Lesson 2.2: Bond Math

A company currently has earnings of $4.00 and pays a $0.50 quarterly dividend. If the market price is $40, what is the current yield? A)10.00% B)5.00% C)15.00% D)1.25%

B)5.00% The quarterly dividend is $0.50, so the annual dividend is $2.00; $2 ÷ $40 (market price) = 5% annual yield (current yield).

GHI common stock has a $10 par value and is selling in the market for $60 per share. If the current quarterly dividend is $1, the current yield is A)10%. B)1%. C)1.7%. D)6.7%

D)6.7%. Current yield is determined by dividing the annual dividend of $4 ($1 per quarter × 4 = $4) by the current stock price of $60 ($4 ÷ $60 = 6.7%). The par value of the common stock has no relevance to this question.

What would likely happen to the market value of existing bonds during an inflationary period coupled with rising interest rates? A)The nominal yield of the bonds would increase. B)The price of the bonds would stay the same. C)The price of the bonds would increase. D)The price of the bonds would decrease.

D)The price of the bonds would decrease. Bond prices fall when interest rates rise because bond prices have an inverse relationship with interest rates.

Several years ago, an investor purchased an investment-grade bond with a 6% coupon. Today, that bond is priced to yield 4.6% to maturity in five years. If the bond is called at par in one year, the bond's yield will be A)more than 4.6%. B)4.6%. C)the coupon rate of 6% because it is called at par value. D)less than 4.6%.

D)less than 4.6%.. Let's take things in order. If a bond with a 6% coupon is showing a YTM below 6%, the bond must be selling at a premium. When bonds selling at a premium are called in advance of the maturity date, the loss (the difference between the premium and the par value) is recognized sooner than expected. This results in a yield to call (YTC) that is less than the YTM.

BFJ Corp.'s 5% convertible bond is trading at 120. The bond is convertible at $50. An investor buying the bond now and immediately converting into common stock would receive A)20 shares. B)24 shares. C)2.4 shares. D)20 shares plus cash for fractional shares.

A)20 shares The conversion ratio always uses the par value ($1,000), never the current market price. With a par value of $1,000 and a conversion price of $50 per share, this bond is convertible into 20 shares ($1,000 / $50). Remember, the number of shares in a conversion never changes. When the market price changes, the parity price changes, but that isn't relevant to this question.

Mitch purchased a 30-year bond for 97¾ with a stated coupon rate of 8.5%. What is the approximate yield to maturity for this investment if Mitch receives semiannual coupon payments and expects to hold the bond to maturity? A)5.68% B)8.67% C)4.36% D)8.50%

B)8.67% No calculation is necessary here. Why not? Because anytime a bond is purchased at a discount from par (97¾% is a discount), the YTM must be greater than the nominal (coupon) rate. There is only one choice greater than 8.5%. It isn't about your computational skills; it is about your understanding of the relationship between prices and yields.

Which of the following expressions describes the current yield of a bond? A)Yield to maturity divided by par value B)Yield to maturity divided by current market price C)Annual interest payment divided by par value D)Annual interest payment divided by current market price

B)Yield to maturity divided by current market price The current yield on a bond is calculated by dividing the annual interest payment by the current market price of the bond.

If a customer buys a 6% bond maturing in eight years on a 7.33 basis, the price of the bond is A)below par. B)above par. C)inverted. D)at par.

B)above par A bond with a basis, or yield to maturity, greater than its coupon is trading at a discount, or below par.

A bond selling for $20 above par would be quoted A)120. B)102. C)1,200. D)1,020.

B)102. Bonds are quoted in percentages of $1,000 (par) (1% of $1,000 = $10). The proper quote would be 102; 102 is 102% of $1,000.

The current yield on a bond with a coupon rate of 5.5% selling at 110 is A)5.5%. B)6.0%. C)5.0%. D)2.0%.

C)5.0% The current yield of any security, equity, or debt is always the income return (dividend or interest) divided by the current market price. In this case, it is the annual interest of $55 ($1,000 × 5.5%) divided by $1,100, and that equals 5%.

If a company's dividend increases by 5% but its market price remains the same, the current yield of the stock will A)remain at 7%. B)decrease. C)increase. D)remain at 5%.

C)increase. The current yield of a stock is the annual dividend divided by the market price. If a company's dividend increases and its market price remains the same, its current yield will increase.

A client approaches the investment adviser representative handling the advisory account with a request to find a preferred stock that will offer a 5.4% income return. The IAR suggests a stock paying a $1.73 quarterly dividend. That stock will meet the income objective if it has a current market price of A)$128.15. B)$78.03. C)$37.37. D)$32.04.

A)$128.15 The first thing to do is annualize the dividend by multiplying the $1.73 by 4. Once we have the annual dividend of $6.92, divide by 5.4% and the result is $128.148148 or $128.15 properly rounded. If you left your math skills at home, all you have to do is multiply each of the 4 choices by 5.4% to see which one is closest to $6.92.

When a bond is selling at a premium, a bond callable at par will A)have a YTM that is more than the coupon. B)have a YTC that is less than the YTM. C)have a current yield that is less than the YTM. D)have a YTC that is more than the coupon.

