Question 1

River Tours has 5.8 percent coupon bonds that pay interest semiannually.The face value of each bond is $1,000,and the current market price is $1,003.54.If the yield to maturity is 5.68 percent,how many years is it until these bonds mature?

Accepted Answer

11ea6c22_9304_1eb8_9716_c7f1df683b03_TB1200_00 Number of years = 6.549 / 2 = 3.27 years

Question 2

Assume an investor has a tax rate of 33 percent.What municipal bond rate is equivalent to a corporate rate of 7.8 percent for this investor?

Accepted Answer

Muni rate = 0.078 × (1 - 0.33)= 0.0523,or 5.23%

Question 3

A $1,000 face value bond has a bid quote of 100.6794 and a bid-ask spread of 0.0155.If you were to purchase this bond,what clean price would you pay?

Accepted Answer

Asked price = (1.006794 + 0.000155)× $1,000 = $1,006.95

Question 4

A U.S.Treasury bond has a face value of $5,000,a coupon rate of 3 percent compounded semiannually,a yield to maturity of 2.97 percent,and 7 years until maturity.What is the clean price quote of this bond?

Accepted Answer

Bond value = [(0.03 × $5,000)/2] × ({1 - 1/[1 + (0.0297/2)]^7×2}/(0.0297/2))+ {$5,000/[1 + (0.0297/2)]^7×2} = $5,009.42 11ea6c22_9305_0923_9716_29f82993c01e_TB1200_00

Question 5

Assume a taxable bond yields 6.38 percent and a comparable municipal bond yields 4.27 percent.At what tax rate would an investor be indifferent between the bonds?

Accepted Answer

0.0638 × (1 - t*)= 0.0427 t* = 0.3307,or 33.07%

Question 6

The 12-year bonds issued by Golf Companies have a quoted yield to maturity of 7.9 percent,a coupon rate of 8 percent,and semiannual payments.What is the effective annual yield on these bonds?

Accepted Answer

Effective annual yield = [1 + (0.079 / 2)]² - 1 = 0.0806,or 8.06%

Question 7

Taylor Bros.bonds have a face value of $5,000,a current market price of $5,248.50,and a coupon rate of 5.3 percent,compounded semiannually.What is the current yield on these bonds?

Accepted Answer

Current yield = (0.053 × $5,000)/ $5,248.50 = 0.0505,or 5.05%

Question 8

TJ Machine bonds have a coupon rate of 5.3 percent,a face value of $1,000,and pay interest semiannually.The bonds mature in 23 years and have a yield to maturity of 5.4 percent.What will be the percentage change in the bond's price if the market rate increases by 1 percent to 6.4 percent?

Accepted Answer

Bond value = [(0.053 × $1,000)/2] × ({1 - 1/[1 + (0.054/2)]^23×2}/(0.054/2))+ {$1,000/[1 + (0.054/2)]^23×2} = $986.92 11ea6c22_9304_45ca_9716_e1a302d559e3_TB1200_00 Bond value = [(0.053 × $1,000)/2] × ({1 - 1 / [1 + (0.064 / 2)]²³^×2} / (0.064 / 2))+ {$1,000 / [1 + (0.064 / 2)]^23×2} = $868.48 11ea6c22_9304_45cb_9716_678c60f367a0_TB1200_00 Percentage change in price = ($868.48 - $986.92)/ $986.92 = -0.1200,or 12.00%

Question 9

A $1,000 face value bond matures in 16 years,pays interest semiannually,and has a market quote of 102.0562.The coupon rate is 5.5 percent,the current yield is ________ percent,and the yield to maturity is ________ percent.

Accepted Answer

Current yield = (0.055 × $1,000)/ (1.020562 × $1,000)= 0.0539,or 5.39% Or: Current yield = 5.5% / 102.0562% = 0.0539,or 5.39% 11ea6c22_9305_0924_9716_1557580ed389_TB1200_00 Yield to maturity = 2.654% × 2 = 5.31%

Question 10

Delray bonds offer a coupon rate of 4.6 percent and currently sell at 99.2 percent of face value.What is the current yield on these bonds?

