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标题: Reading 64: Introduction to the Valuation of Debt Securities [打印本页]

作者: honeycfa 时间: 2010-4-25 13:15 标题: [2010]Session 16-Reading 64: Introduction to the Valuation of Debt Securities

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.

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: honeycfa 时间: 2010-4-25 13:15

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

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: honeycfa 时间: 2010-4-25 13:15

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.

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: honeycfa 时间: 2010-4-25 13:16

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: honeycfa 时间: 2010-4-25 13:16

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: honeycfa 时间: 2010-4-25 13:16

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%.

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

作者: honeycfa 时间: 2010-4-25 13:16

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%.

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: honeycfa 时间: 2010-4-25 13:17

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: honeycfa 时间: 2010-4-25 13:17

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: honeycfa 时间: 2010-4-25 13:17

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%.

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: honeycfa 时间: 2010-4-25 13:18

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)
9.5%.

C)
11.5%.

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: honeycfa 时间: 2010-4-25 13:18

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)
97.38.

C)
100.00.

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: honeycfa 时间: 2010-4-25 13:18

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)
3.59.

B)
1.76.

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: honeycfa 时间: 2010-4-25 13:19

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: honeycfa 时间: 2010-4-25 13:19

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.

作者: honeycfa 时间: 2010-4-25 13:19

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)
$1,095.

B)
$1,196.

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: honeycfa 时间: 2010-4-25 13:20

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)
9%.

B)
1%.

C)
5%.

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

[此贴子已经被作者于2010-4-25 13:20:21编辑过]

作者: honeycfa 时间: 2010-4-25 13:21

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

A)
only the return on the market.

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

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

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.

作者: honeycfa 时间: 2010-4-25 13:21

Consider a 10%, 10-year bond sold to yield 8%. One year passes and interest rates remained unchanged (8%). What will have happened to the bond's price during this period?

A)
It will have increased.

B)
It will have remained constant.

C)
It will have decreased.

The bond is sold at a premium, as time passes the bond’s price will move toward par. Thus it will fall.

N = 10; FV = 1,000; PMT = 100; I = 8; CPT → PV = 1,134

N = 9; FV = 1,000; PMT = 100; I = 8; CPT → PV = 1,125

作者: honeycfa 时间: 2010-4-25 13:21

A coupon bond that pays interest annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10%. What is the value of the bond today if the coupon rate is 8%?

A)
$2,077.00.

B)
$1,500.00.

C)
$924.18.

FV = 1,000
N = 5
I = 10
PMT = 80
Compute PV = 924.18.

作者: honeycfa 时间: 2010-4-25 13:21

A bond with a 12% coupon, 10 years to maturity and selling at 88 has a yield to maturity of:

A)
over 14%.

B)
between 13% and 14%.

C)
between 10% and 12%.

PMT = 120; N = 10; PV = -880; FV = 1,000; CPT → I = 14.3

作者: honeycfa 时间: 2010-4-25 13:22

What value would an investor place on a 20-year, $1,000 face value, 10% annual coupon bond, if the investor required a 9% rate of return?

A)
$920.

B)
$1,091.

C)
$879.

N = 20; I/Y = 9; PMT = 100 (0.10 × 1,000); FV = 1,000; CPT → PV = 1,091.

作者: honeycfa 时间: 2010-4-25 13:22

Today an investor purchases a $1,000 face value, 10%, 20-year, semi-annual bond at a discount for $900. He wants to sell the bond in 6 years when he estimates the yields will be 9%. What is the estimate of the future price?

A)
$1,152.

B)
$1,079.

C)
$946.

In 6 years, there will be 14 years (20 ? 6), or 14 × 2 = 28 semi-annual periods remaining of the bond's life So, N = (20 ? 6)(2) = 28; PMT = (1,000 × 0.10) / 2 = 50; I/Y = 9/2 = 4.5; FV = 1,000; CPT → PV = 1,079.

Note: Calculate the PV (we are interested in the PV 6 years from now), not the FV.

作者: honeycfa 时间: 2010-4-25 13:22

An investor purchased a 6-year annual interest coupon bond one year ago. The coupon rate of interest was 10% and par value was $1,000. At the time she purchased the bond, the yield to maturity was 8%. The amount paid for this bond one year ago was:

A)
$1,092.46.

B)
$1,125.53.

C)
$1,198.07.

