10 year bond of par value Rs.8,000 was issued, with annual coupon rate of 11.5% and required rate of return is 9% per annum. what is the value of bond?
To calculate the value of a bond, you need to use the present value formula. The present value of a bond is the sum of the present value of the coupon payments and the present value of the par value (or face value).
Here's how you can calculate the value of the bond:
1. First, calculate the present value of the coupon payments:
- The annual coupon payment can be calculated as the coupon rate multiplied by the par value: 11.5% * Rs.8,000 = Rs.920.
- Since the bond has a 10-year maturity, you will receive 10 coupon payments of Rs.920 each.
- To calculate the present value of these coupon payments, you need to discount them at the required rate of return. In this case, the required rate of return is 9% per annum.
- You can use the present value of an ordinary annuity formula to calculate the present value of the coupon payments. The formula is:
PV = C * [(1 - (1 + r)^(-n)) / r]
where PV is the present value, C is the coupon payment, r is the required rate of return, and n is the number of periods.
- Plugging the values into the formula, you get:
PV_coupon = Rs.920 * [(1 - (1 + 0.09)^(-10)) / 0.09]
2. Next, calculate the present value of the par value:
- The par value of the bond is Rs.8,000, which will be received at the end of the 10-year period.
- Again, you can use the present value formula, but this time you only have one future payment (the par value) and you need to discount it for 10 years.
- The present value of the par value can be calculated as:
PV_par = Rs.8,000 / (1 + 0.09)^10
3. Finally, calculate the total value of the bond by summing up the present values of the coupon payments and the par value:
Value of the bond = PV_coupon + PV_par
By substituting the values in the formulas, you can calculate the value of the bond.