Which of the following statements about bonds are correct?
(A) When a bond sells at a discount, its yield to maturity is greater than its current yield, and its current yield is greater than its coupon rate.
(B) When a bond sells at a premium, its current yield is greater than its coupon rate.
(C) When a bond sells at par, its yield to maturity, current yield and coupon rate are all equal.
(D) A bond sells at a premium when its market price is less than its face value.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (C) only
Let F be the face value, P the market price and R the yearly coupon. Then
\( \displaystyle \text{Coupon rate} = \frac{R}{F}, \qquad \text{Current yield} = \frac{R}{P} \)
At a discount (P < F) the current yield is above the coupon rate, and the buyer also gains F − P at maturity, so the yield to maturity is higher still. At a premium (P > F) the order is reversed, and at par all three are equal.
So at a discount YTM > current yield > coupon rate, at a premium coupon rate > current yield > YTM, and at par all three are equal.
Checking the statements
(A) When a bond sells at a discount, its yield to maturity is greater than its current yield, and its current yield is greater than its coupon rate. — Correct. P < F makes R/P > R/F, and the gain at maturity raises the YTM further.
(B) When a bond sells at a premium, its current yield is greater than its coupon rate. — Incorrect. P > F makes R/P smaller than R/F.
(C) When a bond sells at par, its yield to maturity, current yield and coupon rate are all equal. — Correct. P = F gives R/P = R/F, with no gain or loss at maturity.
(D) A bond sells at a premium when its market price is less than its face value. — Incorrect. That is a discount; a premium means the price is above the face value.