All practice questions

Question 21Question →

An investor purchases five corporate bonds in the secondary market, each having a $1,000 par value and a stated annual coupon rate of 4.50%. The bonds pay interest semi-annually. What is the total dollar amount of interest income the investor will receive every six months from these bonds?

Show answer & explanation

Answer: 112.5

Answer

$112.50

The total semi-annual interest payment is

112.50. Each bond pays

45.00 annually (

1,000 × 4.50%), which equals

22.50 semi-annually per bond (

45.00 ÷ 2). Multiplying by 5 bonds gives a total payment of

112.50 received every six months ($22.50 × 5).

Step-by-Step Solution

1

Calculate the total principal (par value) for the 5-bond holding.

$5,000.00 total par value

The investor holds 5 bonds, each with a standard par value of

1,000 (

1,000 × 5 = $5,000).

2

Calculate the total annual coupon interest generated by the position.

$225.00 total annual interest

The stated annual coupon rate of 4.50% applies to the total par value (

5,000 × 0.045 =

225.00).

3

Calculate the semi-annual interest payment amount.

$112.50 received every six months

Corporate bonds pay interest semi-annually (twice per year), so the total annual interest is divided by 2 (

225.00 ÷ 2 =

112.50).

Key Concept

Semi-Annual Coupon Interest Payment Calculation

Estimated Time:1m 30s

Question 22Question →

A corporate bond with a par value of $1,000 is currently trading in the secondary market at$ 960. The bond pays a stated annual coupon rate of 6% in semi-annual installments. What is the current yield of this bond?

Show answer & explanation

Answer: 6.25

Answer

The current yield of the bond is 6.25%.

The current yield formula compares the annual dollar interest earned to the bond's current market price. The bond pays 6% of its

1,000 par value annually, which equals

60 per year. Dividing

60 by the current market price of

960 yields 0.0625, or 6.25%.

Step-by-Step Solution

1

Determine the annual coupon payment in dollars

60 annual income (

30 semi-annually)

The stated coupon rate (nominal yield) is always applied to the $1,000 par value regardless of the market price.

2

Calculate the current yield percentage

6.25%

Current yield measures the annual income generated relative to the current secondary market purchase price (

60 /

960).

Key Concept

Current Yield Calculation for Debt Securities

Question 23Question →

An investor purchases a corporate bond with a par value of $1,000 and a stated annual coupon rate of 5.50%. If the bond makes interest payments semi-annually, what is the dollar amount of a single semi-annual interest payment?

Show answer & explanation

Answer: 27.5

Answer

The single semi-annual interest payment is $27.50.

A 5.50% coupon on a

1,000 par value bond pays

55.00 annually (

1,000 × 0.055). Because corporate bond coupons pay semi-annually, the investor receives half of the annual amount per payment, which equals

27.50.

Step-by-Step Solution

1

Calculate annual coupon payment amount

$55.00

Annual Interest = Par Value × Annual Coupon Rate =

1,000 × 0.055 =

55.00.

2

Calculate semi-annual payment amount

$27.50

Corporate bonds pay interest semi-annually (twice per year). Divide annual interest by 2:

55.00 / 2 =

27.50.

Key Concept

Calculating semi-annual coupon payments based on par value and coupon rate

Question 24Question →

An investor in the $30\%$ marginal income tax bracket is considering purchasing a tax-exempt municipal bond offering a yield of $4.2\%$ . What is the tax-equivalent yield of this municipal bond?

Show answer & explanation

Answer: 6

Answer

The tax-equivalent yield of the municipal bond is 6.0%.

The tax-equivalent yield formula determines the interest rate a taxable corporate bond must pay to equal the after-tax yield of a tax-exempt municipal bond. Dividing the municipal yield of

4.2\%

by

(1 - 0.30)

yields

6.0\%

.

Step-by-Step Solution

1

Calculate the tax complement factor

1 - 0.30 = 0.70

This represents the portion of taxable income an investor retains after paying federal income tax.

