You buy an 8% annual coupon bond from CARRIS Inc. that has a 25 year maturity and a required return of 12%. The par value is $1,000. You sell the bond five years later when the required return is 10%. What is the beginning price of the bond when it is issued (to the nearest dollar)?

Question

You buy an 8% annual coupon bond from CARRIS Inc. that has a 25 year maturity and a required return of 12%. The par value is $1,000. You sell the bond five years later when the required return is 10%. What is the beginning price of the bond when it is issued (to the nearest dollar)?

Answer 1

To calculate the beginning price of the bond when it is issued, we need to calculate the present value of future cash flows. In this case, the cash flows consist of the annual coupon payments and the final redemption payment.

Here's how you can calculate the beginning price of the bond:

Step 1: Calculate the present value of the coupon payments.
The bond has an 8% annual coupon rate, and the par value is $1,000. Since the bond has a 25-year maturity, there will be 25 coupon payments.

To calculate the present value of the coupon payments, we need to discount each payment by the required return rate. The required return rate is 12%, which is the rate of return that investors demand for investing in the bond initially.

We'll use the formula for the present value of an annuity to calculate the present value of the coupon payments:

PV = C x [1 - (1 + r)^(-n)] / r

Where:
PV = Present value
C = Coupon payment
r = Required return rate
n = Number of periods

In this case:
C = 0.08 x $1,000 = $80 (annual coupon payment)
r = 0.12 (required return rate)
n = 25 (number of coupon payments)

Using the above values, we can calculate the present value of the coupon payments.

PV(coupons) = $80 x [1 - (1 + 0.12)^(-25)] / 0.12

Step 2: Calculate the present value of the redemption payment.
When the bond matures after 25 years, the bondholder receives the par value of $1,000. To calculate the present value of this payment, we discount it by the required return rate.

PV(redemption payment) = $1,000 / (1 + 0.12)^25

Step 3: Calculate the beginning price of the bond.
The beginning price of the bond is the sum of the present value of the coupon payments and the present value of the redemption payment.

Beginning price of the bond = PV(coupons) + PV(redemption payment)

To find the beginning price of the bond, you need to calculate the PV(coupons) and PV(redemption payment) using the formulas provided above and then add the results together.

The resulting value will be the beginning price of the bond when it is issued, rounded to the nearest dollar.

You buy an 8% annual coupon bond from CARRIS Inc. that has a 25 year maturity and a required return of 12%. The par value is $1,000. You sell the bond five years later when the required return is 10%. What is the beginning price of the bond when it is issued (to the nearest dollar)?

636

To calculate the beginning price of the bond when it is issued, we need to calculate the present value of future cash flows. In this case, the cash flows consist of the annual coupon payments and the final redemption payment.