Ch 5. Municipal securities

An investor purchased a corporate bond with a 6% coupon at a net price of 101. The bond had accrued interest for 45 days. Which of the following statements regarding the confirmation of this trade is correct?

Accrued interest is always added to the price of a bond. When you buy the bond, you pay that accrued interest, and when you sell a bond, you receive that accrued interest. The principal value is 101, or $1,010. Forty-five days of accrued interest is ⅛ of a 360-day year, or ¼ of a 180-day semiannual interest payment. With a 6% coupon, the bond pays $30 every 6 months. One quarter of that is $7.50 so the total cost to the purchaser is the $1,010 plus the $7.50, or $1,017.50.

A municipality has an ad valorem tax rate of 10 mills. A piece of real property is assessed at $100,000 and has a market value of $125,000. The annual taxes paid on the property are

Ad valorem tax rates are based on mills with one mill being equal to $0.001 (1/10th of a cent). The amount of taxes to be paid on the property is determined by multiplying the millage rate—in this case, one cent (10 mils at $0.001 = $0.01)—times the assessed property value ($100,000). The market value is irrelevant. For those who have difficulty determining where the decimal point goes, on any question like this, drop the last three 000s from the assessed value and multiply by the millage rate. In this question, that would be $100 times 10 and that equals the correct answer of $1,000.

The real value of property within the city limits is $100 million. The city uses a 50% assessment rate. A 10 mill tax rate will provide tax revenues of

If 1 mill equals $0.001, then 10 mills equals 0.01 (10 × 0.001). Therefore, $100 million × 50% assessment rate = $50 million. $50,000,000 × 0.01 = $500,000.

The Interstate Bridge Authority has an outstanding revenue bond. For the most recent operating period, the Authority has net revenue of $36 million, operations and maintenance expenses of $16 million, debt service requirements of $18 million, and surplus funds of $2 million. The debt service coverage ratio for the Interstate Bridge Authority's revenue bond is

In the absence of a described revenue pledge (net or gross), the net revenue pledge should be used. This means that the debt is serviced after the expenses for operations and maintenance have been satisfied. The net revenue of the project is revenues after subtracting those expenses. In this question, that is the $36 million figure given. The debt service coverage ratio is determined by dividing the net revenue by the debt service requirement. In this question, the debt service coverage ratio would be 2:1 ($36 million ÷ $18 million = 2). If you subtracted the $16 million of expenses because you did not notice that we gave you the net revenue, your ratio was 20 ÷ 18 = 1.11 to 1. If you added the surplus (not an expense), your ratio was 18 ÷ 18 = 1:1. It is not uncommon to have information in a question that is not needed to arrive at the solution.

Paying a premium of $10 per bond, Tracey bought 10 municipal bonds with 20 years to maturity. Ten years later, she sold the bonds for 103. For tax purposes, she has

The cost per bond is $1,010. The amortization amount each year is 10/20 years, which equals $0.50 per year. $0.50 per year × 10 years = $5 per bond. After 10 years, the adjusted cost basis is $1,005 per bond. She sells the bonds for $1,030 per bond. $1,030 − $1,005 = $25 per bond 25 × 10 = $250 gain.

An investor purchased 10 GO bonds at a discount of 2 points per bond. The bonds mature in 10 years. After holding the bonds for 5 years, they were sold at par. For tax purposes, the investor has

The cost per bond is $980. The accretion amount each year is $20. $20 ÷ 10 years = $2 per year. $2 per year × 5 years = $10 per bond accretion, making the adjusted cost basis $990 per bond. When the bonds are sold at par ($1,000), there is a profit of $10 per bond × 10 bonds, which equals a $100 gain.

Tax Equivalent Yield Formula

The coupon of the municipal bond divided by (100% − tax bracket).

If an M&N 1 corporate bond issued at par with a 6% coupon is later purchased in August for 97 plus accrued interest of $16, how much taxable interest must the investor report for the year?

The purchaser of a bond pays the seller the interest that has accrued since the last interest payment date. A purchaser in August will pay the interest that has accrued since May 1. Then, on November 1, the investor will receive the entire six months of interest. We are told that the investor paid $16 in accrued interest. That is income to the seller. Then, when the November payment of $30 (6% coupon is $30 semiannually) is made, the investor must report the amount over the accrued interest paid out as income. In our question, that is $30 minus $16 = $14.

One of your customers is in the 37% federal income tax bracket. The customer prefers purchasing corporate bonds over municipal bonds because the corporation's financials are much easier to understand. On the customer's next purchase, the instructions are to find a corporate bond that will yield the same after-tax return as would be received from a municipal bond with a 3.20 coupon. The bond you suggest must have a coupon of

This is a tax-equivalent yield question. The interest paid on a corporate bond is taxable, while that of the municipal bond is tax free. The formula is: The coupon of the municipal bond divided by (100% − tax bracket). In our question, that would be 3.20% divided by 63%, or 5.08%

A client is trying to decide between a par value corporate bond carrying a coupon rate of 6.25% per year and a par value municipal bond that pays an annual coupon rate of 4.75%. Assuming all other factors are equal, and your client is in a 28% marginal income tax bracket, which bond do you tell the client to purchase and why?

This is calculated using the tax-equivalent yield formula: municipal yield / (100% − investors tax bracket) 4.75 / (1 − 0.28) = 6.6%. By comparison, the 6.6% tax-equivalent yield of the municipal bond is higher than the 6.25% yield of the taxable corporate bond, making the municipal bond the higher yielding investment, given the investor's 28% tax bracket.

A customer in the 28% tax bracket wants to buy a municipal GO bond with a 7.5% yield that matures in 6 years. The tax-equivalent yield of this bond is

To calculate the taxable return, use the tax-free equivalent yield formula: municipal bond yield ÷ (1 − investor's tax bracket). Using this formula, 0.075 ÷ (1 - 0.28) = 0.104, or 10.4%. This means the investor, who is in the 28% tax bracket, must earn 10.4% in taxable interest to equal the 7.5% tax-free municipal interest yield.

A municipal revenue bond indenture contains a net revenue pledge. The following are reported for the year: $30 million of gross revenues, $18 million of operating expenses, $4 million of interest expenses, and $2 million of principal repayment. What is the debt service coverage ratio?

Under a net revenue pledge, bondholders are paid from net revenue, which equals gross revenue minus operating and maintenance expenses. In this example, net revenue is $12 million ($30 million − $18 million). Debt service is the combination of interest and principal repayment. Here, debt service is $6 million ($4 million + $2 million). To compute the debt service ratio, divide net revenue by debt service: $12 million divided by $6 million equals a ratio of 2:1.