2

Divide the municipal yield by the tax complement factor

4.2% / 0.70 = 6.0%

This converts the tax-free yield of a municipal bond into the equivalent yield required from a fully taxable bond to achieve the same net return.

Key Concept

Tax-Equivalent Yield Calculation

Estimated Time:45s

Question 25Question →

An investor residing in California is subject to a $37\%$ federal marginal income tax rate and a $13\%$ California state income tax rate. The investor is evaluating an in-state California municipal bond offering a yield of $4.25\%$ , which is exempt from both federal and state income taxes. What is the tax-equivalent yield (expressed as a percentage) that a fully taxable corporate bond must offer to match the after-tax yield of this municipal bond?

Show answer & explanation

Answer: 8.5

Answer

The tax-equivalent yield required from a fully taxable corporate bond is

8.50\%

.

Municipal bonds issued within an investor's resident state are exempt from both federal and state income taxes (double tax-exempt). The investor's total effective tax rate for this comparison is

37\% + 13\% = 50\%

. Using the tax-equivalent yield formula

\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Combined Tax Rate}}

, we calculate

\frac{4.25\%}{1 - 0.50} = \frac{4.25\%}{0.50} = 8.50\%

. A fully taxable corporate bond must yield

8.50\%

to equal the

4.25\%

net payout of the municipal bond.

Step-by-Step Solution

1

Calculate the combined tax bracket for double-exempt income.

Combined tax rate =

37\% + 13\% = 50\%

(or

0.50

).

Municipal bonds issued by the investor's state of residence provide double tax exemption from both federal and state income taxes.

2

Apply the tax-equivalent yield formula for a double-exempt bond.

\text{Tax-Equivalent Yield} = \frac{4.25\%}{1 - 0.50} = \frac{4.25\%}{0.50} = 8.50\%

.

To determine what pre-tax corporate yield equals the net municipal yield, divide the tax-free yield by

(1 - \text{Combined Tax Rate})

.

Key Concept

Tax-Equivalent Yield for Double Tax-Exempt Municipal Bonds

Estimated Time:2m 0s

Question 26Question →

A corporate bond is currently trading in the secondary market at a quoted price of $105.00$ (% of par). If the bond's current yield is calculated at $6.00\%$ , what is the annual dollar coupon payment for a single $\$1,000$ par value bond?

Show answer & explanation

Answer: 63

Answer

The annual dollar coupon payment per

\$1,000

par bond is

\$63.00

.

Current yield is defined as the annual dollar interest divided by the current market price of the bond. To find the annual dollar interest, multiply the current yield (

6.00\%

) by the bond's current market price (

\$1,050.00

, which is

105.00\%

of the

\$1,000

par value). Doing so gives

0.0600 \times \$1,050.00 = \$63.00

.

Step-by-Step Solution

1

Calculate the market dollar price of the bond from its percentage-of-par quote.

Market Price =

\$1,000 \times 1.05 = \$1,050.00

Bond price quotes are expressed as a percentage of par value (

105.00\% = 105.00

).

2

Rearrange the Current Yield equation to solve for annual coupon payment.

\text{Annual Coupon Payment} = \text{Current Yield} \times \text{Market Price}

Current yield relates annual coupon income directly to current market value rather than par value.

3

Multiply the current yield by the dollar market price.

0.0600 \times \$1,050.00 = \$63.00

This yields the total annual interest payment in dollars.

Key Concept

Calculating annual coupon payment using Current Yield and secondary market price

Question 27Question →

An investor residing in North Carolina is subject to a $20\%$ federal marginal income tax rate and a $5\%$ state income tax rate. The investor is considering purchasing an out-of-state municipal bond offering a yield of $4.50\%$ . Because the bond is issued by an out-of-state entity, its interest is exempt from federal income tax but subject to North Carolina state income tax. What is the equivalent yield (in percent) that a fully taxable corporate bond must offer to provide the investor with the exact same after-tax yield?

