ABC Industries issued a 5-year, 6% annual coupon bond with a par value of USD 1,000 two years ago. At the time of issuance, the yield to maturity was 7%. Recently, due to an increase in market interest rates, the new yield to maturity on the bond is 7.75%. The current price of the bond is closest to:AUSD 974BUSD 930CUSD 955
Question
ABC Industries issued a 5-year, 6% annual coupon bond with a par value of USD 1,000 two years ago. At the time of issuance, the yield to maturity was 7%. Recently, due to an increase in market interest rates, the new yield to maturity on the bond is 7.75%. The current price of the bond is closest to:AUSD 974BUSD 930CUSD 955
Solution
To find the current price of the bond, we need to calculate the present value of the future cash flows, which are the annual coupon payments and the par value at maturity, discounted at the new yield to maturity.
Step 1: Calculate the annual coupon payment The annual coupon payment is the par value multiplied by the coupon rate. Coupon Payment = 1000 * 6% = USD 60
Step 2: Calculate the present value of the remaining coupon payments The bond has 3 years left until maturity, so there will be 3 more coupon payments. The present value of these payments is calculated by discounting them at the new yield to maturity. PV of Coupon Payments = 60 / (1 + 7.75%) + 60 / (1 + 7.75%)^2 + 60 / (1 + 7.75%)^3 = USD 162.69
Step 3: Calculate the present value of the par value at maturity The par value of the bond will be paid back at the end of the 5-year period. The present value of this payment is calculated by discounting it at the new yield to maturity. PV of Par Value = 1000 / (1 + 7.75%)^3 = USD 816.30
Step 4: Add the present values to find the current price of the bond Current Price = PV of Coupon Payments + PV of Par Value = 162.69 + 816.30 = USD 978.99
The current price of the bond is closest to USD 974 (Option A).
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