Yield to Maturity (YTM)

D is correct. Bond X (discount bond) has a YTM higher than its current yield because YTM includes both the annual coupon income AND the $50 capital gain ($1,000 par - $950 purchase price) realized at maturity, spread over the 10-year holding period. For discount bonds, the yield hierarchy is always: YTM > Current Yield > Coupon Rate.

A is incorrect because it reverses the relationship: discount bonds have YTM HIGHER than current yield, not lower. B is incorrect because premium bonds (like Bond Y) have YTM LOWER than current yield due to the capital loss at maturity. C is incorrect because YTM depends on multiple factors (coupon, price, time to maturity); discount bonds do not automatically have higher YTM than all premium bonds. Without calculating both bonds' YTM, we cannot determine which is higher.

B is correct. The fundamental assumption of YTM is that all coupon payments received during the bond's life are reinvested at the same YTM rate. This reinvestment assumption is critical to achieving the calculated YTM. If coupons are reinvested at lower rates, actual return will be less than YTM. If reinvested at higher rates, actual return will exceed YTM.

A is incorrect because YTM is calculated at a point in time and does not assume rates remain constant; in fact, changing market rates affect the bond's price and thus its YTM for new purchasers. C is incorrect because YTM assumes the bond is held to maturity, not called (Yield to Call addresses callable bonds). D is incorrect because YTM specifically assumes the bond is held until maturity and redeemed at par, not sold early.

C is correct. Current yield = $60 annual coupon / $1,080 price = 5.56%. For premium bonds, the yield hierarchy is: Coupon Rate (6.00%) > Current Yield (5.56%) > YTM (lower than 5.56%). YTM is lower than current yield because it accounts for the $80 capital loss ($1,080 purchase price - $1,000 redemption at maturity) spread over 8 years, which reduces total return below the current yield.

A reverses the premium bond relationship; YTM is LOWER than current yield for premium bonds, not higher. B is incorrect because current yield adjusts the coupon rate for the current market price; at a premium, current yield is less than the 6.00% coupon. D confuses coupon rate with YTM; while the coupon payment is fixed at $60 annually (6% of par), YTM changes based on purchase price and time to maturity.

D is correct (the EXCEPT answer). YTM does NOT increase when bond prices rise; in fact, YTM and bond prices have an inverse relationship. When bond prices increase, YTM decreases, and vice versa. If a bond's price rises from $950 to $1,000, its YTM falls because the investor pays more for the same future cash flows.

A is accurate: YTM incorporates both periodic coupon payments and the capital gain (for discount bonds) or loss (for premium bonds) realized at maturity. B is accurate: the YTM calculation assumes all coupons are reinvested at the YTM rate, which is why actual returns may differ. C is accurate: when a bond trades at exactly par ($1,000), the YTM, current yield, and coupon rate are all identical because there is no capital gain or loss at maturity.

B is correct. Statements 2 and 3 are accurate.

Statement 1 is FALSE: For a discount bond (purchased below par), the current yield is HIGHER than the coupon rate, not lower. Current yield = $50 / $920 = 5.43%, which exceeds the 5% coupon rate.

Statement 2 is TRUE: For discount bonds, YTM is the highest yield because it includes both the annual $50 coupon payments AND the $80 capital gain ($1,000 - $920) realized at maturity. The yield hierarchy for discount bonds is: YTM > Current Yield > Coupon Rate.

Statement 3 is TRUE: The annual coupon payment is fixed at 5% of the $1,000 par value, which equals $50 per year ($25 semi-annually), regardless of the purchase price.

Statement 4 is FALSE: YTM assumes coupons are reinvested at the YTM rate (approximately 5.7% for this bond), not the 5% coupon rate. This is a common misconception; the reinvestment rate equals the YTM, not the coupon.