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标题: Reading 65: Introduction to the Valuation of Debt Securities- [打印本页]

作者: 1215 时间: 2011-3-30 15:08 标题: [2011]Session16-Reading 65: Introduction to the Valuation of Debt Securities-

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

LOS c: Calculate 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)
$964.

B)
$1,122.

C)
$1,091.

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.

作者: 1215 时间: 2011-3-30 15:09

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)

$1,121.23 municipal bond

B)

$1,070.09 corporate bond

C)

$1,070.09 municipal bond

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%

作者: 1215 时间: 2011-3-30 15:09

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.

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.

作者: 1215 时间: 2011-3-30 15:09

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.

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.

作者: 1215 时间: 2011-3-30 15:09

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.

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.

作者: 1215 时间: 2011-3-30 15:10

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)
4%.

B)
9%.

C)
5%.

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

作者: 1215 时间: 2011-3-30 15:10

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)
9.5%.

B)
11.5%.

C)
13.5%.

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%.

作者: 1215 时间: 2011-3-30 15:10

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.

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.

作者: 1215 时间: 2011-3-30 15:10

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.

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.

作者: 1215 时间: 2011-3-30 15:10

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)
8.06%.

B)
8.50%.

C)
8.00%.

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%

作者: 1215 时间: 2011-3-30 15:11

An investor has the following options available to them:

They can buy a 10% semi annual coupon, 10-year bond for $1,000.
The coupons can be reinvested at 12%.
They estimate the bond will be sold in 3 years $1,050.

Based on this information, what would be the average annual rate of return over the 3 years?

A)
13.5%.

B)
11.5%.

C)
9.5%.

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

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

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

1,050.00 (given) + 348.77 (computed in step 1) = 1,398.77

3. Equate FV (1,398.77) with PV (1,000) over 3 years (N = 6); CPT → I = 5.75(2) = 11.5%

作者: 1215 时间: 2011-3-30 15:11

What is the present value of a three-year security that pays a fixed annual coupon of 6% using a discount rate of 7%?

A)
92.48.

B)
100.00.

C)
97.38.

This value is computed as follows:

Present Value = 6/1.07 + 6/1.07² + 106/1.07³ = 97.38

The value 92.48 results if the coupon payment at maturity of the bond is neglected. The coupon rate and the discount rate are not equal so 100.00 cannot be the correct answer.

作者: 1215 时间: 2011-3-30 15:11

Assume an option-free 5% coupon bond with annual coupon payments has two years remaining to maturity. A putable bond that is the same in every respect as the option-free bond is priced at 101.76. With the term structure flat at 6% what is the value of the embedded put option?

A)
1.76.

B)
-3.59.

C)
3.59.

The value of the embedded put option of the putable bond is the difference between the price of the putable bond and the price of the option-free bond.

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 = 101.79 ? 98.17 = 3.59.

作者: 1215 时间: 2011-3-30 15:12

An investor gathered the following information on three zero-coupon bonds:

1-year, $600 par, zero-coupon bond valued at $571
2-year, $600 par, zero-coupon bond valued at $544
3-year, $10,600 par, zero-coupon bond valued at $8,901

Given the above information, how much should an investor pay for a $10,000 par, 3-year, 6%, annual-pay coupon bond?

A)
$10,000.

B)
Cannot be determined by the information provided.

C)
$10,016.

A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The value of the coupon bond should simply be the summation of the present values of the three zero-coupon bonds. Hence, the value of the 3-year annual-pay bond should be $10,016 (571 + 544 + 8,901).

作者: 1215 时间: 2011-3-30 15:12

An investor gathered the following information on two zero-coupon bonds:

1-year, $800 par, zero-coupon bond valued at $762
2-year, $10,800 par, zero-coupon bond valued at $9,796

Given the above information, how much should an investor pay for a $10,000 par, 2-year, 8%, annual-pay coupon bond?

A)
$9,796.

B)
$10,558.

C)
$10,000.

A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The value of the coupon bond should simply be the summation of the present values of the two zero-coupon bonds. Hence, the value of the 2-year annual-pay bond should be $10,558 ($762 + $9,796).

作者: 1215 时间: 2011-3-30 15:12

What is the present value of a 7% semiannual-pay bond with a $1,000 face value and 20 years to maturity if similar bonds are now yielding 8.25%?

A)
$879.52.

B)
$1,000.00.

C)
$878.56.

N = 20 × 2 = 40; I/Y = 8.25/2 = 4.125; PMT = 70/2 = 35; and FV = 1,000.

Compute PV = 878.56.

作者: 1215 时间: 2011-3-30 15:12

Given a required yield to maturity of 6%, what is the intrinsic value of a semi-annual pay coupon bond with an 8% coupon and 15 years remaining until maturity?

A)
$1,196.

B)
$1,095.

C)
$1,202.

This problem can be solved most easily using your financial calculator. Using semiannual payments, I = 6/2 = 3%; PMT = 80/2 = $40; N = 15 × 2 = 30; FV = $1,000; CPT → PV = $1,196.

作者: 1215 时间: 2011-3-30 15:12

Assuming the risk-free rate is 5% and the appropriate risk premium for an A-rated issuer is 4%, the appropriate discount rate for an A-rated corporate bond is:

A)
1%.

B)
5%.

C)
9%.

The yield on a risky bond = appropriate risk-free rate + appropriate risk premium.

作者: 1215 时间: 2011-3-30 15:13

Which of the following statements about a bond’s cash flows is most accurate? The appropriate discount rate is a function of:

A)
the risk-free rate plus the risk premium.

B)
only the return on the market.

C)
the risk-free rate plus the return on the market.

The return on the market would be used only when discounting the cash flows of the market. The risk premium reflects the cost of any incremental risk incurred by the investor above and beyond that of the risk-free security.

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