Reading 64: Introduction to the Valuation of Debt Securities 2010, face, discount, investor, change

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LOS c: Compute the value of a bond and the change in value that is attributable to a change in the discount rate.

An investor buys a 25-year, 10% annual pay bond for $900 and will sell the bond in 5 years when he estimates its yield will be 9%. The price for which the investor expects to sell this bond is closest to:

A) $1,091.

B) $964.

C) $1,122.

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This is a present value problem 5 years in the future.
N = 20, PMT = 100, FV = 1000, I/Y = 9
CPT PV = -1,091.29
The $900 purchase price is not relevant for this problem.

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What is the present value of a 7% semi-annual pay corporate bond with a $1,000 face value and 20 years to maturity if it is yielding 6.375%? If a municipal bond is yielding 4.16% and an investors marginal tax rate is 35%, would the investor prefer the corporate bond or the municipal bond?

Value

Investor preference

A) $1,070.09 municipal bond

B) $1,121.23 municipal bond

C) $1,070.09 corporate bond

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N = 20 × 2 = 40; I/Y = 6.375/2 = 3.1875; PMT = 70/2 = 35; FV = 1,000; CPT → PV = $1,070.09.

The taxable-equivalent yield on the municipal bond is: 4.16% / (1 ? 0.35) = 6.4%

The investor would prefer the municipal bond because the taxable-equivalent yield is greater than the yield on the corporate bond: 6.4% > 6.375%

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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) 2.67.

C) 0.00.

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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.

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What is the probable change in price of a 30-year semiannual 6.5% coupon, $1000 par value bond yielding 8% when the nominal risk-free rate changes from 5% to 4%?

A) $107.31.

B) $98.83.

C) $106.34.

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Price at 8% is N = 60, FV = $1,000, I = 4%, PMT = $32.50, CPT PV = $830.32; price at 7% is N = 60, FV = $1,000, I = 3.5%, FV = $1,000, CPT PV = $937.64. Change in price is $107.31.

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If a bond's coupon is greater than the prevailing market rate on new issues, the bond is called a:

A) premium bond.

B) discount bond.

C) term bond.

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When the coupon rate on a bond is higher than the prevailing market rate the bond will be selling at a premium.  This occurs because the bonds price will be higher than the face value because as interest rate goes down price goes up.

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Assuming the risk-free rate is 5% and the appropriate risk premium for a AAA-rated issuer is 4%, the appropriate discount rate for a 10-year Treasury note is:

A) 5%.

B) 4%.

C) 9%.

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For a 10-year treasury the relevant discount rate is the risk free rate.

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An investor has the following choices available:

• She can buy a 10% semi annual coupon, 10-year bond for $1,000.> >
• She can reinvest the coupons at 12%.> >
• She can sell the bond in three years at an estimated price of $1,050.> >

Based on this information, the average annual rate of return over the three years is:> >

A) 11.5%.

B) 9.5%.

C) 13.5%.

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Step 1. Find the FV of the coupons and interest on interest:

N = 3(2) = 6; I = 12/2 = 6; PMT = 50; compute FV = 348.77

Step 2. Determine the value of the bond at the end of 3 years:

$348.77 + 1,050.00 = $1,398.77

Step 3. Equate FV (1,398.77) with PV (1,000) over 3 years (n = 6):

compute I = 5.75(2) = 11.5%.

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Assume that an option-free 5% coupon bond with annual coupon payments has two years to maturity. A callable bond that is the same in every respect as the option-free bond is priced at 91.76. With the term structure flat at 6% what is the value of the embedded call option?

A) 6.41.

B) -8.24.

C) 4.58.

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The option value is the difference between the option-free bond price and the corresponding callable bond price.

The value of the option free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign).

The option value = 98.17 – 91.76 = 6.41.

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Using the following spot rates for pricing the bond, what is the present value of a three-year security that pays a fixed annual coupon of 6%?

• Year 1: 5.0%
• Year 2: 5.5%
• Year 3: 6.0%

A) 100.10.

B) 95.07.

C) 102.46.

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This value is computed as follows:

Present Value = 6/1.05 + 6/1.055² + 106/1.06³ = 100.10

The value 95.07 results if the coupon payment at maturity of the bond is neglected.

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If an investor purchases a 8 1/2s 2001 Feb. $10,000 par Treasury Note at 105:16 and holds it for exactly one year, what is the rate of return if the selling price is 105:16?

A) 8.50%.

B) 8.00%.

C) 8.06%.

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Purchase Price = [(105 + 16/32)/100] x 10,000 = $10,550.00

Selling price = [(105 + 16/32)/100] x 10,000 = $10,550.00

Interest = 8 1/2% of 10,000 = $850.00

Return = (P_end - P_beg + Interest)/P_beg = (10,550.00 - 10,550.00 + 850.00)/10,550.00 = 8.06%