Consider a coupon bond that pays $105 every year and repays its principal amount of $1,500 at the end of 7 years
To calculate the price of the coupon bond, we need to understand how to value coupon bonds. Coupon bonds are a type of fixed-income security that pays periodic interest (coupon payments) to the bondholder and repays the principal amount at maturity.
In this case, the coupon bond pays $105 every year for 7 years and repays the principal of $1,500 at the end of the 7 years. The bond's cash flows are as follows:
Year 1: $105
Year 2: $105
Year 3: $105
Year 4: $105
Year 5: $105
Year 6: $105
Year 7: $105 + $1,500 (principal repayment)
To calculate the price of the bond, we need to discount each cash flow to its present value using an appropriate discount rate. The discount rate reflects the required rate of return or yield on the bond.
Let's assume that the discount rate is 5% per year. We can use the present value formula to calculate the present value of each cash flow:
PV = CF / (1+r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
Calculating the present value of each cash flow:
Year 1: PV = $105 / (1+0.05)^1 = $100
Year 2: PV = $105 / (1+0.05)^2 = $95.24
Year 3: PV = $105 / (1+0.05)^3 = $90.70
Year 4: PV = $105 / (1+0.05)^4 = $86.34
Year 5: PV = $105 / (1+0.05)^5 = $82.13
Year 6: PV = $105 / (1+0.05)^6 = $78.13
Year 7: PV = ($105 + $1,500) / (1+0.05)^7 = $1,240.71
Now we sum up the present values of all the cash flows:
Price of the bond = $100 + $95.24 + $90.70 + $86.34 + $82.13 + $78.13 + $1,240.71 = $1,773.25
Therefore, the price of the coupon bond is $1,773.25.