Chapter 10 Quiz PDF

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chapter 10 quiz, mock type helpful for the final...

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8/10/2020

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37.14/50

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74.28

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1.

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Award:

A coupon bond paying semiannual interest is reported as having an ask price of 127% of its $1,000 par value. If the last interest payment was made one month ago and the coupon rate is 7%, what is the invoice price of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Invoice price

$ 1,275.77

 References Worksheet

Problem 10-4

Learning Objective: 10-01 Explain the general terms of a bond contract and how bond prices are quoted in the financial press.

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A coupon bond paying semiannual interest is reported as having an ask price of 127% of its $1,000 par value. If the last interest payment was made one month ago and the coupon rate is 7%, what is the invoice price of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) $ 1,275.77 ± 0.1%

Invoice price

 Explanation: Semi-annual coupon = $1,000 × 7% × 0.5 = $35. Accrued interest =

Annual coupon payment 2

×

Days since last coupon payment Days separating coupon payment

= $35 × (30/182) = $5.769 At a price of 127, the invoice price is: $1,270 + $5.769 = $1,275.77

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2.

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Two bonds have identical times to maturity and coupon rates. One is callable at 112, the other at 107. Which should have the higher yield to maturity?

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The bond callable at 107, should have the higher yield to maturity.

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The bond callable at 112, should have the higher yield to maturity.

The bond callable at 107 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should be higher.

Problem 10-7

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Learning Objective: 10-04 Describe call, convertibility, and sinking fund provisions, and analyze how these provisions affect a bonds price and yield to maturity.

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Consider a bond paying a coupon rate of 7.50% per year semiannually when the market interest rate is only 3.0% per half-year. The bond has three years until maturity. a. Find the bond's price today and six months from now after the next coupon is paid. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Current price Price after six months

$ 1,040.63 $ 1,034.35

b. What is the total rate of return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Total rate of return

3.00

% per six months

 References Worksheet

Problem 10-16

Learning Objective: 10-06 Calculate several measures of bond return, and demonstrate how these measures may be affected by taxes.

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Consider a bond paying a coupon rate of 7.50% per year semiannually when the market interest rate is only 3.0% per half-year. The bond has three years until maturity. a. Find the bond's price today and six months from now after the next coupon is paid. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Current price Price after six months

$

1,040.63 ± 0.1%

$

1,034.35 ± 0.1%

b. What is the total rate of return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Total rate of return

3.00 ± 1% % per six months

 Explanation: a. https://ezto.mheducation.com/hm.tpx?todo=printview

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The bond pays $37.50 every six months. Current price: [$37.50 × Annuity factor(3.0%, 6)] + [$1,000 × PV factor(3.0%, 6)] = $1,040.63 Assuming the market interest rate remains 3.0% per half year, price six months from now: [$37.50 × Annuity factor(3.0%, 5)] + [$1,000 × PV factor(3.0%, 5)] = $1,034.35

b. Rate of return =

$37.50 + ($1,040.63 – $1,034.35) $1,040.63

=

$37.50 – $6.28 $1,040.63

= 0.0300 = 3.00% per six months.

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A bond with a coupon rate of 8% makes semiannual coupon payments on January 15 and July 15 of each year. The Wall Street Journal reports the ask price for the bond on January 30 at 100:08. What is the invoice price of the bond? The coupon period has 182 days. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Invoice price

$ 1,003.55

 References Problem 10-22

Worksheet

Learning Objective: 10-01 Explain the general terms of a bond contract and how bond prices are quoted in the financial press.

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A bond with a coupon rate of 8% makes semiannual coupon payments on January 15 and July 15 of each year. The Wall Street Journal reports the ask price for the bond on January 30 at 100:08. What is the invoice price of the bond? The coupon period has 182 days. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Invoice price

$

1,005.80 ± 0.1%

 Explanation: The reported bond price is: 100 8/32 percent of par = $1,002.5000 15 days have passed since the last semiannual coupon was paid, so there is an accrued interest, which can be calculated as: Accrued Interest =

Annual Coupon Payment 2

×

Days since Last Coupon Payment Days Separating Coupon Payment

= $40 × (15/182) = $3.2967 The invoice price is the reported price plus accrued interest: $1,002.5000 + $3.2967 = $1,005.7967 = $1,005.80

