标题: Fixed Income【Reading 57】Sample [打印本页]
作者: hinsafdar 时间: 2012-3-31 13:21 标题: [2012 L1] Fixed Income【Session 16 - Reading 57】Sample
By purchasing a noncallable, nonputable, U.S. Government 30-year bond, an investor is entitled to: A)
| full recovery of face value at maturity or when the bond is retired. |
|
B)
| annuity of coupon payments. |
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C)
| annuity of coupon payments plus recovery of principal at maturity. |
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Bond investors are entitled to two distinct types of cash flows: (1) the periodic receipt of coupon income over the life of the bond, and (2) the recovery of principal (or face value) at the end of the bond’s life.
作者: hinsafdar 时间: 2012-3-31 13:22
Answering an essay question on a midterm examination, a finance student writes these two statements:
Statement 1: The value of a fixed income security is the sum of the present values of all its expected future coupon payments.
Statement 2: The steps in the bond valuation process are to estimate the bond’s cash flows, determine the appropriate discount rate, and calculate the present value of the expected cash flows.
With respect to the student's statements:
Statement 1 is incorrect. The value of a fixed income security is the sum of the present values of its expected future coupon payments and its future principal repayment. Statement 2 is correct. The three steps in the bond valuation process are to estimate the cash flows over the life of the security; determine the appropriate discount rate based on the risk of the cash flows; and calculate the present value of the cash flows using the appropriate discount rate.
作者: hinsafdar 时间: 2012-3-31 13:22
Assume a city issues a $5 million bond to build a new arena. The bond pays 8% semiannual interest and will mature in 10 years. Current interest rates are 9%. What is the present value of this bond and what will the bond's value be in seven years from today? | Present Value | Value in 7 Years from Today |
Present Value:
Since the current interest rate is above the coupon rate the bond will be issued at a discount. FV = $5,000,000; N = 20; PMT = (0.04)(5 million) = $200,000; I/Y = 4.5; CPT → PV = -$4,674,802
Value in 7 Years:
Since the current interest rate is above the coupon rate the bond will be issued at a discount. FV = $5,000,000; N = 6; PMT = (0.04)(5 million) = $200,000; I/Y = 4.5; CPT → PV = -$4,871,053
作者: hinsafdar 时间: 2012-3-31 13:22
A corporate bond with the following data is issued:- $1,000 par value.
- 8% coupon payments.
- 5 years to maturity with semiannual coupon payments.
- Market interest rates are 10%.
What is the total interest expense?
Total interest expense is the difference between the amount paid by the issuer and the amount received from the bondholder.
Present value of the bond is computed as follows: FV = 1,000; PMT = [(1,000)(0.08)] / 2 = 40; I/Y = 5; N = 10; CPT → PV = -923
[($40 coupon payments)(10 periods) + $1,000 par value] – $923 present value of the bond = 477
作者: hinsafdar 时间: 2012-3-31 13:23
A bond is issued with the following data:- $10 million face value.
- 9% coupon rate.
- 8% market rate.
- 3-year bond with semiannual payments.
What is the present value of the bond?
FV = 10,000,000; PMT = 450,000; I/Y = 4; N = 6; CPT → PV = -10,262,107
作者: hinsafdar 时间: 2012-3-31 13:23
It is easier to value bonds than to value equities because: A)
| the future cash flows of bonds are more stable. |
|
B)
| Both of these choices are correct. |
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C)
| there is no maturity value for common stock. |
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Bonds pay out a specified periodic cash flow (coupon payment) throughout the life of the bond and pay out a lump sum at the maturity date. Common stocks don't have a maturity date and have more volatility than bonds.
作者: hinsafdar 时间: 2012-3-31 13:24
Which of the following characteristics would create the least difficulty in estimating a bond’s cash flows?
Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: - increased credit risk;
- the presence of embedded options (i.e., call/put features or sinking fund provisions);
- the use of variable rather than fixed coupon rate; and
- the presence of a conversion or exchange privilege.
作者: hinsafdar 时间: 2012-3-31 13:24
Which of the following characteristics would create the most difficulty in estimating a bond's cash flows?
Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: (1) increased credit risk, (2) the presence of embedded options (i.e., call/put features or sinking fund provisions), (3) the use of variable rather than fixed coupon rate, and (4) the presence of a conversion or exchange privilege.
