Question

Under what circumstances might you be willing to pay more than $1,000 for a coupon bond that matures in three years, has a coupon rate of 10 percent, and a face value of $1,000?
If the interest rate in the market were  (1)  than 10 percent, the present value of the payment flows associated with the bond would be  (2)  than $1,000

1) a) Less b) More

2) a) Lower b) Higher

I don't need the answer to the first question. I just need the answer to 1 & 2.

Answer 1

If the interest rate in the market were less than 10 percent, the present value of the payment flows associated with the bond would be Higher

Bond sells at a premium (more than the face value) we can prove that through the following calculation

Assumption: Frequency of coupon payments is Annual, market rate 9%

Coupon payment = 1000* 10% =100, market rate or r is 9%, maturity or n is 3yrs, FV 1000

Bond Price formula = (Coupon payment* [ 1- (1+r) ^-n] / r) + FV * (1+r) ^-n ]

100*((1-((1.09)^-3)/0.09)) + (1000*((1.09)^-3))

100*((1-(0.7722)/0.09)) + (1000*(0.77218))

100*(0.2278)/0.09)) + (1000*(0.77218))

100*(0.2278)/0.09)) + (772.18)

(100*(2.5313)) + (772.18)

$1025.31