Show answer & explanation

Answer: 5.7

Answer

The taxable corporate bond must offer a yield of 5.70%.

To find the corporate yield that matches the after-tax return of an out-of-state municipal bond, first calculate the municipal bond's after-tax yield accounting for state taxation:

4.50\% \times (1 - 0.05) = 4.275\%

. Next, because corporate bond interest is subject to both federal and state taxes (

20\% + 5\% = 25\%

combined tax rate), set the after-tax corporate return equal to

4.275\%

:

\text{Corporate Yield} \times (1 - 0.25) = 4.275\%

. Solving yields

\text{Corporate Yield} = \frac{4.275\%}{0.75} = 5.70\%

.

Step-by-Step Solution

1

Calculate the after-tax yield of the out-of-state municipal bond

4.275%

Municipal bond interest is exempt from federal income tax but taxable by the investor's home state when issued out-of-state. Thus, After-Tax Yield = 4.50% * (1 - 0.05) = 4.275%.

2

Calculate the combined tax rate applicable to corporate bond interest

25%

Corporate bond interest is fully taxable at both federal (20%) and state (5%) levels: 20% + 5% = 25%.

3

Compute the required corporate tax-equivalent yield

5.70%

Divide the after-tax yield of 4.275% by (1 - combined tax rate): 4.275% / (1 - 0.25) = 5.70%.

Key Concept

Tax-Equivalent Yield for Out-of-State Municipal Bonds vs Fully Taxable Corporate Debt

Question 28Question →

An investor in a $32\%$ federal marginal income tax bracket is evaluating a tax-exempt municipal bond offering a yield of $4.76\%$ . What is the tax-equivalent yield (expressed as a percentage) that a fully taxable corporate bond would need to provide to match the after-tax yield of this municipal bond?

Show answer & explanation

Answer: 7

Answer

The tax-equivalent yield required from a fully taxable corporate bond is

7.0\%

.

The tax-equivalent yield formula calculates the yield a taxable corporate bond must earn to equal the after-tax yield of a tax-exempt municipal bond. Using the formula

\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Marginal Tax Rate}}

, we divide

4.76\%

by

(1 - 0.32) = 0.68

, resulting in

7.00\%

.

Step-by-Step Solution

1

Determine the tax-free factor

1 - 0.32 = 0.68

The investor retains

68\%

of earnings on taxable income after paying a

32\%

marginal income tax rate.

2

Calculate the tax-equivalent yield

\frac{4.76\%}{0.68} = 7.00\%

Dividing the tax-exempt yield by the after-tax retention factor gives the equivalent yield required from a fully taxable security.

Key Concept

Tax-Equivalent Yield (TEY)

Question 29Question →

An investor purchases a 10-year corporate bond with a $1,000 par value trading in the secondary market at a price of$ 920. If the bond pays a semi-annual interest payment of $23.00, what is the bond's current yield?

Show answer & explanation

Answer: 5

Answer

5.0%

Current yield calculates the return an investor receives based on the current market price of a bond (

46.00 annual interest /

920.00 market price = 5.0%).

Step-by-Step Solution

1

Calculate total annual interest income

23.00 × 2 =

46.00

Bonds pay interest semi-annually, so the six-month payment must be annualized to determine total annual income.

2

Calculate current yield

(

46.00 /

920.00) × 100 = 5.0%

Current yield measures annual income as a percentage of the bond's secondary market purchase price.

Key Concept

Current Yield Calculation for Debt Securities

Question 30Question →

An investor purchases a portfolio of municipal bonds with a total par value of $\$50,000$ . The bonds carry a nominal annual coupon rate of $4.50\%$ with interest payable semi-annually. If the current market price of the portfolio is quoted at $90.00$ (% of par), what is the annual current yield of this bond portfolio?

Show answer & explanation

Answer: 5

Answer

The annual current yield of the bond portfolio is 5.00%.