作者: hinsafdar 时间: 2012-3-31 13:25
Which of the following characteristics would create the least difficulty in estimating a bond’s cash flows? A)
| Sinking fund provisions. |
|
|
|
Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: - increased credit risk;
- the presence of embedded options (i.e., call/put features or sinking fund provisions);
- the use of variable rather than fixed coupon rate; and
- the presence of a conversion or exchange privilege.
作者: hinsafdar 时间: 2012-3-31 13:25
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?
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: hinsafdar 时间: 2012-3-31 13:26
A bond with a 12% coupon, 10 years to maturity and selling at 88 has a yield to maturity of:
PMT = 120; N = 10; PV = -880; FV = 1,000; CPT → I = 14.3
作者: hinsafdar 时间: 2012-3-31 13:26
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%?
FV = 1,000
N = 5
I = 10
PMT = 80
Compute PV = 924.18.
作者: hinsafdar 时间: 2012-3-31 13:27
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%
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: hinsafdar 时间: 2012-3-31 13:27
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:
N = 20, I = 9/2 = 4.5, PMT = 80/2 = 40, FV = 1,000, compute PV = $934.96
作者: hinsafdar 时间: 2012-3-31 13:28
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:
N = 6
PMT = (0.10)(1,000) = 100
I = 8
FV = 1,000
PV = ?
PV = 1,092.46
作者: hinsafdar 时间: 2012-3-31 13:28
What is the present value of a three-year security that pays a fixed annual coupon of 6% using a discount rate of 7%?
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: hinsafdar 时间: 2012-3-31 13:28
Assume a city issues a $5 million bond to build a hockey rink. The bond pays 8% semiannual interest and will mature in 10 years. Current interest rates are 6%. What is the present value of this bond?
Since current interest rates are lower than the coupon rate the bond will be issued at a premium. FV = $5,000,000; N = 20; I/Y = 3; PMT = (0.04)($5,000,000) = $200,000. Compute PV = $-5,743,874
作者: hinsafdar 时间: 2012-3-31 13:29
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:
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: hinsafdar 时间: 2012-3-31 13:29
What value would an investor place on a 20-year, 10% annual coupon bond, if the investor required an 11% rate of return?
N = 20, I/Y = 11, PMT = 100, FV = 1,000, CPT PV
作者: hinsafdar 时间: 2012-3-31 13:29
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%?
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: hinsafdar 时间: 2012-3-31 13:29
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?
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 = (Pend - Pbeg + Interest)/Pbeg = (10,550.00 - 10,550.00 + 850.00)/10,550.00 = 8.06%
作者: hinsafdar 时间: 2012-3-31 13:30
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.
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: hinsafdar 时间: 2012-3-31 13:30
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%?
FV = 1,000
N = 5
I = 10
PMT = 120
PV = ?
PV = 1,075.82.
作者: hinsafdar 时间: 2012-3-31 13:30
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 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: hinsafdar 时间: 2012-3-31 13:31
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? |
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C)
| Cannot be determined by the information provided. |
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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: hinsafdar 时间: 2012-3-31 13:31
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 |
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: hinsafdar 时间: 2012-3-31 13:31
What value would an investor place on a 20-year, 10% annual coupon bond, if the investor required a 10% rate of return?
N = 20; I/Y = 10; PMT= 100; FV = 1,000; CPT → PV = 1,000
作者: hinsafdar 时间: 2012-3-31 13:32
Georgia-Pacific has $1,000 par value bonds with 10 years remaining maturity. The bonds carry a 7.5% coupon that is paid semi-annually. If the current yield to maturity on similar bonds is 8.2%, what is the current value of the bonds?
The coupon payment each six months is ($1,000)(0.075 / 2) = $37.50. To value the bond, enter FV = $1,000; PMT = $37.50; N = 10 × 2 = 20; I/Y = 8.2 / 2 = 4.1%; CPT → PV = –952.85.
作者: hinsafdar 时间: 2012-3-31 13:32
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?
FV = 1,000; PMT = 60; N = 30; I = 8; CPT → PV = 774.84
作者: hinsafdar 时间: 2012-3-31 13:33
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. |
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C)
| the risk-free rate plus the risk premium. |
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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: hinsafdar 时间: 2012-3-31 13:34
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?
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: hinsafdar 时间: 2012-3-31 13:34
An investor buys a 10% semi annual coupon, 10-year bond for $1,000. The coupons can be reinvested at 12%. The investor estimates that 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?
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: hinsafdar 时间: 2012-3-31 13:34
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?
