Lesson 2.2: Bond Math

Question 1

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 AA rated corporate bonds trading at par with a 6% coupon rate
C) $200,000 of utility common stock paying a current dividend of 3.5%
D) $100,000 market value of corporate bonds selling at a premium and yielding 6% to maturity

Answer 1

D) $100,000 market value of corporate bonds selling at a premium and yielding 6% to maturity

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).

Question 2

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 (means 105% of $1,000 or $1,050),

Answer 2

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.

Question 3

The bond order, from highest to lowest yield, is:

Answer 3

1) Nominal (coupon) yield
2) Current yield
3) YTM (Yield To Maturity)
4) YTC (Yield To Call)

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.

Question 4

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?

Answer 4

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.

Question 5

Anytime a bond is purchased at a premium over par (103½% is a premium), the:

Answer 5

YTM must be less than the nominal (coupon) rate

Question 6

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:

Answer 6

5.00%

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

Question 7

Bond prices are quoted as a percentage of

Answer 7

par value ($1,000)

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

Question 8

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:

Answer 8

*selling at a discount**

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

Remember the order sequence
1) Nominal (coupon) yield
2) Current yield
3) YTM (Yield To Maturity)
4) YTC (Yield To Call)

Question 9

If a company’s dividend increases by 5% but its market price remains the same, the current yield of the stock will:

Answer 9

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.

Question 10

What indicates a bond selling at a premium?

Answer 10

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.

Question 11

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:

Answer 11

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

Question 12

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 ($1,000 × 5.5% = $55) and is currently rated Aa. The current market price of the bond is 105 (105% of $1,000 or $1,050), resulting in a current yield of approximately:

Answer 12

5.24%

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.

Question 13

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 6 years at 103. In the computation of the bond’s yield to call (YTC), what would be a factor?

Answer 13

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.

Question 14

A customer buys a 5% bond at par. The bond is callable in 5 years at par and matures in 10 years. What does this indicate???

Answer 14

YTC is the same as 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.

Question 15

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?

I. Bought it at a discount
II. Bought it at a premium
III. Sold it at a discount
IV. Sold it at a premium

Answer 15

I & 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.

Question 16

A bond’s yield to maturity (YTM) is:

Answer 16

the annualized return of a bond if it is held to maturity.

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.

Question 17

What happens to outstanding fixed-income securities when interest rates decline?

Answer 17

Prices increase

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

Question 18

In order to compute yield to maturity, all of the following are necessary except

A) the nominal yield.
B) the call price.
C) the maturity date.
D) the current market price.

Answer 18

B) 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.

Question 19

2) Which of the following expressions describes the current yield of a bond?

Answer 19

the current dividend yield has increased.

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.
——————————————————————————–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.

Question 20

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:

Answer 20

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.

Question 21

When an investor notices that a bond’s coupon yield is lower than its current yield, this is an indication that the bond:

Answer 21

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.

Question 22

Inverse Relationship

Answer 22

Bond prices fall when interest rates rise because bond prices have an inverse relationship with interest rates.

Question 23

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?

Answer 23

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.

Question 24

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:

Answer 24

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%.

Question 25

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%. What statements regarding the outstanding 5% debenture are true?

Answer 25

The current yield on the debenture will be higher than 5%. & The dollar price per bond will be lower than par.

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.

Question 26

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?

Answer 26

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.

Question 27

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:

IMPORTANT QUESTION !!!

Answer 27

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.

Question 28

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:

Answer 28

$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.

Question 29

The conversion ratio (for stocks) always uses:

Answer 29

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.

Question 30

When current interest rates are at 6%, you would expect a bond with a nominal yield of 4% to be:

Answer 30

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.

Question 31

An investor purchased a 20-year bond with a duration of 11 years for $1,323.18. The yield to maturity (YTM):

IMPORTANT INFORMATION !!!

Answer 31

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.

Question 32

An investor buys 10M RAN 6.6s of 32 at 67. What is the total purchase price?

Answer 32

$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.

Question 33

The current yield of a callable bond selling at a premium is calculated, as a percentage of its market value.

Answer 33

Current yield for any security is always computed on the basis of the current market value.

Question 34

An investor buys 10M 6.6s of 10 at 67. The investor will receive annual interest of:

Answer 34

$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.

Question 35

The yield to call (YTC) computation involves knowing:

Answer 35

the amount of interest payments to be received, the length of time to the call, the current price, and the call price.

Question 36

EX: A bond purchased at $900 with a 5% coupon and a five-year maturity has a current yield of:
——————————————————————————
Other EX: The current yield on a bond with a coupon rate of 5.5% selling at 110 is:

Answer 36

EX: 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.
——————————————————————————–
Other EX: 5%. 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% ($55/$1,100 = 5%).

Question 37

The price of what bond will fluctuate most with a change in interest rates?

Answer 37

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

Question 38

When a bond is selling at a premium, a bond callable at par will:

Answer 38

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).

Question 39

A corporation has issued a 4% $60 par convertible stock with a conversion price of $20 (FYI: 3 Shares). 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:

Answer 39

$22

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.

Question 40

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:

Answer 40

2%

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 (FYI: $2.50/40% = $1). This dollar divided by the current market price of $50.00 results in a current return of 2% (FYI: $1/$50 = 2%).

Question 41

Treasury notes are quoted in 32nds, where each 32nd equals:

Answer 41

$0.3125

EX: 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 $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.