Current Yield

For a bond bought at a discount, the yields rank:

1. A.Nominal highest, then current, then YTMThis is the premium-bond ordering, memorized correctly but applied to the wrong side of par. A discount buyer pays less than par and is redeemed at par, and that built-in gain lifts the price-sensitive yields above the coupon rather than dropping them below it.
2. B.Current highest, then YTM, then nominalThe bottom of this ranking is right, since nominal yield is indeed lowest on a discount bond, but the top two are swapped. Current yield weighs only the coupon against the discounted price, while YTM adds the capital gain at redemption on top of that, so YTM has to come out higher.
3. C.YTM highest, then current yield, then nominalCorrect - discount-bond yield ranking.
4. D.All equalThe three measures coincide only when a bond trades exactly at par, where the price equals the redemption value and there is no gain or loss to account for. The stem stipulates a discount, and that is precisely what breaks the tie.

Why: On a discount bond: yield to maturity > current yield > nominal (coupon) yield.

A 6% coupon bond is trading at 90 (900 dollars). Its current yield is:

1. A.6.67%Correct - 60 / 900.
2. B.9.00%9.00 is the price quote of 90 relabeled as a percentage, which is a different quantity altogether. Current yield is annual income measured against price, 60 over 900, and the price alone cannot serve as the answer.
3. C.6.00%6.00% is the nominal or coupon yield, which measures the 60 dollars against par. This buyer paid only 900, so the same 60 dollars represents a larger return than 6%. On any discount bond the current yield must sit above the coupon.
4. D.5.40%Backward-solve it: a 5.40% return on 900 dollars implies a coupon near 48.60, but this bond pays 60. The figure comes from scaling the 6% coupon down by the 0.90 price when a below-par price has to scale the yield upward.

Why: Current yield = annual interest / price = 60 / 900 = 6.67%.

A 3% coupon bond trading at 75 (750 dollars) has a current yield of:

1. A.2.25%2.25 is the 3% coupon scaled down by the 0.75 price. A discount means the buyer committed less capital for the same 30 dollars of annual interest, so the return on that smaller outlay must exceed 3%, not fall short of it.
2. B.4%Correct - 30 / 750.
3. C.7.5%7.5 is built from the price alone, the quote of 75 read as a rate. Current yield needs both inputs: 30 dollars of annual interest divided by the 750 actually paid.
4. D.3%3% is the nominal yield, which measures the coupon against par rather than against what this investor paid. Only 750 was committed to collect 30 dollars a year, so the return on invested capital is higher than the stated coupon rate.

Why: Current yield = 30 / 750 = 4%.

For a bond trading at a premium, the yields from highest to lowest are:

1. A.Yield to maturity, then current, then nominalThis is the discount-bond ranking transplanted onto a premium bond. When the buyer pays more than par and is redeemed at par, the built-in capital loss drags yield to maturity to the bottom of the list rather than lifting it to the top.
2. B.They are all equalThe three measures converge only at par, where the purchase price equals the redemption amount and there is nothing to amortize. A premium price is the very condition that pulls them apart.
3. C.Current, then nominal, then yield to maturityCloser than most, since it correctly puts yield to maturity at the bottom. It breaks at the top: current yield divides the coupon by a price above par, which makes it smaller than the coupon, so it cannot outrank nominal. On a premium bond nominal leads.
4. D.Nominal, then current yield, then yield to maturityCorrect - premium bond yield ranking.

Why: On a premium bond: nominal (coupon) yield is highest, then current yield, then yield to maturity is lowest.