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Soru 21Soru →

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?

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Cevap: 112.5

Cevap

$112.50
The total semi-annual interest payment is 112.50.Eachbondpays112.50. Each bond pays 45.00 annually (1,000×4.501,000 × 4.50%), which equals 22.50 semi-annually per bond (45.00÷2).Multiplyingby5bondsgivesatotalpaymentof45.00 ÷ 2). Multiplying by 5 bonds gives a total payment of 112.50 received every six months ($22.50 × 5).

Adım Adım Çözüm

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 ( 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=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=225.00 ÷ 2 = 112.50).

Anahtar Kavram

Semi-Annual Coupon Interest Payment Calculation
Tahmini Süre:1m 30s
Soru 22Soru →

A corporate bond with a par value of 1,000iscurrentlytradinginthesecondarymarketat1,000 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?

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Cevap: 6.25

Cevap

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 1,000parvalueannually,whichequals1,000 par value annually, which equals 60 per year. Dividing 60bythecurrentmarketpriceof60 by the current market price of 960 yields 0.0625, or 6.25%.

Adım Adım Çözüm

1
Determine the annual coupon payment in dollars
60annualincome(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 (60/60 / 960).

Anahtar Kavram

Current Yield Calculation for Debt Securities
Soru 23Soru →

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?

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Cevap: 27.5

Cevap

The single semi-annual interest payment is $27.50.
A 5.50% coupon on a 1,000parvaluebondpays1,000 par value bond pays 55.00 annually (1,000×0.055).Becausecorporatebondcouponspaysemi−annually,theinvestorreceiveshalfoftheannualamountperpayment,whichequals1,000 × 0.055). Because corporate bond coupons pay semi-annually, the investor receives half of the annual amount per payment, which equals 27.50.

Adım Adım Çözüm

1
Calculate annual coupon payment amount
$55.00
Annual Interest = Par Value × Annual Coupon Rate = 1,000×0.055=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=55.00 / 2 = 27.50.

Anahtar Kavram

Calculating semi-annual coupon payments based on par value and coupon rate
Soru 24Soru →

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

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Cevap: 6

Cevap

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%4.2\% by (1−0.30)(1 - 0.30) yields 6.0%6.0\%.

Adım Adım Çözüm

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.

Anahtar Kavram

Tax-Equivalent Yield Calculation
Tahmini Süre:45s
Soru 25Soru →

An investor residing in California is subject to a 37%37\% federal marginal income tax rate and a 13%13\% California state income tax rate. The investor is evaluating an in-state California municipal bond offering a yield of 4.25%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?

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Cevap: 8.5

Cevap

The tax-equivalent yield required from a fully taxable corporate bond is 8.50%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%37\% + 13\% = 50\%. Using the tax-equivalent yield formula TEY=Municipal Yield1−Combined Tax Rate\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Combined Tax Rate}}, we calculate 4.25%1−0.50=4.25%0.50=8.50%\frac{4.25\%}{1 - 0.50} = \frac{4.25\%}{0.50} = 8.50\%. A fully taxable corporate bond must yield 8.50%8.50\% to equal the 4.25%4.25\% net payout of the municipal bond.

Adım Adım Çözüm

1
Calculate the combined tax bracket for double-exempt income.
Combined tax rate = 37%+13%=50%37\% + 13\% = 50\% (or 0.500.50).
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.
Tax-Equivalent Yield=4.25%1−0.50=4.25%0.50=8.50%\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−Combined Tax Rate)(1 - \text{Combined Tax Rate}).

Anahtar Kavram

Tax-Equivalent Yield for Double Tax-Exempt Municipal Bonds
Tahmini Süre:2m 0s
Soru 26Soru →

A corporate bond is currently trading in the secondary market at a quoted price of 105.00105.00 (% of par). If the bond's current yield is calculated at 6.00%6.00\%, what is the annual dollar coupon payment for a single $1,000\$1,000 par value bond?

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Cevap: 63

Cevap

The annual dollar coupon payment per $1,000\$1,000 par bond is $63.00\$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%6.00\%) by the bond's current market price ($1,050.00\$1,050.00, which is 105.00%105.00\% of the $1,000\$1,000 par value). Doing so gives 0.0600×$1,050.00=$63.000.0600 \times \$1,050.00 = \$63.00.

Adım Adım Çözüm

1
Calculate the market dollar price of the bond from its percentage-of-par quote.
Market Price = $1,000×1.05=$1,050.00\$1,000 \times 1.05 = \$1,050.00
Bond price quotes are expressed as a percentage of par value (105.00%=105.00105.00\% = 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×$1,050.00=$63.000.0600 \times \$1,050.00 = \$63.00
This yields the total annual interest payment in dollars.

