A 10-year bond has a coupon rate of 7% annually and a principal payment of $1,000.00. Other similar bonds are paying 9% annually. To determine the value of this bond you must:'
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To determine the value of the 10-year bond with a coupon rate of 7% annually and a principal payment of $1,000.00, you can use a financial formula called the present value of a bond.
The present value of a bond is the sum of the present values of its coupon payments and principal payment. The present value is calculated by discounting each future payment back to its present value using the required rate of return.
Here's how you can calculate the value of this bond:
Step 1: Determine the cash flows:
- The bond has a coupon rate of 7%, which means it pays interest of 7% of the bond's face value annually. Since the face value is $1,000.00, the annual coupon payment is 7% * $1,000.00 = $70.00.
- The bond has a 10-year term, so there will be 10 coupon payments of $70.00 each.
- At the end of the bond's term, it will also repay the principal of $1,000.00.
Step 2: Determine the required rate of return:
Since other similar bonds are paying 9% annually, we will use this rate as the required rate of return in our calculation.
Step 3: Calculate the present value of each cash flow:
To calculate the present value of each coupon payment, we use the formula for the present value of an ordinary annuity:
PV = C * [(1 - (1 + r)^(-n)) / r]
where PV is the present value, C is the cash flow per period, r is the discount rate, and n is the number of periods.
For the coupon payments, set C = $70.00, r = 9% (as the required rate of return), and n = 10 (the number of coupon payments).
To calculate the present value of the principal payment, we simply discount it back to its present value using the required rate of return. Since the principal payment is received at the end of the bond's term, there is no annuity formula to apply in this case.
Step 4: Sum up the present values of all cash flows:
Add up the present values of each coupon payment and the present value of the principal payment to obtain the value of the bond.
This calculation will give you the value of the 10-year bond with a coupon rate of 7% annually and a principal payment of $1,000.00.