Reading 64: Introduction to the Valuation of Debt Securities 2010, par, currently, interest, protect

honeycfa

LOS e: Compute 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) $498.

C) $249.

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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.

 

[此贴子已经被作者于2010-4-25 14:25:24编辑过]

honeycfa

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) $231.38.

C) $239.39.

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

honeycfa

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

A) 6.11%.

B) 7.20%.

C) 3.06%.

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

honeycfa

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) 88.85.

B) 83.75.

C) 100.00.

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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.

honeycfa

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) $103.53

C) $68.77

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

honeycfa

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) $456.39.

B) $200.00.

C) $463.19.

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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.

honeycfa

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.

honeycfa

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) $103.67.

B) $175.30.

C) $99.33.

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

honeycfa

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) $78.29.

B) $782.91.

C) $779.01.

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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.

honeycfa

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) $78.29.

B) $782.91.

C) $779.01.

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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.