Question 1

A bond that pays interest annually yields a rate of return of 7.25 percent.The inflation rate for the same period is 2.31 percent.What is the actual real rate of return on this bond?

Accepted Answer

r = (1 + .0725)/(1 + .0231)- 1 = .0483,or 4.83%

Question 2

A $1,000 face value corporate bond matures in 28 years,pays interest semiannually,and has a market quote of 98.625.The coupon rate is 7.25 percent,the current yield is ___ percent,and the yield to maturity is ____ percent.

Accepted Answer

Current yield = (7.25% × $1,000)/(98.625% × $1,000)= .0735,or 7.35%Or:Current yield = 7.25%/98.625% = .0735,or 7.35% Yield to maturity = 3.68% × 2 = 7.37%

Question 3

If the nominal rate of return on a bond is 8.59 percent and the real rate is 3.87 percent,what is the rate of inflation?

Accepted Answer

h = (1 + .0859)/(1 + .0387)- 1 = .0454,or 4.54%

Question 4

Eastern Sports bonds have a face value of $1,000,mature in 7 years,pay interest semiannually,and have a coupon rate of 7.25 percent.The next interest payment will be paid two months from today.What is the dirty price of this bond if the market rate of return is 7.5 percent?

Accepted Answer

Bond value = [(.0725 × $1,000)/2] × ({1 - 1/[1 + (.075/2)]^{7 × 2}}/(.075/2))+ {$1,000/[1 + (.075/2)]^{7 × 2}} = $986.58 Dirty price = $986.58 + [(.0725 × $1,000/2)× (4/6)] = $1,010.75

Question 5

A $1,000 face value Treasury bond matures in 16 years,pays interest semiannually,and has a market quote of 101.0210.The coupon rate is 3.5 percent,the current yield is ___ percent,and the yield to maturity is ____ percent.

Accepted Answer

Current yield = (3.5% × $1,000)/(101.0210% × $1,000)= .0346,or 3.46%Or:Current yield = 3.5%/101.0210% = .0346,or 3.46% Yield to maturity = 1.71% × 2 = 3.42%

Question 6

Deep Hollow Welding's bond pays a coupon rate of 6.5 percent,has a yield to maturity of 6.98 percent,and a face value of $1,000.The current rate of inflation is 2.68 percent.What is the real rate of return on these bonds?

Accepted Answer

r = (1 + .0698)/(1 + .0268)- 1 = .0419,or 4.19%

Question 7

A corporate bond yields 7.3 percent.What municipal bond rate is equivalent to the corporate rate for an investor with a 25 percent marginal tax rate?

Accepted Answer

.073 × (1 - .25)= .0548,or 5.48%

Question 8

A $5,000 face value zero coupon bond is quoted at a price of 46.874.What is the amount you would pay to purchase this bond today?

Accepted Answer

Market price = 46.874% × $5,000 = $2,343.70

Question 9

Assume a bond yields a real rate of return of 3.6 percent during a time when inflation is 1.87 percent.What would the actual nominal rate of return be?

Accepted Answer

R = (1 + .036)×(1 + .0187)- 1 = .0554,or 5.54%

Question 10

Atlas bonds have a face value of $1,000,mature in 6 years,pay interest semiannually,and have a coupon rate of 4.5 percent.The next interest payment will be paid two months from today.What is the clean price of this bond if the market rate of return is 5.1 percent?

Accepted Answer

Bond value = [(.045 × $1,000)/2] × ({1 - 1/[1 + (.051/2)]^{6 × 2}}/(.051/2))+ {$1,000/[1 + (.051/2)]^{6 × 2}} = $969.32 The clean price excludes any accrued interest.

Question 11

Toy World bonds have a face value of $1,000,mature in13 years,pay interest semiannually,and have a coupon rate of 6.5 percent.The next interest payment will be paid four months from today.What is the dirty price of this bond if the market rate of return is 6.3 percent?