The current yield of a bond or bond portfolio is calculated by dividing the annual dollar coupon payment by the current market price of the bond position. With a total par value of

\$50,000

and a nominal coupon rate of

4.50\%

, the annual coupon income is

\$2,250

. At a quoted price of

90.00

(% of par), the market value of the position is

\$45,000

. Dividing

\$2,250

by

\$45,000

yields an annual current yield of

5.00\%

.

Step-by-Step Solution

1

Determine the dollar market value of the bond portfolio.

Market Value =

\$50,000 \times \(\frac{90.00}{100}\) = \$45,000

.

Bond prices are quoted as a percentage of par value (

100\%

=

\$1,000

per bond).

2

Determine the annual dollar coupon interest received.

Annual Interest =

\$50,000 \times 4.50\% = \$2,250

.

The nominal coupon rate is always based on par value regardless of market price fluctuations.

3

Calculate the current yield by dividing annual coupon income by market price.

Current Yield =

\frac{\$2,250}{\$45,000} = 0.05 = 5.00\%

.

Current yield measures annual interest income relative to the bond's current secondary market price.

Key Concept

Current Yield Calculation and Bond Price/Yield Dynamics

Question 31Question →

An investor purchases 5 corporate bonds, each having a par value of $1,000$ and a stated nominal coupon rate of $4.8\%$ . What is the total annual interest income, in dollars, that the investor will receive from this holding?

Show answer & explanation

Answer: 240

Answer

The total annual interest income received by the investor is $240.

A bond's coupon rate represents the percentage of its par value (

1,000) paid annually in interest. Each bond pays

4.8\% \times \

1,000 = \$48

per year. For an investor holding 5 bonds, the total annual interest income is

5 \times \$48 = \$240

.

Step-by-Step Solution

1

Determine the annual interest payment for one bond

$48 per year

The stated coupon rate is calculated based on the bond's par value of

1,000.

\

1,000 \times 4.8\% = \$48

.

2

Calculate the total annual interest for the portfolio of 5 bonds

$240 per year

Multiply the annual payout of one bond (

48) by the total number of bonds held (5):

\

48 \times 5 = \$240

.

Key Concept

Calculating annual coupon interest income for debt securities

Estimated Time:45s

Question 32Question →

A corporate bond with a par value of $1,000 pays a 6% annual coupon rate ($ 60 in interest per year). If the bond is currently trading in the secondary market at a discounted price of $800, what is the current yield of the bond expressed as a percentage?

Show answer & explanation

Answer: 7.5

Answer

The current yield of the corporate bond is 7.5%.

Current yield reflects the return an investor receives based on the current market price of the bond. It is calculated as Annual Interest divided by Current Market Price. Here, annual interest is

60 (

1,000 par \times 6%). Dividing

60 by the market price of

800 equals 0.075, or 7.5%.

Step-by-Step Solution

1

Calculate the annual interest payment from the coupon rate and par value.

Annual Interest = 6% of

1,000 =

60

Coupon interest is always calculated based on the bond's $1,000 par value.

2

Divide annual interest by the current market price.

60 /

800 = 0.075

Current yield measures annual interest income relative to current market purchase price rather than par value.

3

Convert the decimal to a percentage.

0.075 * 100 = 7.5%

Yields are conventionally expressed as annual percentages.

Key Concept

Calculating current yield on a debt security

Estimated Time:1m 0s

Question 33Question →

An open-end management investment company has total assets of $\$150,000,000$ and total liabilities of $\$10,000,000$ . If the fund has $10,000,000$ shares outstanding, what is the fund's Net Asset Value (NAV) per share in dollars?

Show answer & explanation

Answer: 14

Answer

The Net Asset Value (NAV) per share is

\$14.00

.

