Grossnickle Corporation issued 30-year, noncallable, 8.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 6.5%. What is the current price of the bonds, given that they now have 29 years to maturity?
SI SOY YO OTRA VEZ, YA NO ESTES JODIENDO CON TU PREGUNTITA Y PONTE A LEER LIBROS CULERO. Y NO TE CREAS NO ME DAS ASCO.
To calculate the current price of the bonds, we need to calculate the present value of the future cash flows, which are the annual coupon payments and the face value payment at maturity.
Step 1: Calculate the present value of the coupon payments.
The bonds have an annual coupon rate of 8.5% and a face value of $1,000. The coupon payments remain the same throughout the life of the bond, so each year you will receive $1,000 x 0.085 = $85.
To calculate the present value of these cash flows, you can use the formula for present value of an annuity:
PV = C x (1 - (1 + r)^(-n)) / r
Where:
PV = Present value of the annuity (coupon payments)
C = Cash flow per period (annual coupon payment)
r = Interest rate per period (market interest rate)
n = Number of periods (years to maturity)
In this case, C = $85, r = 6.5%, and n = 29.
Using these values, we can calculate the present value of the coupon payments.
PV_coupon = $85 x (1 - (1 + 0.065)^(-29)) / 0.065
Step 2: Calculate the present value of the face value payment at maturity.
The face value of the bond is $1,000, which will be paid at maturity. We need to calculate the present value of this future cash flow using the formula for present value of a single sum:
PV = F / (1 + r)^n
Where:
PV = Present value of the face value payment
F = Future value (face value)
r = Interest rate per period (market interest rate)
n = Number of periods (years to maturity)
In this case, F = $1,000, r = 6.5%, and n = 29.
Using these values, we can calculate the present value of the face value payment.
PV_facevalue = $1,000 / (1 + 0.065)^29
Step 3: Calculate the total present value of the bond.
To get the current price of the bond, we need to sum up the present value of the coupon payments (PV_coupon) and the present value of the face value payment (PV_facevalue).
Total PV = PV_coupon + PV_facevalue
By plugging in the calculated values, you will get the current price of the bond.