Taxable Equivalent Yield and Call Risk in a Bond Swap
A married couple in the 35% federal bracket and 5% state bracket is considering a $500,000 bond purchase with a 10-year horizon. They need about $18,000 of annual income. Their in-state general obligation municipal bond has a 5.00% coupon, is priced at 108.50, and yields 3.85% to maturity; interest is exempt from federal and state tax, and the bond is not an AMT private-activity issue. It is callable at par in five years. An A-rated corporate bond has a 5.80% coupon, is priced at 99.50, and yields 5.90% to maturity; it is callable at par in three years. The corporate bond last paid a coupon four months ago; the municipal bond last paid two months ago. The client says, 'The corporate bond pays 5.90%, so it must be the better deal.'
1. Compare the after-tax yields and determine whether the municipal bond or the corporate bond provides the better after-tax return for this couple.
Read the worked answer
The municipal bond's taxable-equivalent yield is 3.85% / (1 - 0.35 - 0.05) = 3.85% / 0.60 = 6.42%. Using only the federal bracket, it is 3.85% / 0.65 = 5.92%. The corporate bond's after-tax yield is 5.90% x (1 - 0.40) = 3.54%. On an after-tax basis, the in-state municipal bond is superior by about 31 basis points when state tax is included, and by about 2 basis points on a federal-only basis.
The coupon comparison is misleading. The municipal bond's 5.00% coupon on a price of 108.50 produces a current yield of about 4.61%, but the premium amortization reduces the yield to maturity to 3.85%. The corporate bond's 5.80% coupon on 99.50 produces a current yield of about 5.83%, close to its 5.90% yield to maturity. The couple needs $18,000 of income: the municipal coupon produces $25,000 of tax-exempt income, while the corporate coupon produces $29,000 of taxable income, or $17,400 after tax. The corporate bond therefore fails the income need on an after-tax basis.
The analysis is not complete without call risk. The municipal bond is callable at par in five years while trading at 108.50; if called, the premium is lost and the yield to call is much lower than 3.85%. The corporate bond is callable at par in three years while trading at a discount, which creates reinvestment risk if rates fall. The representative should compare yield to worst, not just yield to maturity, and should consider a ladder rather than a single 10-year maturity.
2. Calculate the accrued interest for each bond and explain how settlement affects the client's cash outlay and yield.
Read the worked answer
Corporate bond accrued interest: the annual coupon is 5.80% x $500,000 = $29,000. Using a 30/360 convention, four months of accrued interest is $29,000 x 4/12 = $9,666.67. The clean price is 99.50, or $497,500 for $500,000 face. The buyer pays $497,500 + $9,666.67 = $507,166.67 at settlement.
Municipal bond accrued interest: the annual coupon is 5.00% x $500,000 = $25,000. Two months of accrued interest is $25,000 x 2/12 = $4,166.67. The clean price is 108.50, or $542,500. The buyer pays $542,500 + $4,166.67 = $546,666.67.
The quoted yields are computed from the dirty price, including accrued interest. The buyer compensates the seller for interest earned but not yet paid, then receives the full next coupon. The municipal accrued interest is tax-exempt to the extent the underlying interest is tax-exempt, while the corporate accrued interest is taxable. The representative should show the client both the clean price and the total cash outlay, because a premium municipal bond requires substantially more capital than the corporate bond for the same $500,000 face amount.
3. What suitability, disclosure, and portfolio-construction issues should the representative address before recommending either bond?
Read the worked answer
The representative should first establish the couple's objective: current income with reasonable safety, not maximum yield. The in-state municipal bond fits the federal and state tax profile, but its 10-year maturity, 108.50 premium price, and five-year par call create interest-rate and reinvestment risk. If the bond is called, the client may not be able to replace the tax-exempt yield. The corporate bond offers a higher pretax yield but a lower after-tax yield, and its three-year call is a significant yield-to-worst issue.
Concentration is a concern if $500,000 is a large part of the couple's liquid net worth. A single issuer, single maturity, and single sector expose them to credit and liquidity risk. A ladder of two- to ten-year maturities, diversified across issuers and sectors, would better match their income need and reduce reinvestment risk. The representative should also confirm that the municipal bond is not an AMT private-activity bond and that the state tax exemption applies to their residency.
Disclosure should include the call features, yield to worst, premium amortization, accrued interest, and the fact that municipal interest can affect Social Security taxation and Medicare premiums. The representative should document the suitability analysis, provide the official statement and trade confirmation, and ensure the markup or commission is fair under MSRB rules. The recommendation should be based on after-tax yield to worst and the couple's need for income, not on the higher nominal coupon.