N = 20; I/Y = 9; PMT = 100 (0.10 × 1,000); FV = 1,000; CPT → PV = 1,091.
作者: hinsafdar 时间: 2012-3-31 13:35
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%?
FV = 1,000; N = 10; PMT = 40; I = 5; CPT → PV = 922.78.
作者: prashantsahni 时间: 2012-3-31 13:36
If a bond sells at a discount and market rates are expected to stay the same until maturity, the price of the bond will: A)
| increase over time, approaching the par value minus the final interest payment at maturity. |
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B)
| increase over time, approaching the par value at maturity. |
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C)
| remain constant until maturity. |
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The bond’s price will increase towards the par value over time.
作者: prashantsahni 时间: 2012-3-31 13:36
A 5-year bond with a 10% coupon has a present yield to maturity of 8%. If interest rates remain constant one year from now, the price of the bond will be:
A premium bond sells at more than face value, thus as time passes the bond value will converge upon the face value.
作者: prashantsahni 时间: 2012-3-31 13:36
An investor buys a 20-year, 10% semi-annual bond for $900. She wants to sell the bond in 6 years when she estimates yields will be 10%. What is the estimate of the future price?
Since yields are projected to be 10% and the coupon rate is 10%, we know that the bond will sell at par value.
作者: prashantsahni 时间: 2012-3-31 13:37
An investor buys a 6% coupon 5-year corporate bond priced to yield 7%. If rates remain unchanged when the investor sells the bond in 2 years, the investor will receive a: |
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C)
| total return equal to the coupon yield. |
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Current yield of a bond = coupon payment / market price of bond. Bonds with a coupon lower than the prevailing interest rate will trade at a discount to par. If interest rates remain the same as the bond nears maturity the price will increase towards its par value. Thus, when they are sold, the investor will receive a capital gain.
作者: prashantsahni 时间: 2012-3-31 13:37
A discount bond (nothing changes except the passage of time): A)
| falls in value as time passes. |
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B)
| rises in value as time passes. |
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C)
| price is not related to time passing. |
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A discount bond sells at less than face value, therefore as time passes the bond value will converge upon the face value.
作者: prashantsahni 时间: 2012-3-31 13:37
If market rates do not change, as time passes the price of a zero-coupon bond will: A)
| approach the purchase price. |
|
|
|
A bond's value may differ substantially from it's maturity value prior to maturity. But as maturity draws nearer the bond's value converges to it's maturity value. This statement is true for regular bonds as well as zero-coupon bonds.
作者: prashantsahni 时间: 2012-3-31 13:38
Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Assume the term structure of interest rates is flat at 6%. If the term structure of interest rates does not change over the next twelve-month interval, the bond's price change (as a percentage of par) will be closest to:
The bond price change is computed as follows: Bond Price Change = New Price − Old Price = (5/1.06 + 105/1.062) − (5/1.06 + 5/1.062 + 105/1.063) = 98.17 − 97.33 = 0.84.
The value -0.84 is the correct price change but the sign is wrong. The value 0.00 is incorrect because although the term structure of interest rates does not change the bond price increases since it is selling at a discount relative to par.
作者: prashantsahni 时间: 2012-3-31 13:38
The price and yield on a bond have:
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: prashantsahni 时间: 2012-3-31 13:38
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. |
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B)
| It will have decreased. |
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C)
| It will have remained constant. |
|
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: prashantsahni 时间: 2012-3-31 13:41
A 12-year, $1,000 face value zero-coupon bond is priced to yield a return of 7.50% compounded semi-annually. What is the bond’s price?
Using an equation: Pricezerocoupon = Face Value × [ 1 / ( 1 + i/n)n × 2]
Here, Pricezerocoupon = 1000 × [ 1 / (1+ 0.075/2)12 × 2] = 1000 × 0.41332 = 413.32.
Using the calculator: N = (12 × 2) = 24, I/Y = 7.50 / 2 = 3.75, FV = 1000, PMT = 0. PV = -413.32
作者: prashantsahni 时间: 2012-3-31 13:42
What would an investor pay for a 25-year zero coupon bond if they required 11%? (Assume semi-annual compounding.)
N = 50, I/Y = 5.5, PMT = 0, FV = 1,000
CPT PV = 68.77
作者: prashantsahni 时间: 2012-3-31 13:42
A zero-coupon bond has a yield to maturity of 9.6% (annual basis) and a par value of $1,000. If the bond matures in 10 years, today's price of the bond would be:
I = 9.6; FV = 1,000; N = 10; PMT = 0; CPT → PV = 399.85
作者: prashantsahni 时间: 2012-3-31 13:42
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?
