A 10 year bond has a coupon rate of 7% annually and a principal payment of $1000.00. Other similar bonds are paying 9% annually. To determine the value of this bond you must find the interest factors, IF at:
A) 9% for 10 periods b) 9% for 20 periods c) 4.5% for 20 periods d) 4.5% for 10 periods
To determine the value of the bond, we need to calculate the present value of its cash flows, which include the annual coupon payments and the principal payment at maturity.
The formula to calculate the present value of a bond is:
PV = ((C/r) * (1 - (1/(1+r)^n))) + (F/(1+r)^n)
Where PV is the present value, C is the coupon payment, r is the interest rate, n is the number of periods, and F is the principal payment.
In this case, the coupon rate is 7%, the principal payment is $1000, and we need to find the interest factors (IF) at different interest rates and periods.
Let's solve for each given scenario:
A) 9% for 10 periods:
Using the formula, we have:
IF = (1 - (1/(1+r)^n))/r
IF = (1 - (1/(1+0.09)^10))/0.09
B) 9% for 20 periods:
Using the formula, we have:
IF = (1 - (1/(1+r)^n))/r
IF = (1 - (1/(1+0.09)^20))/0.09
C) 4.5% for 20 periods:
Using the formula, we have:
IF = (1 - (1/(1+r)^n))/r
IF = (1 - (1/(1+0.045)^20))/0.045
D) 4.5% for 10 periods:
Using the formula, we have:
IF = (1 - (1/(1+r)^n))/r
IF = (1 - (1/(1+0.045)^10))/0.045
To calculate the present value of the bond in each scenario, substitute the calculated interest factors (IF) into the present value formula and solve for PV:
A) PV = ((C/r) * IF) + (F/(1+r)^n)
B) PV = ((C/r) * IF) + (F/(1+r)^n)
C) PV = ((C/r) * IF) + (F/(1+r)^n)
D) PV = ((C/r) * IF) + (F/(1+r)^n)
Substitute the given values (C = 0.07 * $1000, F = $1000) and the calculated interest factors (IF) to find the present value (PV) of the bond in each scenario.