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A newly issued bond pays its coupons once a year. Its coupon rate is 4.9%, its maturity is 10 years, and its yield to maturity is 7.9%. a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.9% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Holding-period return

15.09

%

b. If you sell the bond after one year when its yield is 6.9%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to originalissue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Tax on interest income Tax on capital gain Total taxes

$ 25.21 $ 17.20 $ 42.41

c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) After-tax holding-period return

9.77

%

d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 6.9% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.9% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Realized compound yield before taxes

8.00

%

e. Use the tax rates in part (b) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules. (Do not round intermediate calculations. Round your answer to 2 decimal places.) After-tax two-year realized compound yield

5.22

%

 References Worksheet

Problem 10-44

Learning Objective: 10-06 Calculate several measures of bond return, and demonstrate how these measures may be affected by taxes.

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A newly issued bond pays its coupons once a year. Its coupon rate is 4.9%, its maturity is 10 years, and its https://ezto.mheducation.com/hm.tpx?todo=printview

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yield to maturity is 7.9%. a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.9% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Holding-period return

15.09 ± 1% %

b. If you sell the bond after one year when its yield is 6.9%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to originalissue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Tax on interest income Tax on capital gain Total taxes

25.21 ± 1% 17.20 ± 1% 42.41 ± 1%

$ $ $

c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

9.77 ± 1% %

After-tax holding-period return

d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 6.9% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.9% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Realized compound yield before taxes

10.81 ± 1% %

e. Use the tax rates in part (b) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules. (Do not round intermediate calculations. Round your answer to 2 decimal places.) After-tax two-year realized compound yield

6.90 ± 1% %

 Explanation: a. Initial price, P0 = 797.79 [n = 10; PMT = 49; FV = 1,000; i = 7.9] Next year's price, P1 = 869.14 [n = 9; PMT = 49; FV = 1,000; i = 6.9] HPR =

$49 + ($869.14 – $797.79) $797.79

= 0.1509 = 15.09 %

b. Using OID tax rules, the cost basis and imputed interest under the constant yield method are obtained by discounting bond payments at the original 7.9% yield to maturity and simply reducing maturity by one year at a time: P0 = $797.79 First Year: Constant yield price, = $811.81, so imputed taxable interest over the first year is: $811.81 – $797.79 = $14.03 Coupon received and imputed taxable interest in the year are taxed as the ordinary income: 40% × ($49 + $14.03) = $25.21 Capital gain = Actual price at 6.9% YTM – Constant yield price = P1 – = $869.14 – $811.81 = $57.33 https://ezto.mheducation.com/hm.tpx?todo=printview

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Tax on capital gain = 30.0% × $57.33 = $17.20 Total taxes = $25.21 + $17.20 = $42.41

c. After-tax HPR =

$49 + ($869.14 – $797.79) – $42.41 $797.79

= 0.0977 = 9.77 %

d. Value of the bond after two years equals $880.11 [using n = 8; i = 6.9] Total income from the two coupons, including reinvestment income: ($49 × 1.029) + $49 = $99.42 Total funds after two years: $880.11 + $99.42 = $979.53 Therefore, the $797.79 investment grows to $979.53 after two years. 797.79 × (1 + r)2 = 979.53 r = 0.1081 = 10.81%

e. Coupon received in first year: Tax on coupon @ 40% Tax on imputed interest (40% × $14.03)

$ 49.00 –19.60 –5.61

Net cash flow in first year

$ 23.79

If you invest the year-1 cash flow at an after-tax rate of: 2.9% × (1 – 40%) = 1.74% By year 2, it will grow to: $23.79 × 1.0174 = $24.20 You sell the bond in the second year for: P2 = $826.94, so imputed interest over the second year = $15.13 Selling price of the bond in the second year: Tax on imputed interest in second year: Coupon received in second year, net of tax: Capital gains tax on sales price Using constant yield value: CF from first year's coupon (reinvested):

$ 880.11 –6.05 [40% × $15.13] +29.40 [$49 × (1 – 40%)] –15.95 [30% × ($880.11 – $826.94)]

Total

$ 911.71

+24.20 [from above]

Thus, after two years, the initial investment of $797.79 grows to $911.71: 797.79 × (1 + r)2 = 911.71 r = 0.0690 = 6.90%

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