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.

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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.

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What is the yield to maturity (YTM) of a 20-year, U.S. zero-coupon bond selling for $300?

A) 7.20%.

B) 6.11%.

C) 3.06%.

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N = 40; PV = 300; FV = 1,000; CPT → I = 3.055 × 2 = 6.11.

1215

What is the value of a zero-coupon bond if the term structure of interest rates is flat at 6% and the bond has two years remaining to maturity?

A) 83.75.

B) 100.00.

C) 88.85.

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The bond price is computed as follows:

Zero-Coupon Bond Price = 100/1.03⁴ = 88.85.

The value 83.75 is incorrect because the principal is discounted over a three-year period but the bond has only two years remaining to maturity. The value 100.00 is incorrect because the principal received at maturity has to be discounted over a period of two years.

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

A) $1,035.25

B) $68.77

C) $103.53

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

1215

The value of a 10-year zero-coupon bond with a $1,000 maturity value, compounded semiannually, and has an 8% discount rate is closest to:

A) $200.00.

B) $463.19.

C) $456.39.

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V = (maturity value)/(1 + i)^{number of years x 2} = $1,000/(1.04)^{10 x 2} = $1,000/2.1911 = $456.39

or

n = 20, i = 4, FV = 1,000, compute PV = 456.39.

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.

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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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