Anahtar Kavram

Calculating annual coupon payment using Current Yield and secondary market price
Soru 27Soru →

An investor residing in North Carolina is subject to a 20%20\% federal marginal income tax rate and a 5%5\% state income tax rate. The investor is considering purchasing an out-of-state municipal bond offering a yield of 4.50%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?

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Cevap: 5.7

Cevap

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%×(1−0.05)=4.275%4.50\% \times (1 - 0.05) = 4.275\%. Next, because corporate bond interest is subject to both federal and state taxes (20%+5%=25%20\% + 5\% = 25\% combined tax rate), set the after-tax corporate return equal to 4.275%4.275\%: Corporate Yield×(1−0.25)=4.275%\text{Corporate Yield} \times (1 - 0.25) = 4.275\%. Solving yields Corporate Yield=4.275%0.75=5.70%\text{Corporate Yield} = \frac{4.275\%}{0.75} = 5.70\%.

Adım Adım Çözüm

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%.

Anahtar Kavram

Tax-Equivalent Yield for Out-of-State Municipal Bonds vs Fully Taxable Corporate Debt
Soru 28Soru →

An investor in a 32%32\% federal marginal income tax bracket is evaluating a tax-exempt municipal bond offering a yield of 4.76%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?

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Cevap: 7

Cevap

The tax-equivalent yield required from a fully taxable corporate bond is 7.0%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 TEY=Municipal Yield1−Marginal Tax Rate\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Marginal Tax Rate}}, we divide 4.76%4.76\% by (1−0.32)=0.68(1 - 0.32) = 0.68, resulting in 7.00%7.00\%.

Adım Adım Çözüm

1
Determine the tax-free factor
1−0.32=0.681 - 0.32 = 0.68
The investor retains 68%68\% of earnings on taxable income after paying a 32%32\% marginal income tax rate.
2
Calculate the tax-equivalent yield
4.76%0.68=7.00%\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.

Anahtar Kavram

Tax-Equivalent Yield (TEY)
Soru 29Soru →

An investor purchases a 10-year corporate bond with a 1,000parvaluetradinginthesecondarymarketatapriceof1,000 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?

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Cevap: 5

Cevap

5.0%
Current yield calculates the return an investor receives based on the current market price of a bond (46.00annualinterest/46.00 annual interest / 920.00 market price = 5.0%).

Adım Adım Çözüm

1
Calculate total annual interest income
23.00×2=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
(46.00/46.00 / 920.00) × 100 = 5.0%
Current yield measures annual income as a percentage of the bond's secondary market purchase price.

Anahtar Kavram

Current Yield Calculation for Debt Securities
Soru 30Soru →

An investor purchases a portfolio of municipal bonds with a total par value of $50,000\$50,000. The bonds carry a nominal annual coupon rate of 4.50%4.50\% with interest payable semi-annually. If the current market price of the portfolio is quoted at 90.0090.00 (% of par), what is the annual current yield of this bond portfolio?

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Cevap: 5

Cevap

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\$50,000 and a nominal coupon rate of 4.50%4.50\%, the annual coupon income is $2,250\$2,250. At a quoted price of 90.0090.00 (% of par), the market value of the position is $45,000\$45,000. Dividing $2,250\$2,250 by $45,000\$45,000 yields an annual current yield of 5.00%5.00\%.

Adım Adım Çözüm

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%100\% = $1,000\$1,000 per bond).
2
Determine the annual dollar coupon interest received.
Annual Interest = $50,000×4.50%=$2,250\$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 = $2,250$45,000=0.05=5.00%\frac{\$2,250}{\$45,000} = 0.05 = 5.00\%.
Current yield measures annual interest income relative to the bond's current secondary market price.

Anahtar Kavram

Current Yield Calculation and Bond Price/Yield Dynamics
Soru 31Soru →

An investor purchases 5 corporate bonds, each having a par value of 1,0001,000 and a stated nominal coupon rate of 4.8%4.8\%. What is the total annual interest income, in dollars, that the investor will receive from this holding?

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Cevap: 240

Cevap

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)paidannuallyininterest.Eachbondpays1,000) paid annually in interest. Each bond pays 4.8\% \times \1,000=$481,000 = \$48 per year. For an investor holding 5 bonds, the total annual interest income is 5×$48=$2405 \times \$48 = \$240.

Adım Adım Çözüm

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. \1,000×4.8%=$481,000 \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)bythetotalnumberofbondsheld(5):48) by the total number of bonds held (5): \48×5=$24048 \times 5 = \$240.

