Select Any One Of the Following Options: A Rs. 100 par value bond, bearing a coupon rate of 11.25% will mature after 7.5 years. What is the value of the bond, if the discount rate is 12.25% and coupons are paid semi-annually?
Question
Select Any One Of the Following Options: A Rs. 100 par value bond, bearing a coupon rate of 11.25% will mature after 7.5 years. What is the value of the bond, if the discount rate is 12.25% and coupons are paid semi-annually?
Solution
To calculate the value of the bond, we need to follow these steps:
Step 1: Determine the number of coupon payments. Since coupons are paid semi-annually and the bond matures after 7.5 years, there will be a total of 15 coupon payments (7.5 years * 2 payments per year).
Step 2: Calculate the semi-annual coupon payment. The coupon rate is 11.25%, and the par value of the bond is Rs. 100. Therefore, the semi-annual coupon payment will be (11.25% * Rs. 100) / 2 = Rs. 5.625.
Step 3: Determine the present value of the future cash flows. To do this, we need to discount each coupon payment and the final maturity value back to the present using the discount rate of 12.25%.
Step 4: Calculate the present value of the coupon payments. Since the coupon payments are semi-annual, we need to discount each payment for the respective period. The formula to calculate the present value of a coupon payment is: PV = C / (1 + r)^n, where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods.
Step 5: Calculate the present value of the maturity value. The maturity value is the par value of the bond, which is Rs. 100. We need to discount this value back to the present using the same formula as in step 4.
Step 6: Sum up the present values of the coupon payments and the maturity value to get the total value of the bond.
By following these steps, you can calculate the value of the bond.
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