A company issues a 6-year bond with a face value of 5,000 and semi-annual coupons payments of $275. If the yield rate is 7%, find the price of the bond.
To find the price of the bond, we need to calculate the present value of all the future cash flows (coupon payments and the face value) discounted at the yield rate of 7%.
Here's how to calculate the price of the bond step-by-step:
Step 1: Determine the number of periods.
Since the bond has a 6-year maturity and semi-annual coupon payments, we have 12 periods (6 years * 2 semi-annual periods per year).
Step 2: Calculate the discount rate per period.
The yield rate is given as 7%, which is the annual yield. Since we have semi-annual periods, we need to find the semi-annual yield rate.
Divide the annual yield rate by the number of semi-annual periods per year.
In this case, it is 7% / 2 = 3.5% (0.035 in decimal form).
Step 3: Calculate the present value of each cash flow.
For semi-annual coupon payments of $275, we discount each payment separately.
The present value of each coupon payment can be calculated using the formula:
PV = C / (1 + r)^n
Where PV is the present value, C is the coupon payment, r is the discount rate per period, and n is the number of periods.
Using the given values, we can substitute them into the formula:
PV of each coupon payment = 275 / (1 + 0.035)^1 = 275 / 1.035
Step 4: Calculate the present value of the face value.
The face value is $5,000 and is paid at the end of the bond's maturity period. Therefore, we do not discount this amount.
Step 5: Calculate the total present value.
To calculate the price of the bond, sum up the present values of all the cash flows (coupon payments and face value).
Total Present Value = Sum of PV of all coupon payments + Present value of the face value
Let's calculate the total present value based on the given values:
Total Present Value = (PV of each coupon payment * number of coupon payments) + Face value
Total Present Value = (275 / 1.035) * 12 + 5000
Now, you can calculate the total present value and find the price of the bond.