 4% muni after taxes

With state tax: If the investor is also in a 6% state bracket and the muni is in-state (triple tax-free):

• Combined rate: 32% + 6% = 38%
• TEY = 4% / (1 - 0.38) = 4% / 0.62 = 6.45%

Exam Tip: Gotchas

• TEY is the most frequently tested muni math concept. Worth memorizing: TEY = Tax-exempt yield / (1 - Tax rate).
• For in-state munis (triple tax-free), combine federal and state tax rates in the denominator. Out-of-state munis only use the federal rate.

Bonds in Default

• A bond in default trades flat (without accrued interest)
• The buyer does not pay accrued interest to the seller
• Income bonds (which pay interest only if earned) also trade flat