The Net Asset Value (NAV) per share is calculated using the formula

\text{NAV} = \frac{\text{Total Assets} - \text{Total Liabilities}}{\text{Shares Outstanding}}

. Subtracting liabilities from assets gives net assets of

\$140,000,000

. Dividing

\$140,000,000

by

10,000,000

shares yields an NAV per share of

\$14.00

.

Step-by-Step Solution

1

Subtract total liabilities from total assets to calculate the net asset value of the fund portfolio.

\$150,000,000 - \$10,000,000 = \$140,000,000

Net assets represent the total portfolio market value remaining after deducting all fund liabilities.

2

Divide the total net assets by the number of shares outstanding to find NAV per share.

\frac{\$140,000,000}{10,000,000} = \$14.00

NAV per share measures the per-share value of an open-end investment company.

Key Concept

Net Asset Value (NAV) Calculation

Question 34Question →

An investor purchases a corporate bond with a $\$1,000$ par value at a secondary market price quote of $92.50$ . The bond pays semi-annual interest payments of $\$37.00$ every six months. What is the current yield of this bond, expressed as a percentage?

Show answer & explanation

Answer: 8

Answer

The current yield of the bond is 8.00%.

The current yield of a bond reflects the annual interest income divided by the bond's current market price. Given semi-annual interest of

\$37.00

, the annual interest payment is

\$74.00

. A bond price quote of

92.50

translates to a market price of

\$925.00

(

92.50\%

of

\$1,000

par value). Dividing

\$74.00

by

\$925.00

produces a current yield of

8.00\%

.

Step-by-Step Solution

1

Calculate the annual interest income from the semi-annual payment

\text{Annual Interest} = \$37.00 \times 2 = \$74.00

Bonds typically pay interest semi-annually, so annual income is twice the semi-annual payment.

2

Convert the bond price quote into a dollar amount

\text{Market Price} = 92.50\% \times \$1,000 = \$925.00

Corporate bonds are quoted as a percentage of their

\$1,000

par value.

3

Compute the current yield

\text{Current Yield} = \frac{\$74.00}{\$925.00} = 0.08 = 8.00\%

Current yield measures annual income as a percentage of current market price.

Key Concept

Bond Current Yield Formula

Question 35Question →

An investor in the $32\%$ federal marginal income tax bracket resides in a state with a $5\%$ state marginal income tax rate. The investor is evaluating a qualifying in-state municipal bond offering a yield of $4.41\%$ . What is the tax-equivalent yield (TEY) that a fully taxable corporate bond must offer to provide the investor with an equivalent after-tax return? Express your answer as a percentage rounded to two decimal places.

Show answer & explanation

Answer: 7

Answer

7.00%

To determine the tax-equivalent yield of an in-state municipal bond, the combined federal and state tax rate must be used because the interest is exempt from both federal (

32\%

) and state (

5\%

) income taxes, resulting in a total tax rate of

37\%

. Applying the formula

\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Marginal Tax Rate}}

gives

\frac{4.41\%}{1 - 0.37} = \frac{4.41\%}{0.63} = 7.00\%

. A fully taxable corporate bond must yield

7.00\%

to provide the same net after-tax income.

Step-by-Step Solution

1

Determine the combined marginal tax rate

Combined tax rate is 37% (0.37)

In-state municipal bond interest is triple-tax-exempt (exempt at both federal and state levels for state residents), so both federal (32%) and state (5%) tax rates apply when calculating tax equivalence against fully taxable corporate bonds.

2

Set up the Tax-Equivalent Yield formula

TEY = Municipal Yield / (1 - Combined Tax Rate)

This standard formula adjusts the tax-exempt yield upward to represent the yield a fully taxable security must pay to equal the tax-free return.

3

Perform the calculation

4.41% / (1 - 0.37) = 4.41% / 0.63 = 7.00%

Dividing the municipal yield by 0.63 provides the exact taxable yield needed to match the net after-tax return.

