Which of the following statements is false? 

A. If a bond trades at a premium, its yield to maturity will exceed its coupon rate. 

B. A bond trading at a premium is said to be trading above par.

C. When a coupon-paying bond trades at a premium, the investor's coupon yield decreases as he receives a face value less than the price paid for the bond. 

D. Holding the bond yield fixed to maturity, for a bond that is not trading at par, the present value of the bond's remaining cash flows changes as the time to maturity decreases.

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