B)have a YTC that is less than the YTM. A bond selling at a premium will always have a yield that is lower than the coupon. The highest of the computed yields will be the current yield because, unlike the YTM or the YTC, the loss at payoff of the principal is not included. Comparing YTM and YTC, because in both cases the investor is getting back the same par value, the YTC is lower because the loss is occurring sooner (bonds are always called prior to maturity).

When current interest rates are at 6%, you would expect a bond with a nominal yield of 4% to be A)in danger of default. B)selling at par. C)selling at a discount. D)selling at a premium.

C)selling at a discount. With the market rate of return at 6%, a 4% bond just isn't as valuable, so the only way investors will be interested is if they can acquire it at a discount. That discount works out to be a figure that will result in a 6% return for the purchaser. Remember, as interest rates go up, bond prices go down, and vice versa.

XYZ Corporation's A-rated convertible debenture is currently selling for 90. If the bond's conversion price is $40, what is the parity price of the stock? A)$44.00 per share B)$22.50 per share C)$40.00 per share D)$36.00 per share

D)$36.00 per share If the bond's conversion price is $40, it means the bond is convertible into 25 shares ($1,000 par value divided by the $40 conversion price). Parity means equal, so what does each share have to be worth so that 25 of them are equal to $900? Remember, bonds are quoted as a percentage of the $1,000 par value, so a price of 90 means $900. Dividing $900 by 25 shares results in a parity price of $36. That does not mean the stock is selling for $36 per share (probably a bit less), but at $36, holding the bond, or converting into the stock, gives the investor equal value. Some students quickly see that the bond is 10% below its par value, so the stock—to be equal—must be 10% below the conversion price. Take 10% off $40 and the result is $36. Either way works.

A company with 20 million shares outstanding paid $36 million in dividends. If the current market value of the company's shares is $36, the current yield is A)10%. B)not determinable from the information given. C)2%. D)5%.

D)5% The current yield formula is annual dividends per share divided by current market price. The dividends per share are $36 million ÷ 20 million shares = $1.80 per share. Current yield is $1.80 ÷ $36.00 = 5%.

Currently, a company issues 5% Aaa/AAA debentures at par. Two years ago, the corporation issued 4% AAA rated debentures at par. Which of the following statements regarding the outstanding 4% issue are true? The dollar price per bond will be higher than par. The dollar price per bond will be lower than par. The current yield on the issue will be higher than the coupon. The current yield on the issue will be lower than the coupon. A)I and III B)II and IV C)I and IV D)II and III

D)II and III Explanation Interest rates in general have risen since the issuance of the 4% bonds, so the bond's price will be discounted to produce a higher current yield on the bonds. Remember that as interest rates go up, the price of outstanding debt securities goes down.

The annual interest payment divided by the current dollar price of a bond is A)the nominal yield. B)the yield to maturity. C)the tax-equivalent yield. D)the current yield

D)the current yield. The current yield is the annual interest (in dollars) divided by the bond's market price (in dollars). A bond's nominal yield is the coupon yield, or stated interest rate. Yield to maturity takes into account the bond's price, as well as its interest rate.

A bond is selling at a premium over par value. Therefore, A)its yield to maturity is greater than its current yield. B)none of these are correct. C)its nominal yield is less than its current yield. D)its current yield is less than its nominal yield.

D)its current yield is less than its nominal yield.-> Any bond selling at a premium will yield less than the coupon rate (nominal yield). Conversely, of course, a bond trading at a discount will certainly yield more. Remember, there is an inverse relationship between bond prices and bond yields.

An investor purchases a Treasury note and the confirmation shows a price of $102.21. Rounded to the nearest cent, the investor's cost, excluding commissions, is A)$102.21. B)$1,022.10. C)$1,026.56. D)$1,022.21.

C)$1,026.56. Treasury notes are quoted in 32nds, where each 32nd equals $0.3125. The 102 in the quote equals $1,020 and the 21/32 is an additional $6.56, bringing the total to $1,026.56.

A bond purchased at $900 with a 5% coupon and a five-year maturity has a current yield of A)5.00%. B)7.80%. C)7.40%. D)5.56%

D)5.56%. Current yield is determined by dividing the annual interest payment by the current market price of the bond ($50 ÷ $900 = 5.56%). Years to maturity is not a factor in calculating current yield.

Which of the following expressions describes the current yield of a bond? A)Yield to maturity divided by par value B)Yield to maturity divided by current market price C)Annual interest payment divided by par value D)Annual interest payment divided by current market price

D)Annual interest payment divided by current market price The current yield on a bond is calculated by dividing the annual interest payment by the current market price of the bond.

In order to compute yield to maturity, all of the following are necessary except A)the maturity date. B)the nominal yield. C)the current market price. D)the call price

D)the call price. Computing the yield to maturity (YTM) does not require the call price or call date—that is necessary to compute the yield to call (YTC). We do need to know the current market price, the coupon (nominal yield), and the maturity date.

If investors hold bonds until maturity, their realized rate of return, assuming all interim cash flows are reinvested at that same rate, would be equal to A)the income return. B)the yield to maturity. C)the price return. D)the coupon return.

B)the yield to maturity. The yield to maturity is an investor's total return if they purchase the bond at any point and then hold it until maturity, assuming all interim cash flows are reinvested at that same YTM. This takes into consideration any capital gain or loss; therefore, the yield to maturity will fluctuate with the bond's price.

