A n-year bond with face value F,has a coupon rate equal to the yield rate,r = i.The bond is redeemable at C,where C

Question

A n-year bond with face value F,has a coupon rate equal to the yield rate,r = i.The bond is redeemable at C,where C < F.What can you say about the price,P,that an investor would pay for the bond?
A)It is greater than C
B)It is less than C
C)It is equal to C
D)It is equal to F

Quizplus · Accepted Answer

When the coupon rate equals the yield rate, the price of the bond is equal to its face value if it were redeemable at face value. However, because it is redeemable at C, where C < F, the redemption value is less than the face value, leading to a decrease in the bond's price. Despite this, the bond's price at issuance reflects the present value of its future cash flows (coupons and redemption value), which are discounted at the yield rate. Since the coupons are set to match the yield rate, they essentially ensure that the bond's price is initially set around its face value, F, not C. However, the redemption at C < F introduces a loss at maturity compared to the face value, but this does not mean the price paid for the bond falls below C because the coupons add value above the redemption value. Therefore, the price is greater than C, reflecting the value of receiving the coupon payments plus the redemption amount, even though it's discounted for being below F.

A N-Year Bond with Face Value F,has a Coupon Rate