The Garcia company's bond have a face value of 1000, will mature in 10 years and carry a coupon rate of 16 percent. Assume interest payments are made semi annually. Determine the present value of the bonds cash flow if the required rate of return is 16.64 percent
To determine the present value of the bond's cash flow, we need to calculate the present value of each individual cash flow and then sum them together.
In this case, the bond has a face value of $1000, which will be received at the end of 10 years. The coupon rate is 16 percent, so the bond will make coupon payments semi-annually. Therefore, there will be a total of 20 coupon payments over the 10-year period.
To calculate the present value of the face value at maturity, we can use the formula for the present value of a future amount:
Present Value = Future Value / (1 + r)^t
Where:
- Future Value is the face value of the bond ($1000)
- r is the required rate of return (0.1664 for 16.64%)
- t is the number of years until maturity (10 years)
Present Value of Face Value = $1000 / (1 + 0.1664)^10
Next, we need to calculate the present value of the coupon payments. Since the coupon payments are made semi-annually, we divide the coupon rate by 2 and multiply it by the face value of the bond:
Coupon Payment = (Coupon Rate / 2) * Face Value
Coupon Payment = (0.16 / 2) * $1000
Now, we calculate the present value of each semi-annual coupon payment using the present value of an ordinary annuity formula:
Present Value of Coupon Payment = Coupon Payment * [1 - (1 + r)^(-n)] / r
Where:
- Coupon Payment is the semi-annual coupon payment
- r is the required rate of return (0.1664 for 16.64%)
- n is the number of semi-annual periods (20)
Present Value of Coupon Payments = Coupon Payment * [1 - (1 + 0.1664)^(-20)] / 0.1664
Finally, we sum the present values of the face value and coupon payments to find the total present value of the bond's cash flow:
Total Present Value = Present Value of Face Value + Present Value of Coupon Payments
Now you can use these formulas to calculate the present value of the bond's cash flow using the given values.