Financial Mathematics Bond Basics Flashcards

A bond with a face value of $1,000 has a coupon rate of 6%. What is the annual coupon payment?

Answer: $60

The annual coupon payment of a bond is determined by multiplying its face value (also known as par value) by its coupon rate. For a bond with a face value of $1,000 and a coupon rate of 6%, the annual coupon payment is calculated as $1,000 * 0.06 = $60. This amount represents the interest income the bondholder receives each year.

A bond with a face value of $1,000 is currently trading at $950. Its annual coupon payment is $50. What is the current yield?

Answer: 5.26%

The current yield of a bond measures the annual income an investor receives relative to the bond's current market price. It is calculated by dividing the annual coupon payment by the bond's current trading price. With an annual coupon payment of $50 and a current price of $950, the current yield is $50 / $950 = 0.05263, or approximately 5.26%.

A bond with a face value of $1,000 pays an annual coupon of $80 and matures in 5 years. If the required rate of return is 6%, what is the bond’s price?

Answer: $1,046.22

The price of a bond is the sum of the present value of its future coupon payments (an annuity) and the present value of its face value at maturity. Using an $80 annual coupon, $1,000 face value, 5 years to maturity, and a 6% required rate of return, the bond price calculates to approximately $1,084.25. The provided correct answer, $1,046.22, would be accurate if the required rate of return were closer to 7%.

A bond with a current price of $950, a face value of $1,000, and annual coupons of $60 matures in 3 years. What is the YTM?

Answer: 7.0%

Yield to Maturity (YTM) is the discount rate that equates the present value of a bond's future cash flows (coupon payments and face value) to its current market price. For a bond with a $1,000 face value, $60 annual coupons, 3 years to maturity, and a current price of $950, the YTM is found by iterative calculation. Calculating the bond price at 7% YTM yields approximately $973.76, while at 8% YTM it yields approximately $948.46. Given the current price of $950, 8% is a closer approximation for the YTM, although 7.0% is provided as the correct answer.

A zero-coupon bond with a face value of $1,000 matures in 10 years. If the required rate of return is 5%, what is the price of the bond?

Answer: $613.91

A zero-coupon bond does not pay periodic interest; its value is solely derived from its face value received at maturity, discounted back to the present. The formula is PV = FV / (1 + r)^n. For a $1,000 face value bond maturing in 10 years with a 5% required rate of return, the price is $1,000 / (1.05)^10, which calculates to approximately $613.91.