Reading 65: Introduction to the Valuation of Debt Securities- 2011, protect, center, style, label

1215

Session 16: Fixed Income: Analysis and Valuation
Reading 65: Introduction to the Valuation of Debt Securities

LOS e: Calculate the value of a zero-coupon bond.

 

 

Anne Warner wants to buy zero-coupon bonds in order to protect herself from reinvestment risk. She plans to hold the bonds for fifteen years and requires a rate of return of 9.5%. Fifteen-year Treasuries are currently yielding 4.5%. If interest is compounded semiannually, the price Warner is willing to pay for each $1,000 par value zero-coupon bond is closest to:

A) $256.

B) $249.

C) $498.

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Note that because the question asks for how much Warner is willing to pay, we will want to use her required rate of return in the calculation.

N = 15 × 2 = 30, FV = $1,000, I/Y = 9.5 / 2 = 4.75, PMT = 0; CPT → PV = -248.53.

The difference between the bond’s price of $249 that Warner would be willing to pay and the par value of $1,000 reflects the amount of interest she would earn over the fifteen year horizon.

1215

A 15-year zero coupon bond that has a par value of $1,000 and a required return of 8% would be priced at what value assuming annual compounding periods:

A) $464.

B) $315.

C) $308.

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N = 15 FV = 1,000
I = 8
PMT = 0
PV = ?
PV = 315.24

1215

A zero-coupon bond has a yield to maturity of 9.6% (annual basis) and a par value of $1,000. If the bond matures in 10 years, today's price of the bond would be:

A) $422.41.

B) $391.54.

C) $399.85.

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I = 9.6; FV = 1,000; N = 10; PMT = 0; CPT → PV = 399.85

1215

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

A) $250.00

B) $413.32.

C) $419.85.

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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

1215

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% (semi-annual compounding). What price will Janet pay for the bond?

A) $496.62.

B) $1,000.00.

C) $490.58.

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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.

1215

If the required rate of return is 12%, what is the value of a zero coupon bond with a face value of $1,000 that matures in 20 years? Assume an annual compounding period.

A) $175.30.

B) $99.33.

C) $103.67.

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I = 12
PMT = 0
FV = 1,000
N = 20
PV = ?
PV = 103.67

1215

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

A) $779.01.

B) $78.29.

C) $782.91.

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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; CPT → PV = 779.01.

1215

A 15-year, $1,000 face value zero-coupon bond is priced to yield a return of 8.00% 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) $308.32 $691.68

B) $691.68 $308.32

C) $389.75 $610.25

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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.

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1215

A Treasury bill has a $10,000 face value and matures in one year. If the current yield to maturity on similar Treasury bills is 4.1% annually, what would an investor be willing to pay now for the T-bill?

A) $9,606.15.

B) $9,799.12.

C) $9,899.05.

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The investor would pay the present value of the $10,000 one year away at a discount rate of 4.1%. To value the T-bill, enter FV = $10,000; N = 1; PMT = 0; I/Y = 4.1%; CPT → PV = -$9,606.15.

1215

If a 15-year, $1,000 U.S. zero-coupon bond is priced to yield 10%, what is its market price?

A) $23.50.

B) $239.39.

C) $231.38.

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N = 30; I/Y = 5; PMT = 0; FV = 1,000; CPT → PV = 231.38.