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.
作者: prashantsahni 时间: 2012-3-31 13:43
A 15-year, $1,000 face value zero-coupon bond is priced to yield a return of 8.00% compounded semi-annually. What is the price of the bond, and how much interest will the bond pay over its life, respectively?
Using an equation: Pricezerocoupon = Face Value × [ 1 / ( 1 + i/n)n × 2 ]
Here, Pricezerocoupon = 1000 × [ 1 / (1+ 0.080/2)15 × 2] = 1000 × 0.30832 = 308.32. So, interest = Face – Price = 1000 – 308.32 = 691.68.
Using the calculator: N = (15 × 2) = 30, I/Y = 8.00 / 2 = 4.00, FV = 1000, PMT = 0. PV = -308.32. Again, Face – Price = 1000 – 308.32 = 691.68.
作者: prashantsahni 时间: 2012-3-31 13:43
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?
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.
作者: prashantsahni 时间: 2012-3-31 13:43
What is the yield to maturity (YTM) of a 20-year, U.S. zero-coupon bond selling for $300?
N = 40; PV = 300; FV = 1,000; CPT → I = 3.055 × 2 = 6.11.
作者: prashantsahni 时间: 2012-3-31 13:44
If a 15-year, $1,000 U.S. zero-coupon bond is priced to yield 10%, what is its market price?
N = 30; I/Y = 5; PMT = 0; FV = 1,000; CPT → PV = 231.38.
作者: prashantsahni 时间: 2012-3-31 13:44
A 15-year zero coupon bond that has a par value of $1,000 and a required return of 8% would be priced at what value assuming annual compounding periods:
N = 15 FV = 1,000
I = 8
PMT = 0
PV = ?
PV = 315.24
作者: prashantsahni 时间: 2012-3-31 13:45
Janet Preen is considering buying a 10-year zero-coupon bond that has a $1,000 face value and is priced to yield 7.25% (semi-annual compounding). What price will Janet pay for the bond?
N = 10 × 2 = 20; I/Y = 7.25/2 = 3.625; PMT = 0; FV = 1,000; Compute PV = 490.58 or $1,000/(1.03625)20 = $490.58.
作者: prashantsahni 时间: 2012-3-31 13:45
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.
I = 12
PMT = 0
FV = 1,000
N = 20
PV = ?
PV = 103.67
作者: prashantsahni 时间: 2012-3-31 13:45
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?
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.
作者: prashantsahni 时间: 2012-3-31 13:45
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:
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.
作者: prashantsahni 时间: 2012-3-31 13:46
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:
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.
作者: prashantsahni 时间: 2012-3-31 13:47
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:
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.
作者: prashantsahni 时间: 2012-3-31 13:47
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:
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
作者: prashantsahni 时间: 2012-3-31 13:47
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?
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: prashantsahni 时间: 2012-3-31 13:48
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. |
|
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: prashantsahni 时间: 2012-3-31 13:48
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:
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.
作者: prashantsahni 时间: 2012-3-31 13:48
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?
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
作者: prashantsahni 时间: 2012-3-31 13:49
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:
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.
作者: prashantsahni 时间: 2012-3-31 13:49
The arbitrage-free bond valuation approach can best be described as the: A)
| use of a series of spot interest rates that reflect the current term structure. |
|
B)
| use of a single discount factor. |
|
C)
| geometric average of the spot interest rates. |
|
The use of multiple discount rates (i.e., a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in so doing, will eliminate any meaningful arbitrage opportunities. That is why the use of a series of spot rates to discount bond cash flows is considered to be an arbitrage-free valuation procedure.
作者: prashantsahni 时间: 2012-3-31 13:55
Which of the following statements concerning the arbitrage-free valuation of non-Treasury securities is CORRECT? The credit spread is: A)
| only a function of the bond's term to maturity. |
|
B)
| a function of default risk and the term to maturity. |
|
C)
| only a function of the bond's default risk. |
|
For valuing non-Treasury securities, a credit spread is added to each treasury spot yields. The credit spread is a function of default risk and the term to maturity.
作者: prashantsahni 时间: 2012-3-31 13:56
You are considering the purchase of a three-year annual coupon bond with a par value of $1,000 and a coupon rate of 5.5%. You have determined that the spot rate for year 1 is 5.2%, the spot rate for year two is 5.5%, and the spot rate for year three is 5.7%. What would you be willing to pay for the bond now?
