Question

Remington, Inc. issued a new series of bonds on April 1, 2020. These non-callable bonds were sold at par, have a 9.25 percent coupon and mature in 25 years on March 31, 2045. Coupon payments are made on October 1 and April 1. Assume that you purchased an outstanding Remington bond on March 17, 2023. At the time you purchased the bond, the current yield was 10.57 percent.

a. Do you expect the current yield to be a good approximation of the bond’s yield to maturity? Explain why.
b. Assume the bond’s yield to maturity is 10.74 percent and the bond is based on a 30/360 day-count method. Compute the bond’s clean price.
c. What will be the actual price you pay for the bond? (i.e., the invoice/dirty price)

Answer 1

The current yield is not a perfect approximation of yield to maturity because the bond's yield at purchase differs from the coupon rate, implying that market rates have changed. The clean price can be calculated using the yield to maturity of 10.74%, considering the bond's semi-annual coupon payments and the 30/360 day-count method. The dirty price includes the clean price plus accrued interest from the last coupon payment date to the purchase date.

Step-by-step explanation:

The current yield on a bond is a good approximation of the yield to maturity when the bond is selling at or close to par value. As the question indicates the bond's current yield is 10.57%, which is quite different from the coupon rate of 9.25%, we can infer that the market interest rates have risen since the bond's issuance. This suggests that the current yield may not be a good approximation of the bond's yield to maturity due to changes in market rates affecting bond prices.

To calculate the bond's clean price, we need to use its yield to maturity of 10.74%. The bond pays a semi-annual coupon of 9.25%, which means a $46.25 coupon payment every six months ($92.50 per year). Using the 30/360 day-count method to adjust for the time between the last coupon payment and the purchase date, we can find the present value of the expected cash flows discounted at the yield to maturity.

The invoice price or dirty price of the bond includes the clean price plus accrued interest from the last coupon date (October 1, 2022) to the purchase date (March 17, 2023). The accrued interest would be the coupon amount, prorated for the portion of the coupon period that has elapsed since the last coupon payment.