Anahtar Kavram

Calculating annual coupon interest income for debt securities
Tahmini Süre:45s
Soru 32Soru →

A corporate bond with a par value of 1,000paysa61,000 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?

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Cevap: 7.5

Cevap

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(60 ( 1,000 par \times 6%). Dividing 60bythemarketpriceof60 by the market price of 800 equals 0.075, or 7.5%.

Adım Adım Çözüm

1
Calculate the annual interest payment from the coupon rate and par value.
Annual Interest = 6% of 1,000=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.
60/60 / 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.

Anahtar Kavram

Calculating current yield on a debt security
Tahmini Süre:1m 0s
Soru 33Soru →

An open-end management investment company has total assets of $150,000,000\$150,000,000 and total liabilities of $10,000,000\$10,000,000. If the fund has 10,000,00010,000,000 shares outstanding, what is the fund's Net Asset Value (NAV) per share in dollars?

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Cevap: 14

Cevap

The Net Asset Value (NAV) per share is $14.00\$14.00.
The Net Asset Value (NAV) per share is calculated using the formula NAV=Total Assets−Total LiabilitiesShares Outstanding\text{NAV} = \frac{\text{Total Assets} - \text{Total Liabilities}}{\text{Shares Outstanding}}. Subtracting liabilities from assets gives net assets of $140,000,000\$140,000,000. Dividing $140,000,000\$140,000,000 by 10,000,00010,000,000 shares yields an NAV per share of $14.00\$14.00.

Adım Adım Çözüm

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\$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.
$140,000,00010,000,000=$14.00\frac{\$140,000,000}{10,000,000} = \$14.00
NAV per share measures the per-share value of an open-end investment company.

Anahtar Kavram

Net Asset Value (NAV) Calculation
Soru 34Soru →

An investor purchases a corporate bond with a $1,000\$1,000 par value at a secondary market price quote of 92.5092.50. The bond pays semi-annual interest payments of $37.00\$37.00 every six months. What is the current yield of this bond, expressed as a percentage?

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Cevap: 8

Cevap

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\$37.00, the annual interest payment is $74.00\$74.00. A bond price quote of 92.5092.50 translates to a market price of $925.00\$925.00 (92.50%92.50\% of $1,000\$1,000 par value). Dividing $74.00\$74.00 by $925.00\$925.00 produces a current yield of 8.00%8.00\%.

Adım Adım Çözüm

1
Calculate the annual interest income from the semi-annual payment
Annual Interest=$37.00×2=$74.00\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
Market Price=92.50%×$1,000=$925.00\text{Market Price} = 92.50\% \times \$1,000 = \$925.00
Corporate bonds are quoted as a percentage of their $1,000\$1,000 par value.
3
Compute the current yield
Current Yield=$74.00$925.00=0.08=8.00%\text{Current Yield} = \frac{\$74.00}{\$925.00} = 0.08 = 8.00\%
Current yield measures annual income as a percentage of current market price.

Anahtar Kavram

Bond Current Yield Formula
Soru 35Soru →

An investor in the 32%32\% federal marginal income tax bracket resides in a state with a 5%5\% state marginal income tax rate. The investor is evaluating a qualifying in-state municipal bond offering a yield of 4.41%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.

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Cevap: 7

Cevap

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%32\%) and state (5%5\%) income taxes, resulting in a total tax rate of 37%37\%. Applying the formula TEY=Municipal Yield1−Marginal Tax Rate\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Marginal Tax Rate}} gives 4.41%1−0.37=4.41%0.63=7.00%\frac{4.41\%}{1 - 0.37} = \frac{4.41\%}{0.63} = 7.00\%. A fully taxable corporate bond must yield 7.00%7.00\% to provide the same net after-tax income.

Adım Adım Çözüm

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.

Anahtar Kavram

Tax-Equivalent Yield (TEY) for In-State Municipal Debt
Soru 36Soru →

An investor subject to a 32%32\% federal marginal income tax bracket is evaluating a corporate bond offering a 6.25%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?

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Cevap: 4.25

Cevap

The tax-exempt municipal bond must offer a yield of 4.25%4.25\% to provide the exact same after-tax return as the 6.25%6.25\% corporate bond.
Because municipal bond interest is exempt from federal income taxes, an investor keeps 100%100\% of the interest paid by a qualifying municipal bond. To compare a taxable corporate bond paying 6.25%6.25\% against a tax-free municipal bond, calculate the corporate bond's after-tax yield: After-Tax Yield=Corporate Yield×(1−Tax Rate)\text{After-Tax Yield} = \text{Corporate Yield} \times (1 - \text{Tax Rate}). For an investor in a 32%32\% tax bracket, this yields 6.25%×(1−0.32)=4.25%6.25\% \times (1 - 0.32) = 4.25\%. A municipal bond yielding 4.25%4.25\% delivers the exact same net cash income.