DERP Corporation's 5% convertible debentures maturing in 2030 are currently selling for 120. The conversion price is $40. One would expect the DERP common stock to be selling A)somewhat above $30 per share. B)somewhat below $30 per share. C)somewhat below $48 per share. D)somewhat above $48 per share.

C)somewhat below $48 per share. The first step here is to compute the parity price. A conversion price of $40 means the debenture is convertible into 25 shares of the common stock (par of $1,000 divided by $40 = 25 shares). With a current market price of $1,200, the parity price of the stock would be $48. Because convertible securities generally sell at a slight premium over their parity price, the stock should have a current market value a bit less than $48 per share.

Which of the following indicates a bond selling at a discount? A)5% coupon yielding 5% B)7% coupon yielding 6.5% C)10% coupon yielding 9% D)7% coupon yielding 7.5%

D)7% coupon yielding 7.5% Explanation Whenever the yield is higher than the coupon, the bond is selling at a discount from the par value. When the question says "yielding," it is generally referring to the yield to maturity. However, whether referring to the YTM or the current yield, the answer here is the same: the yield is higher than the coupon.

A bond with a par value of $1,000 and a nominal yield of 6% paid semiannually is currently selling for $1,300. The bond matures in 25 years and is callable in 15 years at $1,080. In the computation of the bond's yield to call, which of these would be a factor? A)Future value of $1,300 B)50 payment periods C)Present value of $1,080 D)Interest payments of $30

D)Interest payments of $30 Explanation The YTC computation involves knowing the amount of interest payments to be received, the length of time to the call, the current price, and the call price. With a 15-year call, there are only 30 semiannual interest payment periods, not 50. The present value is $1,300 and the future value is $1,080, the reverse of the numbers indicated in the answer choices.

An investor is trying to decide whether to purchase $10,000 face amount of a U.S. Treasury bond or a highly rated corporate bond. The price of the Treasury bond is 102.20 while the price of the corporate bond is 99 3/8. If the investor decides to purchase the Treasuries, disregarding commissions, the price difference is A)$28.25. B)$325.00. C)$32.50. D)$282.50.

A)$28.25. The first step is remembering that Treasuries are quoted in 32nds. That means that 102.20 is 102 and 20/32 which is 102 5/8. Subtract 99 3/8 from 102 5/8 to get 3 2/8 or 3 1/4. On a $1,000 bond, that is $32.50. Then, note that this investor is purchasing 10 bonds, so the difference in price is $32.50 times 10 or $325.

An investor buys 10M 6.6s of 10 at 67. The investor will receive annual interest of A)$670. B)$660. C)$1,000. D)$820.

B)$660. Interpret "10M" as "$10,000 worth of." The investor receives the nominal yield of the bonds, which is 6.6% of $10,000. The M is from the roman numeral for 1,000.

An investor buys 10M RAN 6.6s of 32 at 67. What is the total purchase price? A)$10,000 B)$10,200 C)$6,700 D)$6,600

C)$6,700. For those of you not familiar with bond listings, this means that the investor bought $10,000 (10M) of the RAN Corporation bonds with a 6.6% coupon (interest rate stated on the face of the bond) that mature in 2032 (32). The price is 67, which represents 67% of $10,000, or $6,700.

A bond with a par value of $1,000 and a coupon rate of 8% paid semiannually is currently selling for $1,150. The bond is callable in 10 years at $1,100. In the computation of the bond's yield to call, which of these would be a factor? A)60 payment periods B)Future value of $1,150 C)Present value of $1,100 D)Interest payments of $40

D)Interest payments of $40 The YTC computation involves knowing the amount of interest payments to be received, the length of time to the call, the current price, and the call price. A bond with an 8% coupon will make $40 semiannual interest payments. With a 10-year call, there are only 20 payment periods, not 60. The present value is $1,150 and the future value is $1,100, the reverse of the numbers indicated in the answer choices.

During the past year, the market price of Kapco common stock has increased from $47 to $50 per share. Over that period, Kapco's earnings per share (EPS) have increased from $2.00 to $2.50 per share, and their dividend payout ratio has decreased from 50% to 40%. Based on this information, the current yield on Kapco common stock is A)2.13%. B)2.00%. C)4.26%. D)6.34%.

B)2.00%. The current yield on a stock is computed by dividing the annual dividend rate by the current market price. With EPS of $2.50 and a 40% payout ratio, the annual dividend is $1.00. This dollar divided by the current market price of $50.00 results in a current return of 2%.

An investor sells ten 5% bonds at a profit and buys another 10 bonds with a 5¼% coupon rate. The investor's yearly return will increase by A)$1.00 per bond. B)$2.50 per bond. C)$2.00 per bond. D)$1.50 per bond

B)$2.50 per bond. The first bonds are 5% and pay $50 per year per bond. The new bonds are 5¼% and pay $52.50 per year per bond. A 5% coupon rate × $1,000 face value = $50 per year per bond; a 5¼% coupon rate × $1,000 face value = $52.50 per year per bond.

ABC's stock has paid a regular dividend every quarter for the past several years. If the price of the stock has remained the same over the past year but the dividend amount per share has increased, it may be concluded that ABC's A)current yield per share has decreased. B)current yield per share has increased. C)yield to maturity has gone up. D)current yield per share has been unaffected.

