Q: A 30-year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments. What is the amount of each coupon payment?

$$ \frac{0.055 \times 1000}{2} = 27.50 $$

Question 1

A 30-year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments. What is the amount of each coupon payment?

Accepted Answer

$$ \frac{0.055 	imes 1000}{2} = 27.50 $$

Question 2

If a zero-coupon bond with a face value of $$1000 matures in 3 years and is currently priced at 863.38$$, what is its yield to maturity (YTM)?

Accepted Answer

$$ YTM = \left( \frac{1000}{863.38} \$$right)^{1/3}$$ - 1 = 5.04\% $$

Question 3

A 10-year, $$1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of 1043.74. If $$the bond’s yield to maturity changes to 7% APR with semiannual compounding, what will the bond’s price be?

Accepted Answer

$$ P = \sum_{t=1}^{20} \frac{40}{(1+0.035)^t} + \frac{1000}{(1+0.035$$)^{20}$$} = 1094.46 $$

Question 4

Which of the following best describes the relationship between bond prices and yields?

Accepted Answer

Bond prices and yields are inversely related; as yields increase, prices decrease.

Question 5

Suppose you purchase a 10-year bond with a 6% annual coupon for $$107.72 per 100 $$face value and sell it after 4 years when the yield to maturity is 5%. What is the internal rate of return (IRR) of your investment?

Accepted Answer

$$ IRR = 5\% $$

Question 6

A 5-year, zero-coupon, default-free security with a face value of $$1000 is priced at 765.51. $$What is its yield to maturity?

Accepted Answer

$$ YTM = \left( \frac{1000}{765.51} \$$right)^{1/5}$$ - 1 = 5.5\% $$

Question 7

If the yield to maturity of a bond increases, what happens to the price of the bond?

Accepted Answer

The price of the bond decreases.

Question 8

Consider a 2-year, default-free, zero-coupon bond with a face value of $1000 and an annual coupon rate of 6%. If the yield to maturity is 4.5%, what is the price of the bond?

Accepted Answer

$$ P = \frac{1000}{(1+0.045)^2$} = 915.03 $$

Question 9

Which bond is most sensitive to interest rate changes?

Accepted Answer

A long-term zero-coupon bond.

Question 10

A 7-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 7%. Is the bond trading at a discount, at par, or at a premium?

Accepted Answer

At a premium, because the coupon rate is higher than the yield to maturity.

Question 11

Suppose the price of a 10-year, $$1000 bond with a 6% coupon rate and annual payments is 900. $$What is the bond’s yield to maturity (YTM)?

Accepted Answer

$$ YTM = \frac{60 + \frac{1000 - 900}{10}}{\frac{1000 + 900}{2}} = 7.11\% $$

Question 12

If a bond is trading at par, what does this indicate about its coupon rate and yield to maturity?

Accepted Answer

The coupon rate equals the yield to maturity.

Question 13

A 3-year, default-free, zero-coupon bond with a face value of $$1000 is priced at 863.38. $$What is the price per $100 face value?

Accepted Answer

$$ \frac{863.38}{10} = 86.34 $$

Question 14

If the yield curve is upward sloping, what does this indicate about the relationship between yields and maturities?

Accepted Answer

Yields increase as maturities increase.

Question 15

Suppose you buy a 10-year bond with a 6% annual coupon for $$107.72 per 100 $$face value and sell it after 4 years when the yield to maturity is 7%. What is the internal rate of return (IRR) of your investment?

Accepted Answer

$$ IRR = 7\% $$

Question 16

A 2-year, default-free, zero-coupon bond with a face value of $$1000 is priced at 907.03. $$What is its yield to maturity?

Accepted Answer

$$ YTM = \left( \frac{1000}{907.03} \$$right)^{1/2}$$ - 1 = 5\% $$

Question 17

If a bond’s yield to maturity falls from 6% to 5%, which bond will experience the largest percentage price increase?

Accepted Answer

A long-term zero-coupon bond.

Question 18

A 4-year, default-free security with annual coupon payments and a face value of $1000 is issued at par. What is the coupon rate of this bond?

Accepted Answer

$$ Coupon\ Rate = \frac{1000}{\sum_{t=1}^{4} \frac{1}{(1+r)^t}} $$ where $$r is $$the yield to maturity.

Chapter 6: Valuing Bonds: Concepts, Calculations, and Applications

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