Accepted Answer

Assuming a $1,000 face value: (0.046 × $1,000)/ (0.992 × $1,000)= 0.0464,or 4.64% You can also compute this as: 4.6% / 99.2% = 0.0464,or 4.64%

Question 11

Westover Company needs $1.8 million to expand its business.To accomplish this,the firm plans to sell 25-year,$1,000 face value zero-coupon bonds.The bonds will be priced to yield 7.15 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 + 0.0715 / 2)]²⁵^×2 = $172.68 11ea6c22_9304_baff_9716_37ebf190e372_TB1200_00 Number of bonds = $1,800,000 / $172.68 = 10,424

Question 12

The ABT Co.zero coupon bonds have a $1,000 face value,a required rate of return of 8 percent,and semiannual compounding.What is one of these bonds worth today if they mature in 12 years?

Accepted Answer

Bond value = $1,000 / [1 + (0.08 / 2)]¹²^×2 = $390.12 11ea6c22_9304_e212_9716_1dd5b7ab5b4b_TB1200_00

Question 13

Autos and More offers a zero coupon bond with a yield to maturity of 9.3 percent.The bond matures in 11 years and has a face value of $1,000.What is this bond worth today? Assume semiannual compounding.

Accepted Answer

Bond value = $1,000 / [1 + (0.093 / 2)]¹¹^×2 = $367.91 11ea6c22_9304_93ee_9716_0f00a102e18d_TB1200_00

Question 14

A Treasury bond is quoted at a price of 99.4062 with a current yield of 3.17 percent.What is the coupon rate?

Accepted Answer

0.0317 = C / (0.994062 × $1,000) C = $31.51 Coupon rate = $31.51 / $1,000 = 0.03151,or 3.151%

Question 15

A $1,000 Treasury bond matures in 13.5 years,pays interest semiannually,and carries a coupon rate of 3.53 percent.What is the price of this bond if the discount rate is 4 percent?

Accepted Answer

Bond value = [(0.0353 × $1,000)/2] × ({1 - 1 / [1 + (0.04 / 2)]^13.5^×2} / (0.04 / 2))+ {$1,000 / [1 + (0.04 / 2)]^13.5×2} = $951.34 11ea6c22_9304_e211_9716_31045716a0af_TB1200_00

Question 16

A zero coupon bond has a yield to maturity of 7.48 percent,semiannual compounding,a $1,000 face value,and a market quote of 41.0932.How many years is it until this bond matures?

Accepted Answer

$1,000 = (0.410932 × $1,000)[1 + (0.0748 / 2)^T] T = 24.22 semiannual periods 11ea6c22_9304_bb00_9716_0d54bce0035c_TB1200_00 Number of years = 24.22 / 2 = 12.11 years

Question 17

A zero coupon bond with a face value of $1,000 is issued at an initial price of $474.20 and a 25-year maturity.What is the implicit interest,in dollars,for the first year of the bond's life? Assume semiannual interest.

Accepted Answer

$474.20 = $1,000 / (1 + r)²⁵^×2 r = 1.5034% 11ea6c22_9304_93ec_9716_ffca18dedf98_TB1200_00 Bond value = $1,000 / (1 + 0.015034)^24×2 = $488.57 11ea6c22_9304_93ed_9716_c1c88306e5fc_TB1200_00 Implicit interest = $488.57 - $474.20 = $14.37

Question 18

What is the market price of a bond with a $5,000 face value if the price quote is 101.1629?

Accepted Answer

Market price = 1.011629 × $5,000 = $5,058.15

Question 19

A $1,000 face value bond is currently callable at a quoted price of 101.What is the amount of the call premium?

Accepted Answer

Call premium = (1.01 × $1,000)- $1,000 = $10

Question 20

The Beta Co.bonds have a maturity of 13 years,a face value of $1,000,a coupon rate of 6.5 percent,and pay interest annually.What is the percentage change in the price of these bonds if the market yield rises to 6.9 percent from its current level of 6.5 percent?

Accepted Answer

At 6.5%,the bond sells at par.At 6.9%,the bond sells at a discount. Bond value = (0.065 × $1,000)× {[1 - 1 / (1 + 0.069)¹³] / 0.069} + [$1,000 / (1 + 0.069)¹³] = $966.38 11ea6c22_9304_45c9_9716_fd9a48735cd5_TB1200_00 Percentage change in price = ($966.38 - $1,000)/ $1,000 = -0.0336 or - 3.36%

Quiz 5: Interest Rates and Bond Valuation