# How to read/decipher the percent % in a bond's interest versus coupon rate question or example

I was studying about bonds, more so accreted/coupon bonds that were discounted. As far as I know and believe to be true is that when a question says:

A.You need to take the \$200 difference and divide it by 10 years to get \$20. Mr. Dancer’s reported income would be \$70 (\$50 interest plus \$20 accretion).

The % is the annual interest, but when I came across another question from somewhere else

2) Q. "A customer buys a 5% municipal bond with 10 years left to maturity in the secondary market priced at 90 to yield 6.32%. After taking taxes into consideration, the customer's yield will be:" I believe that the second one mentioned is wrong. Is that correct to say the second one is wrong? The answer for the second says this:

A. "The return on this bond has 2 components: the 5% coupon rate and the 1% annual earning of the discount (10 point discount accreted over 10 years = 1 point or 1% per year gain). While the 5% coupon is not taxed, the 1% annual gain is taxed as interest income received. For someone in the 30% tax bracket, .3% of the 1% annual gain goes to tax, and .7% of the return is kept after tax. Thus, the after tax return is about 5.7%. This is a very difficult question."

Do you see what I am saying: the first question says 5% corporate bond, the second question says 5% municipal bond, but the two different sources identify them as different things. I thought the percentage before the term bond is the annual interest like question 1 says.

Thank you

• Yes, they both describe bonds that pay 5% annual interest. Can you be more specific on which part is confusing? Are you saying that the yield of the second bond is wrong? Or is the after tax analysis throwing you off? May 12, 2020 at 18:41
• Hi, so the first one is saying 5% corporate, and this 5% is referring to 5% x \$1000 of annual interest. The coupon for this is \$20 per year (1000- 800)/10. The other one is 5% municipal, but it uses that 5% to compute the coupon, unlike the prior one. Shouldn't the coupon for the second one be (1000-900)/10 and the annual interest should be \$50 like the other one? May 12, 2020 at 18:45
• I think you're confusing coupon and discount. They both pay \$50/year in interest (coupon), but the corporate bond was bought at a 20% discount, so there's additional "income" of \$20/year. The municipal bond was bought at a 10% discount for \$10/year of additional "income". May 12, 2020 at 18:54

They both describe bonds that pays 5% annual interest (i.e. \$50/year for a \$1,000 bond), but the second is asking about the income after taxes. It's meant to illustrate that the interest from a municipal bond is not taxable (at least not at the Federal level in the US), but the \$10/year gain from buying it at a discount is.

In the first example, all of the income (the \$50 coupon and the \$20 discount) is taxable, so the after-tax income would just be the income times (1 - the tax rate).

Also, the "6.32% yield" mentioned in the second example is correct, but it's irrelevant for the specific question asked.

The second question includes a yield-to-maturity calculation result of 6.32%.

The first question doesn't include a yield-to-maturity calculation result.

• I thought the CY should be < YTM for a discount bond. May 12, 2020 at 19:16
• The bond coupons are 5%. Bond coupons are actual cash flow. May 12, 2020 at 19:25
• Thank you but I meant current yield should be less than yield to maturity right? May 12, 2020 at 19:35
• current yield is the annual income in dollars / Market Price and in my book, it is saying if a bond trades at a Discount, Coupon < CY < YTM. I believe the CY is referring to the current yield, which would be \$60/\$900, but that is greater than the YTM. May 12, 2020 at 19:52
• I see, there is a terminology of "current yield" that is not yield-to-maturity. But the current yield is the cash flow, or coupon payment, divided by the bond market price. investopedia.com/terms/c/currentyield.asp . So that's 50/900 or 5.56% . May 12, 2020 at 20:06