prashantsahni

A 3-year option-free bond (par value of $1,000) has an annual coupon of 9%. An investor determines that the spot rate of year 1 is 6%, the year 2 spot rate is 12%, and the year 3 spot rate is 13%. Using the arbitrage-free valuation approach, the bond price is closest to:

A) $912.

B) $1,080.

C) $968.

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We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Price = [90 / (1.06)] + [90 / (1.12)2] + [1,090 / (1.13)3] = 912. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:
N = 1; I/Y = 6.0; PMT = 0; FV = 90; CPT → PV = 84.91
N = 2; I/Y = 12.0; PMT = 0; FV = 90; CPT → PV = 71.75
N = 3; I/Y = 13.0; PMT = 0; FV = 1,090; CPT → PV = 755.42
Price = 84.91 + 71.75 + 755.42 = $912.08.

prashantsahni

A three-year bond with a 10% annual coupon has cash flows of $100 at year 1, $100 at year 2, and pays the final coupon and the principal for a cash flow of $1,100 at year 3. The spot rate for year 1 is 5%, the spot rate for year 2 is 6%, and the spot rate for year 3 is 6.5%. What is the arbitrage-free value of the bond?

A) $1,050.62.

B) $975.84.

C) $1,094.87.

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Spot interest rates can be used to price coupon bonds by taking each individual cash flow and discounting it at the appropriate spot rate for that year’s payment. To find the arbitrage-free value:
Bond value = [$100 / (1.05)] + [$100 / (1.06)2] + [$1,100 / (1.065)3] = $95.24 + $89.00 + $910.63 = $1,094.87

prashantsahni

A 2-year option-free bond (par value of $1,000) has an annual coupon of 6%. An investor determines that the spot rate of year 1 is 5% and the year 2 spot rate is 8%. Using the arbitrage-free valuation approach, the bond price is closest to:

A) $992.

B) $966.

C) $1,039.

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The arbitrage free valuation approach is the process of valuing a fixed income instrument as a portfolio of zero coupon bonds. We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Bond price = [60 / (1.05)] + [1,060 / (1.08)2] = $966. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:
N = 1; I/Y = 5.0; PMT = 0; FV = 60; CPT → PV = 57.14
N = 2; I/Y = 8.0; PMT = 0; FV = 1,060; CPT → PV = 908.78
Price = 57.14 + 908.78 = $966.

prashantsahni

A year ago a company issued a bond with a face value of $1,000 with an 8% coupon. Now the prevailing market yield is 10%. What happens to the bond? The bond:

A) is traded at a market price higher than $1,000.

B) is traded at a market price of less than $1,000.

C) price is not affected by the change in market yield, and will continue to trade at $1,000.

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A bonds price/value has an inverse relationship with interest rates. Since interest rates are increasing (from 8% when issued to 10% now) the bond will be selling at a discount.  This happens so an investor will be able to purchase the bond and still earn the same yield that the market currently offers.

prashantsahni

Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Suppose the term structure of interest rates is flat at 6%. How much does the bond price change if the term structure of interest rates shifts down by 1% instantaneously?

A) -2.67.

B) 0.00.

C) 2.67.

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This value is computed as follows: Bond Price Change = New Price – Old Price = 100 – (5/1.06 + 5/1.062 + 105/1.063) = 2.67.
-2.67 is the correct value but the wrong sign. The value 0.00 is incorrect because the bond price is not insensitive to interest rate changes.

prashantsahni

Randy Harris is contemplating whether to add a bond to his portfolio. It is a semiannual, 6.5% bond with 7 years to maturity. He is concerned about the change in value due to interest rate fluctuations and would like to know the bond’s value given various scenarios. At a yield to maturity of 7.5% or 5.0%, the bond’s fair value is closest to:

7.5%

5.0%

A) 974.03 1,052.36

B) 946.30 1,087.68

C) 1,032.67 959.43

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Given a YTM of 7.5%, calculate the value of the bond as follows:
N = 14; I/Y = 7.5/2 = 3.75%; PMT = 32.50; FV = 1,000; CPT → PV = 946.30
Given a YTM of 5.0%, calculate the value of the bond as follows:
N = 14; I/Y = 5/2 = 2.5%; PMT = 32.50; FV = 1,000; CPT → PV = 1,087.68

prashantsahni

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.

prashantsahni

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.

prashantsahni

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) $456.39.

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.

prashantsahni

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) $9,799.12.

B) $9,899.05.

C) $9,606.15.

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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.