Suppose that five years ago Cisco Systems sold a 15-year bond issue that had a $1,000 par value and a 7 percent coupon rate. Interest is paid semiannually.

a. If the going interest rate has risen to 10 percent, at what price would the bonds be selling today?

b. Suppose that the interest rate remained at 10 percent for the next 10 year. What would happen to the price of the Cisco Systems bonds over time?

Pmt=35 i=5% n=20

Price=813.07

a. To find the price at which the bonds would be selling today, we need to calculate the present value of the bond's future cash flows. The cash flows consist of semiannual coupon payments and the principal repayment at maturity.

The bond has a 15-year maturity, which means there are 30 semiannual periods (15 years * 2 periods per year).

Step 1: Calculate the coupon payment per period:
Coupon payment = Coupon rate * Par value / 2
Coupon payment = 0.07 * $1,000 / 2
Coupon payment = $35

Step 2: Calculate the present value of the coupon payments:
PV of coupon payments = Coupon payment * [1 - (1 + r)^(-n)] / r
where r is the going interest rate per period (10% / 2), and n is the total number of periods (30).

PV of coupon payments = $35 * [1 - (1 + 0.10 / 2)^(-30)] / (0.10 / 2)
PV of coupon payments = $636.05

Step 3: Calculate the present value of the principal repayment:
PV of principal repayment = Par value / (1 + r)^n
where r is the going interest rate per period (10% / 2), and n is the total number of periods (30).

PV of principal repayment = $1,000 / (1 + 0.10 / 2)^30
PV of principal repayment = $201.05

Step 4: Calculate the total present value of the bond's cash flows:
Bond price = PV of coupon payments + PV of principal repayment
Bond price = $636.05 + $201.05
Bond price = $837.10

Therefore, the bonds would be selling today at a price of $837.10.

b. If the interest rate remained at 10 percent for the next 10 years, the price of the Cisco Systems bonds would not change significantly. The bond price is primarily affected by changes in the market interest rate. Since the interest rate remains constant, the present value of the bond's cash flows would remain the same, resulting in a relatively stable bond price over time.

To calculate the price of the Cisco Systems bonds today and understand what would happen to the price over time, we need to analyze the bond's features and the impact of changing interest rates.

a. To determine the price of the bonds today, we can use the present value formula. The present value of a bond's future cash flows is the sum of the present values of its coupon payments and the present value of its face value.

The coupon payments can be calculated using the semiannual coupon rate and the number of periods remaining until maturity. In this case, the bonds have a 15-year maturity, so there are 30 six-month periods remaining.

The semiannual coupon payment can be calculated as follows:
Coupon Payment = (Coupon Rate / 2) * Par Value
Coupon Payment = (7% / 2) * $1,000 = $35

The present value of the coupon payments can be calculated using the formula for the present value of an ordinary annuity:
Present Value of Coupon Payments = Coupon Payment * [1 - (1 + Interest Rate / 2)^(-Number of Periods)] / (Interest Rate / 2)
Present Value of Coupon Payments = $35 * [1 - (1 + 10% / 2)^(-30)] / (10% / 2) = $614.07

To calculate the present value of the face value, we use the formula for the present value of a single payment:
Present Value of Face Value = Face Value / (1 + Interest Rate / 2)^(Number of Periods)
Present Value of Face Value = $1,000 / (1 + 10% / 2)^(30) = $239.39

Finally, we can calculate the price of the bonds today by summing the present values of the coupon payments and the face value:
Price of Bonds = Present Value of Coupon Payments + Present Value of Face Value
Price of Bonds = $614.07 + $239.39 = $853.46

Therefore, the bonds would be selling today for $853.46.

b. If the interest rate remains at 10 percent for the next 10 years, the price of the Cisco Systems bonds will stay relatively stable. Since the interest rate remains consistent, the present value of the coupon payments and the face value will not change significantly over time. Consequently, the overall price of the bonds should remain relatively constant.

However, it's important to note that other factors, such as changes in market conditions and the company's creditworthiness, can also affect the price of the bonds. It's always recommended to monitor market conditions and consider a comprehensive analysis before making any investment decision.

BLA