B)current yield per share has increased. The current yield would have increased because current yield is the income (dividend) divided by price. A higher dividend divided by the same price results in a higher yield. Stocks do not have a yield to maturity.

An investor purchased a 20-year bond with a duration of 11 years for $1,323.18. Which of these statements is correct? A)The current yield is higher than both the coupon rate and the YTM. B)The yield to maturity (YTM) is less than both the current yield and the coupon rate. C)The coupon rate is lower than the YTM, and the current yield should be higher than the coupon rate. D)The coupon rate is higher than the YTM, and the YTM is higher than the current yield.

B)The yield to maturity (YTM) is less than both the current yield and the coupon rate. CR = coupon rate CY = current yield YTM = yield to maturity Premium bonds: CR > CY > YTM Par bonds: CR = CY = YTM Discount bonds: CR < CY < YTM Because the bond was purchased at a premium, the yield to maturity is less than both the current yield and the coupon rate. The duration has nothing to do with the question.

For a bond selling at a discount, the yield to maturity will be A)lower than the nominal yield. B)higher than the nominal yield. C)higher than the yield to call. D)equal to the nominal yield.

B)higher than the nominal yield. Yield to maturity is a measure of the total return on a long-term bond, including capital appreciation and interest, while nominal yield measures the interest rate stated on the face of the bond. An investor who buys a $1,000 bond at a discount (for less than $1,000) will receive the interest payments on the bond at the nominal rate and will still receive $1,000 for the bond when it matures. As a result, the total return will be higher than the nominal yield. When a bond is selling at a discount, the YTC will always be higher than the YTM.

Your client with $100,000 to invest is looking for maximum current income. Which of the following would offer the highest current return? A) $100,000 of zero-coupon bonds with a yield to maturity of 6% B) $100,000 market value of corporate bonds selling at a premium and yielding 6% to maturity C)$100,000 AA rated corporate bonds trading at par with a 6% coupon rate D)$200,000 of utility common stock paying a current dividend of 3.5%

C)$100,000 AA rated corporate bonds trading at par with a 6% coupon rate When you read the full question, including the answer choices, you can immediately disregard two of the four options. With $100,000 to invest, the answer cannot be to purchase $200,000 of anything. Maximizing current income excludes zero-coupon bonds because there is no current income. Now, to the correct choice. Why does a bond sell at a premium over par? Although there are exceptions, primarily it is because the coupon rate on that bond is higher than the current market interest rate. Therefore, with a higher coupon rate, the current income on the same amount of principal invested ($100,000 in our question) will always be higher for a bond selling at a premium. That is the KISS (Keep It Simple Student) answer. For those who want to delve further, here we go. For example, if current market interest rates are 6% (likely the case here because the AA rated bonds with a 6% coupon are trading at par), then a bond with a 7% coupon will be selling at a premium. The current yield on $100,000 of the 6% bonds would be $6,000 per year. If a bond's yield to maturity is 6% and it is selling at a premium, it must be that the coupon is higher than 6%. For example (and we're doing the math that you won't have to do), $93,000 par (93 times $1,000) value of bonds with a 7% coupon, selling at $100,000 (a premium over the $93,000), and maturing in 10 years has a YTM of 6%. Investing $100,000 into these bonds will result in current income of $6,510 per year ($93,000 par times the 7% coupon).

One year ago, ABC Widgets, Inc., funded an expansion to its manufacturing facilities by issuing a 20-year first mortgage bond. The bond is secured by the new building and land. The bond was issued with a 5.5% coupon and is currently rated Aa. The current market price of the bond is 105, resulting in a current yield of approximately A)5.61%. B)5.24%. C)4.99%. D)5.50%.

C)4.99%. Corporate bonds are quoted as a percentage of the $1,000 par value. A market price of 105 is equal to $1,050 (105% × $1,000). Each $1,000, 5.5% bond pays $55 of interest annually ($1,000 × 5.5% = $55). Current yield equals the annual interest divided by the current price of $1,050. The calculation is $55 ÷ $1,050, which is equal to approximately 5.24%. Because the bond is at a premium, the current yield must be below the nominal yield, which removes two of the choices from consideration.

A bond with a par value of $1,000 and a coupon rate of 5%, paid semiannually, is currently selling for $1,200. The bond matures in 10 years and is callable in six years at 103. In the computation of the bond's yield to call, which of the following would be a factor? A)20 payment periods B)Interest payments of $25 C)Future value of $1,200 D)Present value of $1,030

B)Interest payments of $25 The YTC computation involves knowing the amount of interest payments to be received, the length of time to the call, the current price, and the call price. A bond with a 5% coupon will make $25 semiannual interest payments. With a six-year call, there are only 12 payment periods, not 20. The present value is $1,200 and the future value is $1,030, the reverse of the numbers indicated in the answer choices.

On the initial public offering, an investor buys a $10,000 Aa-rated, 20-year corporate bond with a 4% coupon rate. One year later, the prevailing market rate is 5% and the bond has had its rating increased to Aa1. Which of the following statements is most likely true with reference to the current market price of this bond? A)The bond would be selling at par value. B)The bond would be selling at a discount. C)The yield to maturity of this bond is above 4%. D)The bond would be selling at a premium.