Key Concept

Tax-Equivalent Yield (TEY) for In-State Municipal Debt

Question 36Question →

An investor subject to a $32\%$ federal marginal income tax bracket is evaluating a corporate bond offering a $6.25\%$ annual yield. What minimum yield (in percent) must a tax-exempt municipal bond offer to provide the exact same after-tax return as the corporate bond?

Show answer & explanation

Answer: 4.25

Answer

The tax-exempt municipal bond must offer a yield of

4.25\%

to provide the exact same after-tax return as the

6.25\%

corporate bond.

Because municipal bond interest is exempt from federal income taxes, an investor keeps

100\%

of the interest paid by a qualifying municipal bond. To compare a taxable corporate bond paying

6.25\%

against a tax-free municipal bond, calculate the corporate bond's after-tax yield:

\text{After-Tax Yield} = \text{Corporate Yield} \times (1 - \text{Tax Rate})

. For an investor in a

32\%

tax bracket, this yields

6.25\% \times (1 - 0.32) = 4.25\%

. A municipal bond yielding

4.25\%

delivers the exact same net cash income.

Step-by-Step Solution

1

Determine the taxable corporate bond yield and the investor's tax rate.

Corporate yield =

6.25\%

, marginal tax rate =

32\%

(

0.32

).

Taxable fixed-income interest is subject to federal income taxation at the investor's marginal tax bracket.

2

Calculate the percentage of interest retained after federal taxes.

1 - 0.32 = 0.68

(or

68\%

retained).

The investor keeps

(1 - \text{marginal tax rate})

of any taxable interest earned.

3

Multiply the nominal corporate yield by the retained percentage.

6.25\% \times 0.68 = 4.25\%

.

This calculation determines the net after-tax yield generated by the corporate bond.

4

Equate the after-tax corporate yield to the required municipal bond yield.

Municipal bond yield required =

4.25\%

.

Interest from municipal bonds is exempt from federal income tax, so its nominal yield equals its after-tax yield.

Key Concept

Municipal Bond After-Tax Yield and Tax-Equivalent Yield

Question 37Question →

An investor in a $35\%$ federal income tax bracket and a $5\%$ state income tax bracket is evaluating a taxable corporate bond with a yield of $7.20\%$ . The investor is considering purchasing an out-of-state municipal bond instead. In the investor's home state, interest income from out-of-state municipal bonds is subject to state income tax, but remains exempt from federal income tax. What is the minimum yield percentage (rounded to two decimal places) that the out-of-state municipal bond must pay to offer an after-tax yield equivalent to that of the corporate bond?

Show answer & explanation

Answer: 4.55

Answer

The out-of-state municipal bond must offer a minimum yield of

4.55\%

.

To find the equivalent yield of an out-of-state municipal bond, first compute the net after-tax yield of the corporate bond. Corporate bond interest is subject to both federal (

35\%

) and state (

5\%

) taxes, making the combined tax rate

40\%

. The corporate bond's after-tax yield is

7.20\% \times (1 - 0.40) = 4.32\%

. Interest from out-of-state municipal bonds is exempt from federal tax but subject to the

5\%

state tax. Setting the municipal bond's after-tax yield equal to

4.32\%

gives

Y \times (1 - 0.05) = 4.32\%

. Solving for

Y

yields

Y = \frac{4.32\%}{0.95} = 4.547368\%

, which rounds to

4.55\%

.

Step-by-Step Solution

1

Determine the combined marginal tax rate applicable to fully taxable corporate bond interest.

Combined tax rate =

35\% + 5\% = 40\%

.

Interest earned on corporate bonds is fully taxable at both federal and state income tax levels.

2

Calculate the net after-tax yield of the corporate bond.

After-tax yield =

7.20\% \times (1 - 0.40) = 4.32\%

.

The investor retains

60\%

of the gross corporate yield after satisfying both tax obligations.

3

Identify the tax status of out-of-state municipal bond interest for this investor.

Applicable tax rate =

5\%

state income tax (

0\%

federal tax).

Municipal bond interest earned from out-of-state issuers is exempt from federal income tax but subject to state income tax in the resident's home state.

