Reading 67: Introduction to the Valuation of Fixed Income price, black, percent, class

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1.Janet Preen is considering buying a 10-year zero-coupon bond that has a $1,000 face value and is priced to yield 7.25 percent (semi-annual compounding). What price will Janet pay for the bond?

A)   $496.62.

B)   $490.58.

C)   $1,072.50.

D)   $1,000.00.

2．A 12-year, $1,000 face value zero-coupon bond is priced to yield a return of 7.50 percent compounded semi-annually. What is the bond’s price?

A)   $250.00

B)   $419.85.

C)   $413.32.

D)   $389.75

3．A 15-year, $1,000 face value zero-coupon bond is priced to yield a return of 8.00 percent compounded semi-annually. What is the price of the bond, and how much interest will the bond pay over its life, respectively?

Bond Price

Interest

 

A)                                        $691.68 $308.32

B)                                        $610.25 $389.75

C)                                        $389.75 $610.25

D)                                        $308.32 $691.68

4．A zero-coupon bond matures three years from today, has a par value of $1,000 and a yield to maturity of 8.5 percent (assuming semi-annual compounding). What is the current value of this issue?

A)   $779.01.

B)   $78.29.

C)   $782.91.

D)   $1,000.00.

5．What would an investor pay for a 25-year zero coupon bond if they required 11%? (Assume semi-annual compounding.)

A)   $68.77

B)   $103.53

C)   $1,035.25

D)   $95.21

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答案和详解如下：

1.Janet Preen is considering buying a 10-year zero-coupon bond that has a $1,000 face value and is priced to yield 7.25 percent (semi-annual compounding). What price will Janet pay for the bond?

A)   $496.62.

B)   $490.58.

C)   $1,072.50.

D)   $1,000.00.

The correct answer was B)

N = 10 * 2 = 20; I/Y = 7.25/2 = 3.625; PMT = 0; FV = 1,000; Compute PV = 490.58 or $1,000/(1.03625)²⁰ = $490.58.

2．A 12-year, $1,000 face value zero-coupon bond is priced to yield a return of 7.50 percent compounded semi-annually. What is the bond’s price?

A)   $250.00

B)   $419.85.

C)   $413.32.

D)   $389.75

The correct answer was C)

Using an equation: Price_zerocoupon = Face Value * [ 1 / ( 1 + i/n)^n*2] Here, Price_zerocoupon = 1000 * [ 1 / (1+ 0.075/2)^12*2] = 1000 * 0.41332 = 413.32.

Using the calculator: N = (12*2) = 24, I/Y = 7.50 / 2 = 3.75, FV = 1000, PMT = 0. PV = -413.32

3．A 15-year, $1,000 face value zero-coupon bond is priced to yield a return of 8.00 percent compounded semi-annually. What is the price of the bond, and how much interest will the bond pay over its life, respectively?

Bond Price

Interest

 

A)                                        $691.68 $308.32

B)                                        $610.25 $389.75

C)                                        $389.75 $610.25

D)                                        $308.32 $691.68

The correct answer was D)

Using an equation: Price_zerocoupon = Face Value * [ 1 / ( 1 + i/n)^n*2 ]

Here, Price_zerocoupon = 1000 * [ 1 / (1+ 0.080/2)^15*2] = 1000 * 0.30832 = 308.32. So, interest = Face – Price = 1000 – 308.32 = 691.68.

Using the calculator: N = (15*2) = 30, I/Y = 8.00 / 2 = 4.00, FV = 1000, PMT = 0. PV = -308.32. Again, Face – Price = 1000 – 308.32 = 691.68.

4．A zero-coupon bond matures three years from today, has a par value of $1,000 and a yield to maturity of 8.5 percent (assuming semi-annual compounding). What is the current value of this issue?

A)   $779.01.

B)   $78.29.

C)   $782.91.

D)   $1,000.00.

The correct answer was A)

The value of the bond is computed as follows:

Bond Value = $1,000/1.0425⁶ = $779.01.
N = 6, I/Y = 4.25, PMT = 0, FV = 1,000, CMP PV = 779.01.

5．What would an investor pay for a 25-year zero coupon bond if they required 11%? (Assume semi-annual compounding.)

A)   $68.77

B)   $103.53

C)   $1,035.25

D)   $95.21

The correct answer was A)

N = 50, I/Y = 5.5, PMT = 0, FV = 1,000
CPT PV = 68.77