Accepted Answer

Bond value = [(.065 × $1,000)/2] × ({1 - 1/[1 + (.063/2)]^{13 × 2}}/(.063/2))+ {$1,000/[1 + (.063/2)]^{13 × 2}} = $1,017.57 Dirty price = $1,017.57 + [(.065 × $1,000/2)× (2/6)] = $1,028.40

Question 12

A Treasury bond is quoted at a price of 101.2462 with a current yield of 3.68 percent.What is the coupon rate?

Accepted Answer

.0368 = C/(101.2462% × $1,000)C = $37.26Coupon rate = $37.26/$1,000 = .0373,or 3.73%

Question 13

A $1,000 face value bond has a bid quote of 101.087 and a bid-ask spread of .185.What price will you receive if you sell your bond today? Ignore any accrued interest or trading costs.

Accepted Answer

Purchase price = Bid price = 101.087% × $1,000 = $1,010.87

Question 14

You are purchasing a bond with a face value of $1,000 and a coupon rate of 6.65 percent.The bond pays interest semiannually and has a yield to maturity of 7.23 percent.The bond matures in 6.5 years and pays its next interest payment in four months.What amount you accrued interest must you pay to purchase this bond today?

Accepted Answer

Accrued interest = [(.0665 × $1,000/2)× (2/6)] = $11.08

Question 15

Assume a taxable bond yields 8.25 percent and a comparable municipal bond yields 6.85 percent.At what tax rate would an investor be indifferent between the bonds?

Accepted Answer

.0825 × (1 - t*)= .0685;t* = .1697 or 16.97%

Question 16

A $1,000 face value bond has a bid quote of 101.123 and a bid-ask spread of .205.What price must you pay to purchase this bond? Ignore any accrued interest or trading costs.

Accepted Answer

Asked price = (101.123% + .205%)× $1,000 = $1,013.28

Question 17

A 25-year zero coupon bond with a face value of $1,000 is issued at an initial price of $463.34.What is the implicit interest,in dollars,for the first year of the bond's life? Assume semiannual interest.

Accepted Answer

$463.34 = $1,000/(1 + r)^{25 × 2};r = 1.55% Bond value = $1,000/(1 + .0155)^{24 × 2} = $477.93 Implicit interest = $477.82 - 463.34 = $14.48

Question 18

Westover Company needs $2.5 million to expand its business.To accomplish this,the firm plans to sell 30-year,$1,000 face value zero-coupon bonds.The bonds will be priced to yield 6.25 percent with interest compounded semiannually.What is the minimum number of bonds the company must sell? Ignore all issue costs.

Accepted Answer

Bond value = $1,000/[1 + .0625/2)]^{30 × 2} = $157.82 Number of bonds = $2,500,000/$157.82 = 15,841 bonds

Question 19

LIAS Inc.bonds have a face value of $1,000,mature in 14 years,pay interest semiannually,and have a coupon rate of 5.75 percent.The next interest payment will be paid four months from today.What is the clean price of this bond if the market rate of return is 5.6 percent?

Accepted Answer

Bond value = [(.0575 × $1,000)/2] × ({1 - 1/[1 + (.056/2)]^{14 × 2}}/(.056/2))+ {$1,000/[1 + (.056/2)]^{14 × 2}} = $1,014.42 The clean price excludes any accrued interest.

Question 20

A U.S.Treasury bond has a face value of $10,000,a coupon rate of 4 percent compounded semiannually,a yield to maturity of 4.15 percent,and 18 years until maturity.What is the clean price quote of this bond?

Accepted Answer

Bond value = [(.04 × $10,000)/2] × ({1 - 1/[1 + (.0415/2)]^{18 × 2}}/(.0415/2))+ {$1,000/[1 + (.0415/2)]^{18 × 2}} = $9,811.12 Bond quote = ($9,811.12/$10,000)= .981112,or 98.1112 percentBonds are quoted as a percentage of face value;so the quoted price is 98.1112

Quiz 5: Interest Rates and Bond Valuation