N = 6
PMT = (0.10)(1,000) = 100
I = 8
FV = 1,000
PV = ?
PV = 1,092.46

作者: honeycfa 时间: 2010-4-25 13:23

A bond with a face value of $1,000 pays a semi-annual coupon of $60. It has 15 years to maturity and a yield to maturity of 16% per year. What is the value of the bond?

A)
$697.71.

B)
$774.84.

C)
$832.88.

FV = 1,000; PMT = 60; N = 30; I = 8; CPT → PV = 774.84

作者: honeycfa 时间: 2010-4-25 13:38

A coupon bond that pays interest semi-annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10%. What is the value of the bond today if the coupon rate is 8%?

A)
$922.78.

B)
$1,221.17.

C)
$1,144.31.

FV = 1,000; N = 10; PMT = 40; I = 5; CPT → PV = 922.78.

作者: honeycfa 时间: 2010-4-25 13:38

A coupon bond that pays interest annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10%. What is the value of the bond today if the coupon rate is 12%?

A)
$927.90.

B)
$1,075.82.

C)
$1,077.22

FV = 1,000
N = 5
I = 10
PMT = 120
PV = ?
PV = 1,075.82.

作者: honeycfa 时间: 2010-4-25 13:39

Value a semi-annual, 8% coupon bond with a $1,000 face value if similar bonds are now yielding 10%? The bond has 10 years to maturity.

A)
$1,373.87.

B)
$875.38.

C)
$1,000.00.

Using the financial calculator: N = 10 × 2 = 20; PMT = $80/2 = $40; I/Y = 10/2 = 5%; FV = $1,000; Compute the bond’s value PV = $875.38.

作者: honeycfa 时间: 2010-4-25 13:39

What value would an investor place on a 20-year, 10% annual coupon bond, if the investor required an 11% rate of return?

A)
$879.

B)
$1,035

C)
$920.

N = 20, I/Y = 11, PMT = 100, FV = 1,000, CPT PV

作者: honeycfa 时间: 2010-4-25 13:40

What value would an investor place on a 20-year, 10% annual coupon bond, if the investor required a 10% rate of return?

A)
$1,104.

B)
$1,000.

C)
$920.

N = 20; I/Y = 10; PMT= 100; FV = 1,000; CPT → PV = 1,000

作者: honeycfa 时间: 2010-4-25 13:40

An investor plans to buy a 10-year, $1,000 par value, 8% semiannual coupon bond. If the yield to maturity of the bond is 9%, the bond’s value is:

A)
$1,067.95.

B)
$934.96.

C)
$935.82.

N = 20, I = 9/2 = 4.5, PMT = 80/2 = 40, FV = 1,000, compute PV = $934.96

作者: honeycfa 时间: 2010-4-25 13:40

Deep discount bonds have:

A)

less call protection than bonds selling at par.

B)

greater price volatility than bonds selling at par.

C)

greater reinvestment risk than bonds selling at par.

A deep discount bond is a bond selling at a discount of at least 20%. This means that a $1000 face value bond will be selling at $800. Using the duration method to show risk, a deep discount bond will have a significantly greater duration than the bond selling at par. Thus having a duration higher than the face value duration means there is more price volatility for the deep discount bond.

作者: honeycfa 时间: 2010-4-25 13:40

The price and yield on a bond have:

A)
positive relation.

B)
inverse relation.

C)
no relation.

Interest rates and a bond's price have an inverse relationship. If interest rates increase the bond price will decrease and if interest rates decrease the bond price will increase.

作者: honeycfa 时间: 2010-4-25 13:41

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:

A)

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

B)

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

C)

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

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.

作者: honeycfa 时间: 2010-4-25 13:41

Suppose the term structure of interest rates makes an instantaneous parallel upward shift of 100 basis points. Which of the following securities experiences the largest change in value? A five-year:

A)
zero-coupon bond.

B)
floating rate bond.

C)
coupon bond with a coupon rate of 5%.

The duration of a zero-coupon bond is equal to its time to maturity since the only cash flows made is the principal payment at maturity of the bond. Therefore, it has the highest interest rate sensitivity among the four securities.

A floating rate bond is incorrect because the duration, which is the interest rate sensitivity, is equal to the time until the next coupon is paid. So this bond has a very low interest rate sensitivity.

A coupon bond with a coupon rate of 5% is incorrect because the duration of a coupon paying bond is lower than a zero-coupon bond since cash flows are made before maturity of the bond. Therefore, its interest rate sensitivity is lower.

作者: honeycfa 时间: 2010-4-25 13:41

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

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

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