A bond sells at discount. Which of the following is feasible?
[YTM = yield to maturity]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → YTM = 12%, current yield = 11%, coupon yield = 10%
A bond sells at a discount when its price is below its face value.
The current yield is the annual coupon divided by the price. With a price below face value, it is more than the coupon rate.
The YTM also includes the gain from buying below face value and receiving the full face value at maturity, so it is more than the current yield.
Hence, for a discount bond:
\( \displaystyle \text{coupon rate}\lt\text{current yield}\lt\text{YTM} \)
Only 10% < 11% < 12% in Option (1) follows this order.
Why the other options are incorrect
Option (2) YTM = 10%, current yield = 11%, coupon yield = 12% — Incorrect. Coupon 12% > current yield 11% > YTM 10% is the order for a bond selling at a premium.
Option (3) YTM = current yield = coupon yield = 12% — Incorrect. All three yields are equal only for a bond selling at par.
Option (4) YTM = 10%, current yield = 12%, coupon yield = 11% — Incorrect. The current yield 12% is above the coupon 11%, as it should be, but a discount bond cannot have YTM 10% below its current yield.
Tip: Remember the chain: discount ⇒ coupon < current yield < YTM; premium ⇒ the order reverses; at par all three are equal.
CBSE Applied Mathematics (Class XII):
Relationship Between Bond, YTM and Coupon Yield
