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Assume that you are considering the purchase of a 10-year bond with coupon rate of 9.75%. The bond

has a par value of $1,000 and makes semiannual interest payments. If you require a 10% yield to
maturity on this investment, what is the maximum price you should be willing to pay for the bond
(round your answer to two decimal places)?

1 Answer

3 votes

Answer:

the maximum price you should be willing to pay for the bond is $1,141.85.

Explanation:

To calculate the maximum price you should be willing to pay for the bond, we need to calculate the present value of all future cash flows at a discount rate of 10%:

First, we need to calculate the semiannual coupon payment:

Coupon payment = (Coupon rate * Par value) / 2

Coupon payment = (9.75% * $1,000) / 2 = $48.75

Next, we need to calculate the number of periods, which is twice the number of years since the bond makes semiannual payments:

Number of periods = 2 * 10 = 20

Using the present value formula for an annuity, we can calculate the present value of the semiannual coupon payments:

PV of coupon payments = (Coupon payment / Discount rate) * [1 - 1 / (1 + Discount rate)^Number of periods]

PV of coupon payments = ($48.75 / 0.05) * [1 - 1 / (1 + 0.05)^20] = $764.96

Finally, we need to calculate the present value of the par value:

PV of par value = Par value / (1 + Discount rate)^Number of periods

PV of par value = $1,000 / (1 + 0.05)^20 = $376.89

The maximum price you should be willing to pay for the bond is the sum of the present value of the coupon payments and the present value of the par value:

Maximum price = PV of coupon payments + PV of par value

Maximum price = $764.96 + $376.89 = $1,141.85

Therefore, the maximum price you should be willing to pay for the bond is $1,141.85.

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