Assuming annual compounding, the prices of a one-year 4% coupon bond and a two-year 5% coupon bond are $101 and $99, respectively. Assume coupons are paid annually. The fair price of a two-year 6% coupon bond will be
A) $99.86
B) $100.11
C) $100.57
D) $100.87

Question

Assuming annual compounding, the prices of a one-year 4% coupon bond and a two-year 5% coupon bond are $101 and $99, respectively. Assume coupons are paid annually. The fair price of a two-year 6% coupon bond will be 
A) $99.86
B) $100.11
C) $100.57
D) $100.87

Quizplus · Accepted Answer

To find the fair price of a two-year 6% coupon bond, we first need to calculate the yield to maturity (YTM) for the one-year and two-year bonds given. For the one-year 4% coupon bond priced at $101, the YTM can be found using the formula: $$P = \frac{C}{(1+r)} + \frac{F}{(1+r)^n}$$ where $P$ is the price of the bond, $C$ is the annual coupon payment, $r$ is the YTM, and $F$ is the face value of the bond (usually $100), and $n$ is the number of years. For a one-year bond, this simplifies to $101 = \frac{4}{(1+r)} + \frac{100}{(1+r)}$, solving for $r$ gives us the YTM for the one-year bond.For the two-year 5% coupon bond priced at $99, we use the formula considering two periods, but we need to find the YTM in a similar manner, which is a bit more complex due to the quadratic nature of the equation for two periods.Once we have the YTMs, we can calculate the price of the two-year 6% coupon bond. The coupon payment for this bond is $6 (since it's 6% of the $100 face value), and we use the YTMs found earlier as the discount rates for the respective years.The calculation involves discounting the future cash flows (the annual $6 coupon payments and the $100 face value at maturity) back to their present value using the YTMs as the discount rates. The sum of these present values gives us the fair price of the bond.Given the choices provided and the process to calculate the fair price of a bond, the correct answer involves accurately applying these principles and calculations, leading to the conclusion that the fair price of the two-year 6% coupon bond is closest to the value given in option D, $100.87. This option reflects the correct application of the bond pricing formula, taking into account the specific details provided for the bonds in question.

Assuming Annual Compounding, the Prices of a One-Year 4% Coupon