B)The bond would be selling at a discount. Explanation When interest rates go up, bond prices go down. Had interest rates remained the same, the slight improvement in rating would have probably caused the bond to sell at a very slight premium, but that rating increase is not nearly strong enough to offset a 25% increase in market interest rates. Because this bond would be selling at a discount, its YTM would be above 4%, but the question is asking about the current market price, not the yield.

A client of yours owns some convertible preferred stock. She notices an article in the business section of her local newspaper that reports the company is going to pay a 20% stock dividend on their common stock. How will this affect her? A)There will be no effect. B)More than likely, the price of the preferred stock will rise. C)If there is an antidilution clause, her conversion privilege will permit her to acquire 20% more shares than before the stock dividend. D)She will also receive 20% more shares because preferred stock has a priority claim ahead of common.

C)If there is an antidilution clause, her conversion privilege will permit her to acquire 20% more shares than before the stock dividend. Most convertible securities are sold with antidilutive clauses that provide for an adjustment in the number of shares based on stock splits or stock dividends.

One year ago, ABC Widgets, Inc., funded an expansion to its manufacturing facilities by issuing a 20-year first mortgage bond. The bond is secured by the new building and land and is callable at par 15 years after the issue date. The bond was issued with a 5.5% coupon and is currently rated Aa. If the current market price of the bond is 105, A)the yield to maturity is higher than the current yield. B)the nominal yield is lower than the current yield. C)the yield to call is higher than the current yield. D)the yield to call is lower than the yield to maturity.

D)the yield to call is lower than the yield to maturity. When a bond is selling at a premium (105 means 105% of $1,000, or $1,050), the order—from highest to lowest yield—is nominal (coupon) yield, current yield, YTM, and YTC. If the bond is callable at a premium, the order could be changed, but it is highly unlikely that the exam will present that situation in a question.

ABC Corporation's 5% mortgage bond is currently trading at a premium. The bond is callable at par in 10 years and matures in 15 years. When comparing the returns available to an investor, it would be accurate to state A)the yield to maturity is higher than the current yield. B)the current yield is higher than the nominal yield. C)the yield to call is higher than the current yield. D)the yield to maturity is higher than the yield to call.

D)the yield to maturity is higher than the yield to call. Whenever a bond is selling at a premium, the return—in descending order—is nominal yield, current yield, YTM, and YTC. It is the reverse order when the bond is selling at a discount. When the bond is at par, all are the same (if the call is at par).

A customer purchased a 5% U.S. government bond yielding 6%. A year before the bond matures, new U.S. government bonds are being issued at 4%, and the customer sells the 5% bond. The customer probably did which of the following? Bought it at a discount Bought it at a premium Sold it at a discount Sold it at a premium A)I and III B)II and III C)II and IV D)I and IV

D)I and IV The customer purchased the 5% bond when it was yielding 6% (at a discount). The customer sold the bond when other bonds of like kind, quality, and maturity were yielding 4%. The bond is now at a premium. Therefore, the customer realized a capital gain.

Your customer owns 1,000 shares of the XYZ $100 par 5½% callable convertible preferred stock convertible into four shares of XYZ common stock at $25. What should she be advised to do if the board of directors were to call all the preferred at 106 when the XYZ common stock is trading at $25.50? A)Place irrevocable instructions to convert the preferred stock into common stock and sell short the common stock immediately. B)Hold the preferred stock to continue the 5½% yield. C)Convert her preferred stock into common stock because it is selling above parity. D)Present the preferred stock for the call because the call price is $4 above the parity price.

D)Present the preferred stock for the call because the call price is $4 above the parity price. If the preferred stock is called, the client will receive $106 per share or $106,000. Tendering the preferred stock will provide the highest value. The value of converting the preferred stock into four shares of common is worth $102 (4 × $25.50 = $102), which is less than the call value of $106. On the 1,000 shares, this is a $4,000 difference. The dividends will cease on the call date if the preferred stock is held beyond the call date.

A client approaches the investment adviser representative handling the advisory account with a request to find a preferred stock that will offer a 6% income return. The investment adviser representative suggests a stock paying a $0.28 quarterly dividend. That stock will exactly meet the income objective if it has a current market price of A)$4.67. B)$18.67. C)$11.91. D)$6.72.

B)$18.67. The first thing to do is annualize the dividend by multiplying the $0.28 by 4. Once we have the annual dividend of $1.12, divide by 6% and the result is $18.6666, or $18.67 properly rounded. If you left your math skills at home, all you have to do is multiply each of the choices by 6% to see which one is closest to $1.12.

A corporation issued a bond with a coupon of 6%, callable at 103. The bond matures in 2059. Current interest rates are 8%. It is most likely that A)the coupon will be increased. B)the bond is selling at a discount. C)the bond will go into default. D)the bond will be called.

B)the bond is selling at a discount. -> There is excess information in this question (a favorite trick of the test authors). We don't need to know the call price or the maturity date. We have a 6% bond when current market interest rates are 8%. The inverse relationship between interest rates and bond prices teaches us that this bond is going to be selling at a discount. Bonds are called when interest rates go down, not when they rise. The coupon on a bond is fixed.