4

Solve for the gross municipal yield required to deliver a

4.32\%

net after-tax return.

Required municipal yield =

\frac{4.32\%}{1 - 0.05} = \frac{4.32\%}{0.95} \approx 4.55\%

.

Dividing the net required return by

(1 - \text{state tax rate})

determines the nominal yield the municipal bond must pay.

Key Concept

Tax Treatment of Out-of-State Municipal Bonds vs. Corporate Bonds

Question 38Question →

An investor holds $10$ corporate bonds with a par value of $\$1,000$ each. The bonds pay a stated annual coupon rate of $5.80\%$ in semi-annual installments. What total dollar amount of interest will the investor receive every six months?

Show answer & explanation

Answer: 290

Answer

The investor will receive a total interest payment of $290 every six months.

The correct semi-annual payment is

290. To find this, multiply

10 bonds by their par value of

1,000 to get a total par value of

10,000. Applying the annual coupon rate of 5.80% yields

580 in total annual interest. Dividing

580 by 2 gives the semi-annual payment of $290 received every six months.

Step-by-Step Solution

1

Calculate total par value

$10,000

Multiply the number of bonds owned by the face value of each bond (

10 \times \$1,000 = \$10,000

).

2

Calculate annual interest income

$580

Multiply the total par value by the annual coupon rate (

\$10,000 \times 0.058 = \$580

).

3

Calculate semi-annual payment amount

$290

Divide the total annual interest by 2 because corporate bonds pay interest semi-annually (

\$580 / 2 = \$290

).

Key Concept

Calculating semi-annual coupon payments based on total bond par value and nominal coupon rate.

Question 39Question →

A corporate bond with a par value of $\$1,000$ currently trades at a secondary market price of $\$960$ and offers a current yield of $6.25\%$ . What is the annual coupon rate (stated nominal yield) of this bond expressed as a percentage?

Show answer & explanation

Answer: 6

Answer

The annual coupon rate (stated nominal yield) of the bond is 6.0%.

The current yield of a bond equals the annual dollar interest payment divided by the current market price. Given a market price of

\$960

and a current yield of

6.25\%

, the bond pays

\$960 \times 0.0625 = \$60

in annual interest. To find the stated nominal yield (annual coupon rate), divide the annual interest payment by the bond's face value (

\$1,000

):

\frac{\$60}{\$1,000} = 6.0\%

.

Step-by-Step Solution

1

Determine the annual dollar interest payment using the market price and current yield.

Annual interest payment =

960 * 0.0625 =

60.

Current yield is defined as the annual dollar interest divided by the current market price.

2

Calculate the stated nominal yield (coupon rate) relative to par value.

Coupon rate = (

60 /

1,000) * 100% = 6.0%.

The nominal yield is fixed at issuance as a percentage of the bond's par value ($1,000).

Key Concept

Relationship between nominal yield, current yield, market price, and par value in bond pricing.

Question 40Question →

An investor purchases a corporate bond with a par value of $1,000 and a 6% annual coupon rate. If the bond is currently trading in the secondary market for$ 800, what is the bond's current yield expressed as a percentage?

Show answer & explanation

Answer: 7.5

Answer

7.5%

Current yield is calculated by taking the bond's annual dollar interest payment and dividing it by its current market price. With a 6% coupon rate on a

1,000 par value, the annual interest payment is

60. Dividing

60 by the market price of

800 gives a current yield of 7.5%.

Step-by-Step Solution

1

Calculate the annual dollar interest paid by the bond.

$60 annual interest

Multiply the $1,000 par value by the 6% coupon rate.

2

Divide the annual dollar interest by the bond's current market price.

60 /

800 = 0.075

Current yield measures the annual income generated relative to the current purchasing cost.

3

Convert the decimal to a percentage.

7.5%

Yields are standardly stated in percentage terms.

Key Concept

Bond Current Yield

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept