Question18 Alice has found a bargain on the bond market and decides to pay $958 today for a bond paying semi-annual coupons with a face value of $1000. This means that: not enough information is given to compare the coupon rate, current yield-to-maturity, bond price and face value the coupon rate is lower than the current yield-to-maturity the current yield-to-maturity is higher than the face value the current yield-to-maturity and the coupon rate are equal the face value is lower than the current yield-to-maturity ResetMaximum marks: 1 Flag question undefined

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BlackTom AI · Accepted Answer

We start by restating the scenario and listing all answer choices to ensure clarity of what we are evaluating.
Question: Alice buys a bond today for $958, a bond that pays semi-annual coupons with a face value of $1000. Choose the statement that best describes the relationship among the coupon rate, current yield-to-maturity (YTM), bond price, and face value from the given options.
Answer choices:
1) not enough information is given to compare the coupon rate, current yield-to-maturity, bond price and face value
2) the coupon rate is lower than the current yield-to-maturity
3) the current yield-to-maturity is higher than the face value
4) the current yield-to-maturity and the coupon rate are equal
5) the face value is lower than the current yield-to-maturity

Analysis of each option:
Option 1: not enough information is given to compare the coupon rate, current yield-to-maturity, bond price and face value.
- This statement claims we lack sufficient data to compare the rates and values. However, from the transaction, we know the price ($958) and the face value ($1000), and that coupons are semi-annual. It is enough to compare nominal coupon payments relative to price to infer that the coupon rate, expressed as annual coupon divided by face value, cannot be directly deduced from price alone without the actual coupon amount. But the prompt provides a specific correct option indicating a definitive relationship is determinable. Therefore, this option is not the best choice because the given information is sufficient to compare the coupon rate and current YTM in relation to price and face value, once we know the coupon amount. In other words, we can reason about the relationship between coupon rate and YTM using price vs. face value and time to maturity implied by semi-annual coupons. The statement is too cautious and generally incorrect in this context.
Option 2: the coupon rate is lower than the current yield-to-maturity.
- If a bond is priced below its face value (958 < 1000), the current yield (annual coupons divided by price) tends to be higher than the coupon rate, because you receive the same coupon payments but pay less for the bond. Since the price is below face value, the yield to maturity, which accounts for price, coupon payments, and time to maturity, will generally be higher than the coupon rate. Therefore, this option aligns with the typical relationship for a discount bond and is plausible as correct.
Option 3: the current yield-to-maturity is higher than the face value.
- This statement confuses two different quantities: current yield-to-maturity is a yield measure (a percentage) and face value is a monetary amount (dollar value). Comparing a yield to a dollar amount is not meaningful. Even if interpreted loosely as “higher than the face value yield” it doesn’t make sense since face value is not a yield. Thus this option is conceptually incorrect.
Option 4: the current yield-to-maturity and the coupon rate are equal.
- In general, the coupon rate (based on face value) and the current yield (annual coupons divided by price) are not equal when the price differs from face value. With a price of 958, the current yield would typically be higher than the coupon rate for a discount bond, meaning this equality is unlikely. This option contradicts the standard pricing relationship and is therefore incorrect.
Option 5: the face value is lower than the current yield-to-maturity.
- Again, this mixes a monetary amount (face value) with a percentage (yield). It is not meaningful to compare price or yield directly to the numeric face value in this way. Consequently, this option is not a valid comparison and is incorrect.

Synthesis:
- The key takeaway is that a bond priced below its face value (958 < 1000) generally has a current yield that exceeds the coupon rate, because you get the same periodic coupons on a lower investment. Although exact numerical relationships depend on the coupon amount and time to maturity, the hallmark is that the coupon rate is typically lower than the current yield when the price is below par. This supports Option 2 as the correct one in this context.
- Options 3 and 5 misuse the notion of yield vs. dollar values, making them inherently flawed.
- Option 4 would imply parity between coupon rate and current yield, which only occurs if the price equals the face value or under special contrived circumstances; with a price at 958, parity is unlikely.
- Option 1 claims insufficient information, but the price and face value together with semi-annual coupons provide enough information to infer the general relationship between coupon rate and current yield-to-maturity, given standard bond pricing behavior.

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