Adım Adım Çözüm

1
Determine the taxable corporate bond yield and the investor's tax rate.
Corporate yield = 6.25%6.25\%, marginal tax rate = 32%32\% (0.320.32).
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=0.681 - 0.32 = 0.68 (or 68%68\% retained).
The investor keeps (1−marginal tax rate)(1 - \text{marginal tax rate}) of any taxable interest earned.
3
Multiply the nominal corporate yield by the retained percentage.
6.25%×0.68=4.25%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%4.25\%.
Interest from municipal bonds is exempt from federal income tax, so its nominal yield equals its after-tax yield.

Anahtar Kavram

Municipal Bond After-Tax Yield and Tax-Equivalent Yield
Soru 37Soru →

An investor in a 35%35\% federal income tax bracket and a 5%5\% state income tax bracket is evaluating a taxable corporate bond with a yield of 7.20%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?

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Cevap: 4.55

Cevap

The out-of-state municipal bond must offer a minimum yield of 4.55%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%35\%) and state (5%5\%) taxes, making the combined tax rate 40%40\%. The corporate bond's after-tax yield is 7.20%×(1−0.40)=4.32%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%5\% state tax. Setting the municipal bond's after-tax yield equal to 4.32%4.32\% gives Y×(1−0.05)=4.32%Y \times (1 - 0.05) = 4.32\%. Solving for YY yields Y=4.32%0.95=4.547368%Y = \frac{4.32\%}{0.95} = 4.547368\%, which rounds to 4.55%4.55\%.

Adım Adım Çözüm

1
Determine the combined marginal tax rate applicable to fully taxable corporate bond interest.
Combined tax rate = 35%+5%=40%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%×(1−0.40)=4.32%7.20\% \times (1 - 0.40) = 4.32\%.
The investor retains 60%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%5\% state income tax (0%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%4.32\% net after-tax return.
Required municipal yield = 4.32%1−0.05=4.32%0.95≈4.55%\frac{4.32\%}{1 - 0.05} = \frac{4.32\%}{0.95} \approx 4.55\%.
Dividing the net required return by (1−state tax rate)(1 - \text{state tax rate}) determines the nominal yield the municipal bond must pay.

Anahtar Kavram

Tax Treatment of Out-of-State Municipal Bonds vs. Corporate Bonds
Soru 38Soru →

An investor holds 1010 corporate bonds with a par value of $1,000\$1,000 each. The bonds pay a stated annual coupon rate of 5.80%5.80\% in semi-annual installments. What total dollar amount of interest will the investor receive every six months?

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Cevap: 290

Cevap

The investor will receive a total interest payment of $290 every six months.
The correct semi-annual payment is 290.Tofindthis,multiply290. To find this, multiply 10 bonds by their par value of 1,000togetatotalparvalueof1,000 to get a total par value of 10,000. Applying the annual coupon rate of 5.80% yields 580intotalannualinterest.Dividing580 in total annual interest. Dividing 580 by 2 gives the semi-annual payment of $290 received every six months.

Adım Adım Çözüm

1
Calculate total par value
$10,000
Multiply the number of bonds owned by the face value of each bond (10×$1,000=$10,00010 \times \$1,000 = \$10,000).
2
Calculate annual interest income
$580
Multiply the total par value by the annual coupon rate ($10,000×0.058=$580\$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\$580 / 2 = \$290).

Anahtar Kavram

Calculating semi-annual coupon payments based on total bond par value and nominal coupon rate.
Soru 39Soru →

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

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Cevap: 6

Cevap

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\$960 and a current yield of 6.25%6.25\%, the bond pays $960×0.0625=$60\$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\$1,000): $60$1,000=6.0%\frac{\$60}{\$1,000} = 6.0\%.

Adım Adım Çözüm

1
Determine the annual dollar interest payment using the market price and current yield.
Annual interest payment = 960∗0.0625=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 = (60/60 / 1,000) * 100% = 6.0%.
The nominal yield is fixed at issuance as a percentage of the bond's par value ($1,000).

Anahtar Kavram

Relationship between nominal yield, current yield, market price, and par value in bond pricing.
Soru 40Soru →

An investor purchases a corporate bond with a par value of 1,000anda61,000 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?

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Cevap: 7.5

Cevap

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 1,000parvalue,theannualinterestpaymentis1,000 par value, the annual interest payment is 60. Dividing 60bythemarketpriceof60 by the market price of 800 gives a current yield of 7.5%.

Adım Adım Çözüm

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.
60/60 / 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.

Anahtar Kavram

Bond Current Yield
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