You need the find the present value of each cash flow using the spot rate that coincides with each cash flow.
The present value of cash flow 1 is: FV = $55; PMT = 0; I/Y = 5.2%; N = 1; CPT → PV = -$52.28.
The present value of cash flow 2 is: FV = $55; PMT = 0; I/Y = 5.5%; N = 2; CPT → PV = –$49.42.
The present value of cash flow 3 is: FV = $1,055; PMT = 0; I/Y = 5.7%; N = 3; CPT → PV = –$893.36.
The most you pay for the bond is the sum of: $52.28 + $49.42 + $893.36 = $995.06.
作者: prashantsahni 时间: 2012-3-31 13:57
Which of the following packages of securities is equivalent to a three-year 8% coupon bond with semi-annual coupon payments and a par value of 100? A three-year zero-coupon bond: A)
| with a par of 100 and six zero-coupon bonds with a par value of 8 and maturities equal to the time to each coupon payment of the coupon bond. |
|
B)
| with a par value of 150 and six 8% coupon bonds with a maturity equal to the time to each coupon payment of the above bond. |
|
C)
| with a par of 100 and six zero-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond. |
|
This combination of zero-coupon bonds has exactly the same cash flows as the above coupon bond and therefore it is equivalent to it.
作者: prashantsahni 时间: 2012-3-31 13:57
Which of the following statements concerning arbitrage-free bond prices is NOT correct? A)
| It is not possible to strip coupons from U.S. Treasuries and resell them. |
|
B)
| Credit spreads are affected by time to maturity. |
|
C)
| The determination of spot rates is usually done using risk-free securities. |
|
It is possible to both strip coupons from U.S. Treasuries and resell them, as well as to aggregate stripped coupons and reconstitute them into U.S. Treasury coupon bonds. Therefore, arbitrage arguments ensure that U.S. Treasury securities sell at or very near their arbitrage free values. For valuing non-Treasury securities, a credit spread is added to each treasury spot yields. The credit spread is a function of default risk and the term to maturity.
作者: prashantsahni 时间: 2012-3-31 13:57
Current spot rates are as follows:1-Year: 6.5%
2-Year: 7.0%
3-Year: 9.2%
Which of the following is CORRECTA)
| For a 3-year annual pay coupon bond, all cash flows can be discounted at 9.2% to find the bond's arbitrage-free value. |
|
B)
| For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond's arbitrage-free value. |
|
C)
| The yield to maturity for 3-year annual pay coupon bond can be found by taking the geometric average of the 3 spot rates. |
|
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. Note that the yield to maturity is the bond’s internal rate of return that equates all cash flows to the bond’s price. Current spot rates have nothing to do with the bond’s yield to maturity.
作者: prashantsahni 时间: 2012-3-31 13:58
A 2-year option-free bond (par value of $10,000) has an annual coupon of 15%. An investor determines that the spot rate of year 1 is 16% and the year 2 spot rate is 17%. Using the arbitrage-free valuation approach, the bond price is closest to:
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 = [1,500/(1.16)] + [11,500/(1.17)2] = $9,694. 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=16.0, PMT=0, FV=1,500, CPT PV=1,293
N=2, I/Y=17.0, PMT=0, FV=11,500, CPT PV=8,401
Price = 1,293 + 8,401 = $9,694.
作者: prashantsahni 时间: 2012-3-31 13:58
Assume that there are no transaction costs and that securities are infinitely divisible. If an 8% coupon paying Treasury bond that has six months left to maturity trades at 97.54, and there is a Treasury bill with six months remaining to maturity that is correctly priced using a discount rate of 9%, is there an arbitrage opportunity? A)
| The coupon bond is not correctly priced but no arbitrage trade can be set up using the T-bill. |
|
B)
| Yes, the coupon bond price is too high. |
|
C)
| Yes, the coupon bond price is too low. |
|
The coupon bond has a cash flow at maturity of 104, which discounted at 9% results in a bond price of 99.52. Therefore, the bond is underpriced. An arbitrage trade can be set up by short-selling 1.04 units of the T-bill at 99.52 and then using the proceeds to buy 1.02 units of the coupon bond.
作者: mrcon 时间: 2018-3-19 18:09
thanks for sharing
不过R57这一节整个8页的习题质量都很一般 非常基础
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