Question

Bond P is a premlum bond with a coupon rate of 8.9 percent. Bond D is a discount bond with a coupon rate of 4.9 percent. Both bonds make annual payments, a YTM of 6.9 percent, a par value of $1,000, and have fourteen years to maturity. a. What is the current yield for Bond P? For Bond D ? Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. b. If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.9., 32.16.

Answer 1

The current yield for premium Bond P and discount Bond D is calculated by dividing their respective annual coupon payments by their current bond prices. The capital gains yield for both relies on the tendency of bond prices to converge toward their $1000 par value as they near maturity, affecting the premium and discount bonds inversely.

Step-by-step explanation:

To calculate the current yield for Bond P and Bond D, which are a premium bond and a discount bond respectively, we follow this formula: Current Yield = Annual Coupon Payment / Current Bond Price. Since both have a yield to maturity (YTM) of 6.9%, we can initially assume Bond P sells for more than its par value and Bond D sells for less.

For Bond P with a coupon rate of 8.9%, the annual interest is $89 (8.9% of $1000). If the YTM is 6.9%, the bond price is such that the YTM equals the coupon divided by the price, rearranged as Price = Coupon / YTM. This gives us the price of Bond P. The current yield is then $89 divided by the price of Bond P.

For Bond D with a coupon rate of 4.9%, the annual interest is $49. We use the same formula as above to find the price of Bond D based on a YTM of 6.9%. The current yield for Bond D is then $49 divided by the price of Bond D.

An expected capital gains yield over the next year for both bonds would depend on the bond prices changing as they approach maturity. Bond prices tend to move towards par value as maturity comes closer. For Bond P (premium bond), the price is expected to decrease towards $1000, and for Bond D (discount bond), the price is expected to increase towards $1000.