## Example 24 Computing Accrued Interest with 30360 Day Counts

Compute the accrued interest on an 8 percent corporate bond that settles on June 30. The last coupon date was February 25.

Answer: There are 25 days of accrued interest: 6 days in February; 30 in March, April, and May; and 29 in June. 125/360 = .3472222. The product of .3472222 and $8 is $2.77778. Thus, the bond has $2.77778 of accrued interest per $100 of face value.

### Yields to Maturity and Coupon Yields

The coupon yield of a bond is its annual interest payment divided by its current flat price.29 For example, a bond with a flat price (that is, net of accrued interest) of $92, which pays coupons amounting to $10 each year, has a coupon yield of 10/92 = 10.87 percent.

It is easy of show that a straight-coupon bond with a yield to maturity of 10 percent and a price of 100 has a coupon yield of 10 percent on a coupon payment date and vice versa. Try it on a financial calculator. More generally, we have:

Result 2.2 Straight coupon bonds that (1) have flat prices of par (that is, $100 per $100 of face value)

and (2) settle on a coupon date, have yields to maturity that equal their coupon yields.

Result 2.2 at first seems rather striking. The yield to maturity is a compound interest rate while the coupon yield is a simple quotient. It appears to be a remarkable coincidence that these two should be the same when the bond trades for $100 per $100 of face value, or par. The obviousness of this "coincidence" only will become apparent when you have mastered Chapter 9's material on perpetuities and compounding conventions.

When a bond is trading at par on a coupon date, discounting at the coupon yield is the same as discounting at the yield to maturity. However, coupon yields can give only approximate yields to maturity when a bond is trading at a premium or a discount.

28It is comforting to know that most financial calculators have internal date programs to compute the number of days between two dates using the 30/360 day/count method.

29Whenever the term yield is used alone, it refers to the yield to maturity, not the coupon yield.

Chapter 2 Debt Financing

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