1) What is the price of an 7% bond with 10 years to maturity that is trading at a yield of 7%? Assume the face value is $1000 and coupon is paid semi-annually.(Keep your answer to 2 decimal places.)
2) What is the modified duration of an 7% bond with 8 years to maturity that is trading at a yield of 7%? Assume coupon is paid semi-annually.(Keep your answer to 2 decimal places.)
3) A debt of $37,000 is to be amortized over n=6 years at r =5% annual interest rate. What value of quarterly payments will achieve this? (Keep your answer to 2 decimal places.)
4) Suppose you have a debt of $48,000, and you budget $3,341 for semi-annual payment. Interest rate is 5%. How long (in years) will the debt be completely repaid? (keep 2 decimal places.)
5) An 6% coupon bond with 2 years to maturity has a yield of 5%. Assume that coupon is paid quarterly and face value is $1,000.
(a) Calculate the price of the bond. (Keep 2 decimal places)
(b) Calculate the duration of the bond. (Keep 4 decimal places)
(c) Calculate this bond's modified duration. (Keep 4 decimal places)
(d) Assume that the bond's yield to maturity increases from 5% to 5.2%, estimate the new price of the bond. (Keep 2 decimal places)
6) Assume that you have a liability with following four required payments:
$8,000 due in 1 year
$4,000 due in 2 years
$4,000 due in 3 years
$8,000 due in 4 years
At a r = 18% rate of interest,
(a) What is the present value of this liability? (No need to key-in the answer here.)
(b) What is the duration of this liability? (Keep your answer to 2 decimal places.)
7) A (yearly) cash flow stream is x = (-42, 19, 19, 19, 19, 19, 19). The spot rates (yearly in percentage) are s = (5.0, 5.3, 5.6, 5.8, 6.0, 6.1).
(a) Find the current discount factors dk.
(b) Use the discount factors to determine the (net) present value of the stream. (Keep your answer to 2 decimal places)
8) Starting from today, every month you save $500 into a bank account which earns interest at annual rate of 4%.
How much money do you have in the account at the end of 3 years? (Keep 2 decimal places.)
9) Consider the following spot rate curve:
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S1
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S2
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S3
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S4
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S5
|
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0.050
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0.055
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0.061
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0.065
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0.071
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(a) What is the forward interest rate that applies from period 3 to period 5? That is, what is the value of f3,5? Assume annual compounding. (Keep your answer to 4 decimal places.)
(b) If the market forward rate from period 3 to period 5 is not equal to the value derived in (a), how can you create an arbitrage opportunity?
10) Suppose that the 6-month US Treasury bill rate is equal to 5.89%, and the forward rate on a 6-month Treasury bill 6 months from now is 7.32%. (Both are in yearly terms).
What is the 1-year bill rate? (Keep 4 decimal places, e.g 0.1234)
11) Suppose ABC Corporation has an obligation to pay $10,000 and $40,000 at the end of 5 years and 7 years respectively. In order to meet this obligation, it plans to invest money by selecting from the following three bonds:
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Coupon Rate
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Maturity
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Yield
|
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Bond 1
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4%
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3 yr
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6%
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|
Bond 2
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5%
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6 yr
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6%
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Bond 3
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7%
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10 yr
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6%
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All bonds have the same face value $1000. Assume that the annual rate of interest to be used in all calculations is 7%. Consider semi-annual compounding. (Keep your answers to 2 decimal places.)
(a) Find the present value and duration of the obligation.
Obligation price:
Obligation duration:
(b) Find the price for each of these bonds.
Bond 1:
Bond 2:
Bond 3:
(c) Determine Macaulay durations D1, D2, and D3 of these three bonds, respectively. (Keep 2 decimal places.)
D1:
D2:
D3:
(d) Can the Corporation choose bonds 1 and 2 to construct its portfolio? Justify your answer.
(e) Suppose the Corporation decides to use bonds 2 and 3. Denote by V2 and V3 to be the amounts of money to be invested in the two bonds, respectively. To get an immunized portfolio, write down appropriate equations in V2 and V3 first, and solve for V2 and V3.
V2:
V3:
12) Consider the following three bonds:
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Bond
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Coupon Rate
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Maturity (years)
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Price
|
|
A
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0%
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1.0
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947.19
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B
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6%
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1.0
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1004.87
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C
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7%
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1.5
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1011.72
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Assume that coupons are paid every 6 months and the face values of all the bonds are $1,000.
(a) Determine the spot rate curve. (That is, determine s0.5, s1, and s1.5 in yearly terms.) (Keep 4 decimal places, e.g 0.1234)
(b) Suppose that the 0.5- and 1.5-year zero-coupon bonds are available. Determine their respective prices. (Keep 2 decimal places, e.g xxx.12)
(c) Determine the forward rate f 0.5,1 (in yearly term) on a 6-month Treasury bill 6 months from now. (Keep 4 decimal places, e.g 0.1234)
(d) Determine the forward rate f0.5,1.5 (in yearly term) on a 12-month Treasury bill 6 months from now. (Keep 4 decimal places) (Keep 4 decimal places, e.g 0.1234)
(e) Price the 1.5-year coupon bond 6 months from now. (Keep 2 decimal places, e.g xxx.12)?
13) Consider two 5-year bonds: one has a 6% coupon and sells for $96; the other has a 9% coupon and sells for $105. What is the price of a 5-year zero coupon bond? (Assume that coupons are paid annually, and the face values of all the bonds are $100.) (Keep your answer to 2 decimal places.)
14) Refer to the following table:
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Years to Maturity
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1-year
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2-year
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3-year
|
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Zero-Coupon Bonds
|
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Prices
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$93.02
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PZ2
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PZ3
|
|
Coupon Bonds
|
|
Coupon Rate
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7%
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8%
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9%
|
|
Prices
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PC1
|
$98.34
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$96.73
|
All bonds have the face value F = $100.00. For simplicity, assume that coupons are paid annually. Determine the prices PZ2, PZ3, and PC1, respectively. (Keep 2 decimal places, e.g 21.12)
15) Suppose you have $250,000 of loan. The terms of the loan are that the yearly interest is 6% compounded quarterly. You are to make equal quarterly payments of such magnitude as to repay this loan over 30 years. (Keep all your answers to 2 decimal places)?
(a) How much are the quarterly payments?
(b) After 5 years' payments, what principal remains to be paid?
(c) How much interest is paid in the first quarter of the 6th year?
(d) How much is the total interest paid over the 30 years?
(e) If you have a lump sum payment of $20,000 at the end of 5 years, and maintain the same level of quarterly payment, when will you pay off your loan, i.e. how many years in total will you pay off the loan?