GHI currently has earnings of $4.00 and pays a $0.50 quarterly dividend. If GHI's market price is $40.00, the current yield is A)5.00%. B)10.00%. C)1.25%. D)15.00%.

A)5.00% The quarterly dividend is $0.50, so the annual dividend is $2.00; $2 ÷ $40 market price = 5% current yield.

If GHI currently has earnings of $3.00 and pays an annual dividend of $1.75 and GHI's market price is $35, the current yield is A)5.00%. B)3.00%. C)8.60%. D)1.75%

A)5.00%. The current yield is calculated by dividing the annual dividend by the current market value ($1.75 ÷ $35.00 = 5%).

Which of the following indicates a bond selling at a premium? A)8% coupon yielding 7.5% B)8% coupon yielding 8.5% C)10% coupon yielding 11.0% D)5% coupon yielding 5.0%

A)8% coupon yielding 7.5% Whenever the yield is less than the coupon, the bond is selling at a premium over the par value. In our question, the coupon or nominal rate is 8%, but the bond is selling at a price that makes its current yield 7.5%. That happens only when the investor pays more than par (face) value, a premium, for the bond.

A company has two outstanding bond issues, both with a coupon rate of 10%. Bond A will mature in 3 years while Bond B will mature in 20 years. If interest rates were to decrease to 8%, which of the following statements is correct? A)Bond B will be selling at a greater premium than Bond A. B)The issuer will attempt to call in Bond A. C)Both bonds will be selling at a discount. D)Bond B will be selling at a greater discount than Bond A.

A)Bond B will be selling at a greater premium than Bond A. When interest rates go down, bond prices will go up. As far as which bond will sell at the higher premium using the discounted cash flow method, it is clear that the bond with the longer duration will be worth more.

An 8% corporate bond is offered on an 8.25 basis. Which of the following statements are true? Nominal yield is higher than YTM. Current yield is higher than nominal yield. Nominal yield is lower than YTM. Current yield is lower than nominal yield. A)II and III B)I and III C)II and IV D)I and IV

A)II and III A bond offered on an 8.25 basis is the same as at a YTM of 8.25%. Because the yield quoted is higher than the 8% coupon, the bond is trading at a discount to par. For discount bonds, the nominal yield is lower than both the current yield and the yield to maturity.

Which of the following statements regarding a $1,000 corporate 8.50% bond offered at 110 is true? A)The bond's current yield is calculated by dividing its annual interest by its current market price. B)To determine the bond's current yield, its stated rate must be compared against other fixed-rate investments in the client's portfolio. C)The bond's current yield is lower than its yield to maturity. D)The bond is a discount bond.

A)The bond's current yield is calculated by dividing its annual interest by its current market price. Explanation A bond's current yield is calculated by dividing its annual interest by its current (market) price. In this case, it would be $85 ÷ $1,100. The current yield will be higher than its yield to maturity, which takes into consideration the $100 difference between the purchase price and the par value (a loss of $100). The determination of a bond's yield is unrelated to other bonds. In addition, this bond is selling at a premium (more than $1,000), not at a discount (less than $1,000).

The current yield of a callable bond selling at a premium is calculated A)as a percentage of its call price. B)as a percentage of its par value. C)to its maturity date. D)as a percentage of its market value.

A)as a percentage of its call price. Current yield for any security is always computed on the basis of the current market value.

A municipal bond has a coupon of 6.25%, and at the present time, its yield to maturity is 6.75%. From this information, it can be determined that the municipal bond is trading A)at a discount. B)at a premium. C)at par. D)flat.

A)at a discount. The YTM is greater than the nominal yield, or coupon yield. Therefore, the bond is trading at a discount.

A customer bought a 10-year 6% AAA bond at par when it was issued. Two years later, if the CPI has increased from 2% to 4%, the price of the bond most likely A)has declined. B)has increased. C)cannot be determined. D)has stayed at par.

A)has declined. Explanation When inflation is on the rise, interest rates often rise. When interest rates increase, bond prices may be expected to decline.

Bond prices are quoted as a percentage of A)par value. B)conversion value. C)stated value. D)market value.

A)par value. Bond prices are quoted as a percentage of par value. On the exam, the par value of bonds is always $1,000.

The yield to maturity is A)the annualized return of a bond if it is held to maturity. B)the annualized return of a bond if it is held to call date. C)set at issuance and printed on the face of the bond. D)determined by dividing the coupon rate by the current market price of the bond.

A)the annualized return of a bond if it is held to maturity. The yield to maturity reflects the annualized return of a bond if it is held to its maturity. The computation reflects the internal rate of return and is frequently referred to as the market required rate of return for a debt security. The rate set at issuance and printed on the face of the bond is the nominal or coupon rate. Dividing the coupon rate by the current market price of the bond provides the current yield. The return of a bond if it is held to the call date is the yield to call. LO 2.e

An investor purchases a Treasury note and the confirmation shows a price of $102.25. Rounded to the nearest cent, the investor's cost, excluding commissions, is A)$102.25. B)$1,027.81. C)$1,022.50. D)$1,020.25.

B)$1,027.81. Treasury notes are quoted in 32nds, where each 32nd equals $0.3125. The 102 in the quote equals $1,020 and the 25/32 is an additional $7.81, bringing the total to $1,027.81.

