If an investor requires a 10 percent return on a $1000 bond with a 7% coupon rate, what will the investor be willing to pay for the bond today if it matures in 8 years and interest is paid semiannually? What if interest is compounded and paid annually?

A) $839.95; $837.43
B) $1,194.80; $837.33
C) $837.43; $839.95
D) $840.45; $1,194.80

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durga lakshmi · Accepted Answer

Final Answer : C, Explanation :  First, we need to calculate the semi-annual coupon payments. The coupon rate is 7% and the face value is $1000, so the semi-annual coupon payment is $35 ($1000 x 0.07 / 2).To calculate the present value of the bond with semi-annual payments, we need to use the following formula:PV = (C / r) x [1 - 1 / (1 + r)^n] + FV / (1 + r)^nwhere PV is the present value, C is the coupon payment, r is the required rate of return (10% or 0.05 in decimal form), n is the number of periods (8 years or 16 semi-annual periods), and FV is the face value of the bond ($1000).Using this formula, we get:PV = ($35 / 0.05) x [1 - 1 / (1 + 0.05)^16] + $1000 / (1 + 0.05)^16PV = $837.43Therefore, the investor would be willing to pay $837.43 for the bond today if interest is paid semi-annually.To calculate the present value of the bond with annual compounding, we need to use the same formula but adjust the number of periods to 8 and divide the required rate of return by 2 (since interest is now compounded annually instead of semi-annually).Using this formula, we get:PV = ($70 / 0.05) x [1 - 1 / (1 + 0.05)^8] + $1000 / (1 + 0.05)^8PV = $839.95Therefore, the investor would be willing to pay $839.95 for the bond today if interest is compounded and paid annually.

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