Richard purchased a 30-year bond for 103½ with a stated coupon rate of 8.5%. What is the approximate yield to maturity for this investment if Richard receives semiannual coupon payments and expects to hold the bond to maturity? A)9.36% B)8.19% C)8.68% D)8.50%

B)8.19% No calculation is necessary here. Why not? Because anytime a bond is purchased at a premium over par (103½% is a premium), the YTM must be less than the nominal (coupon) rate. There is only one choice lower than 8.5%. It isn't about your computational skills; it is about your understanding of the relationship between prices and yields.

What happens to outstanding fixed-income securities when interest rates decline? A)Coupon rates increase B)Prices increase C)Yields increase D)No change

B)Prices increase When interest rates drop, prices rise, decreasing effective yield. Thus, there is an inverse relationship between interest rates and bond prices.

A customer purchased new issue bonds at par two years ago. Since then, the cost of living as measured by the consumer price index (CPI) has declined by almost half and the current yield on the bonds has also declined. Which of the following best describes the value of the bonds purchased? A)It cannot be determined from the information presented. B)Their market price has increased. C)Their market price has remained unchanged. D)Their market price has declined.

B)Their market price has increased. The annual coupon interest payment on the bonds has not changed, but the current yield has. If the yield has decreased, it means the market price of the bonds must have increased. For example, if the bond has a 5% coupon but the current yield is now 4%, the bond's price must be 125 ($1,250) because $50 annual interest on $1,250 is a current return of 4%. Remember the inverse relationship: if interest rates decline, bond price rise (and vice versa).

A customer buys a 5% bond at par. The bond is callable in 5 years at par and matures in 10 years. Which of the following statements is true? A)YTC is the same as YTM. B)YTC is higher than YTM. C)YTC is lower than YTM. D)Nominal yield is higher than either YTM or YTC.

B)YTC is higher than YTM If a bond is trading at par, the nominal yield (coupon rate) = current yield = yield to maturity = yield to call (unless the call price is at a premium, in which case the YTC would be higher). YTC is higher than YTM if the bond is trading at a discount to par. YTC is lower than YTM if the bond is trading at a premium over par. Nominal yield is higher than either YTM or YTC if the bond is trading at a premium over par.

An agent is discussing a specific bond that would be a good addition to the client's portfolio. The client comments that the nominal yield is lower than its current yield. The agent would explain that the bond is A)a high-yield bond B)selling at discount C)selling at a premium D)issued by an unseasoned company, and the market hasn't yet realized how well secured the debt is

B)selling at discount Anytime the current yield on a bond is higher than its nominal or coupon rate, the bond must be selling at a discount.

A corporate bond that pays interest semiannually has a par value of $1,000, matures in five years, and has a yield to maturity of 10%. What is the value of the bond today if the coupon rate is 8%? A)$1,051.23 B)$1,144.31 C)$922.78 D)$1,221.17

C)$922.78 How did we calculate that? We used a tool that you won't have available at the test center (a financial calculator), but there is a great tool you will have—common sense. When a bond has a yield to maturity that is greater than its coupon rate, the bond must be selling at a discount, and that only leaves one possible answer. The only way to get a 10% return on an 8% bond is to buy it at a price below par.

DERP Corporation has issued 5% convertible debentures maturing in 2040. The conversion price is $40 and the common is currently trading at $48 per share. One would expect the DERP debentures to be selling somewhat A)below $1,000. B)below $1,200. C)above $1,200. D)above $1,000.

C)above $1,200. The first step here is to compute the parity price. A conversion price of $40 means the debenture is convertible into 25 shares of the common stock (par of $1,000 divided by $40 = 25 shares). With a current market price of $48 per share, the parity price of the convertible would be $1,200 (25 × $48). Because convertible securities generally sell at a slight premium over their parity price, the debentures should have a current market value a bit higher than $1,200.

A bond offered at par has a coupon rate A)greater than its yield to maturity. B)less than its current yield. C)equal to its current yield. D)less than its yield to maturity.

C)equal to its current yield. When a bond is selling at par, its coupon or nominal rate, current yield, and yield to maturity are all the same.

A company has paid a dividend every quarter for the past 20 years. If the stock's price has fallen dramatically over the past quarter but the dividend has remained the same, it may be concluded that A)the dividend yield to maturity has decreased. B)the current dividend yield has decreased. C)the current dividend yield has increased. D)the current dividend yield has remained the same.

C)the current dividend yield has increased. Explanation The current dividend yield is income dividend divided by price. If the price of a stock decreases and the dividend remains the same, the dividend yield will increase. LO 2.e

A bond of standard size has a nominal yield of 6%, paid in the customary fashion. The bond matures in 10 years, is callable at $105 in 5 years, and is currently priced at $110. An investor calculating the bond's yield to call would include A)the loss of $100 at maturity. B)the gain of $50 when called. C)20 payment periods. D)the semiannual interest payments of $30.

D) the semiannual interest payments of $30. The yield to call computation involves knowing the amount of interest payments to be received, the length of time to the call, the current price, and the call price. A bond with a 6% coupon (nominal yield) will make $30 interest payments twice each year. Remember, unless otherwise stated, bonds have a par value of $1,000 and customarily pay interest semiannually. With a 5-year call, there are only 10 payment periods, not 20. The loss at call is $50 ($1,100 - $1,050); there is no gain, and the loss at maturity of $100 is only relevant for YTM, not YTC.

If a convertible bond is purchased at its $1,000 par value and is convertible at $83.33 per common share, what is the conversion ratio of common shares per bond? A)2 shares for each bond B)1.2 shares for each bond C)8 shares for each bond D)12 shares for each bond

D)12 shares for each bond Explanation The conversion ratio is determined by dividing the par value of the bond, or $1,000, by its conversion price of $83.33 per common share. This results in a conversion ratio of 12 shares for each bond.

Assume that a corporation issued a 5% Aaa/AAA rated debenture at par. Two years later, similarly rated debt issues are being offered in the primary market at 5.5%. Which of the following statements regarding the outstanding 5% debenture are true? The current yield on the debenture will be higher than 5%. The current yield on the debenture will be lower than 5%. The dollar price per bond will be higher than par. The dollar price per bond will be lower than par. A)II and IV B)I and III C)II and III D)I and IV

D)I and IV Because interest rates have risen after the issue of the 5% debenture, the bond's price will be discounted to result in a higher current yield (computed as annual income divided by current market price). Accordingly, the discounting of the issue will make the 5% debenture competitive with new issues offered with a 5.5% coupon.

The price of which of the following will fluctuate most with a change in interest rates? A)Common stock B)Short-term bonds C)Money market instruments D)Long-term bonds

D)Long-term bonds Long-term debt prices fluctuate more than short-term debt prices as interest rates rise and fall.

An investor owns a debenture convertible into 20 shares of the issuer's common stock. After a 2-for-1 stock split, the terms of the debenture provide for conversion into 40 shares. This is because the debenture has A)warrants attached. B)increased its par value to $2,000 to account for the split. C)preemptive rights. D)an antidilution clause.

D)an antidilution clause. Most convertible securities are sold with antidilutive clauses that provide for an adjustment in the number of shares based on stock splits or stock dividends.

A bond's yield to maturity is A)determined by dividing the coupon rate by the bond's current market price. B)set at issuance and printed on the face of the bond. C)the annualized return of a bond if it is held to call date. D)the annualized return of a bond if it is held to maturity.

D)the annualized return of a bond if it is held to maturity. Explanation The yield to maturity is the annualized return of a bond if it is held to maturity. The computation reflects the internal rate of return and is frequently referred to as the market required rate of return for a debt security. The rate set at issuance and printed on the face of the bond is the nominal or coupon rate. Dividing the coupon rate by the current market price of the bond provides the current yield. The return of a bond if it is held to the call date is the YTC.

The DERP Corporation has an outstanding convertible bond issue that is convertible into eight shares of stock. If the current market price of the bond is 80, the parity price of the stock is A)$100 per share. B)$80 per share. C)$125 per share. D)$64 per share.

A)$100 per share. Parity means equal. With a conversion ratio of eight shares per bond, the investor can convert the bond into eight shares. If the bond is currently selling for $800, then, to be of equal value (parity), the eight shares must be selling at $100 each.

When an income-oriented investor wishes to compute the current yield of a specific investment, which one of these items would not be considered? A)Interest coupon B)Net present value C)Dividends paid D)Current market price

B)Net present value The current yield of any investment is the income return (dividends on equity; interest on debt) divided by the current market price. The NPV is a tool that evaluates the reasonableness of the price of an investment.

When an investor notices that a bond's coupon yield is lower than its current yield, this is an indication that the bond A)is selling at a premium. B)is selling at a discount. C)is in danger of going into default. D)is nearing its maturity date.

B)is selling at a discount. A bond's current yield is the coupon (nominal) yield divided by the current market price. When those two are the same, the bond is selling at its par (face) value. When selling below par (at a discount), the coupon yield will be lower than the current yield (if you pay less, you get more). Although a bond's market price will generally get closer to par as the maturity date approaches, anytime the price of the bond is below par (selling at a discount), its current yield will be higher than the coupon.

When an investor owns a convertible security where, upon conversion, the account value would remain the same, it is considered that the convertible and the common are selling at A)equivalent value. B)parity. C)the arbitrage level. D)the nominal yield.

B)parity. Parity means equal. When one can convert the security and realize the same value, it is said that both are at parity.

A $1,000 bond with a nominal yield of 8% will pay how much interest each year? A)$40 B)$160 C)$80 D)$800

C)$80 The nominal yield (or coupon rate) is the interest rate stated on the bond and is the rate the bondholder promises to pay on the bond until the bond matures. A $1,000 bond with an 8% nominal yield will pay $80 per year in interest.

A corporation has issued a 4% $60 par convertible stock with a conversion price of $20. With the preferred stock selling at $66 per share, an investor holding 100 shares of this stock will benefit by converting if the price of the common stock is A)above $20.00 per share. B)above $18.20 per share. C)below $22.00 per share. D)above $22.00 per share

D)above $22.00 per share. With a conversion price of $20 and a par value of $60, this preferred stock is convertible into three shares of the company's common stock. We divide the current price of the preferred ($66) by the three shares to arrive at the parity price of $22. If the common stock is selling for more than the parity price, the investor can benefit by converting and selling the stock in the marketplace.