A $5,000 6% three-year bond has semiannual coupons and redemption amount $5,265. It is purchased to provide the investor with a 4% annual effective yield. Find the Macaulay convexity C(4%, \infty) and compute the modified convexity C(4%, 2).
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- If you have a coupon bond, its face value is $1,000 and the coupon rate is 4%. Complete the following table, then calculate the rate of return for the bond. If you know that it was purchased at the nominal value, comment on the results. due date return at maturity the price 2 0.02 3 0.04 5 0.06 Present Value Annuity value % n value % n 0.961 0.02 2 1.97 0.02 2 0.925 0.04 2 1.89 0.04 2 0.889 0.04 3 2.78 0.04 3 0.906 0.02 5 4.71 0.02 5 0.747 0.06 5 4.21 0.06 5. A 7,000, 5% bond with annual coupons, redeemable at 108 at the end of 5 years is pricedto yield 4%, m=1. Construct a table showing the amortization of premium. (Amortization ofPremium)A $1000 bond with coupons at j2 = 8% is purchased to yield j2 = 7%. The write down in the first period after purchase is $4.01. What is the purchase price of the bond?
- A 7,000, 5% bond with annual coupons, redeemable at 108 at the end of 5 years is priced to yield 4%, m=1. Construct a table showing the amortization of premium. (Amortization of Premium)Solve each of the following questions using both pricing formulas and Excel. 4. A bond with a face value of $1,000 pays a 10% (APR) semiannual coupon and matures in 10 years. Similar bonds trade at a YTM of 8% (APR). What is the price of the bond?For example, assume Sophia wants to earn a return of 7.00% and is offered the opportunity to purchase a $1,000 par value bond that pays a 7.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond’s intrinsic value: Intrinsic ValueIntrinsic Value = = A(1+C)1+A(1+C)2+A(1+C)3+A(1+C)4+A(1+C)5+A(1+C)6+B(1+C)6A1+C1+A1+C2+A1+C3+A1+C4+A1+C5+A1+C6+B1+C6 Complete the following table by identifying the appropriate corresponding variables used in the equation. Unknown Variable Name Variable Value A Bond’s semiannual coupon payment B Bond’s par value $1,000 C Semiannual required return Now, consider the situation in which Sophia wants to earn a return of 5.00%, but the bond being considered for purchase offers a coupon rate of 7.00%. Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the bond’s…
- Compute the Macaulay duration under the following conditions: a. A bond with a four-year term to maturity, a 10% coupon (annual payments), and a market yield of 8%. Do not round intermediate calculations. Round your answer to two decimal places. Assume $1,000 par value. _________ years b. A bond with a four-year term to maturity, a 10% coupon (annual payments), and a market yield of 12%. Do not round intermediate calculations. Round your answer to two decimal places. Assume $1,000 par value. _________ years c. Compare your answers to Parts a and b, and discuss the implications of this for classical immunization. As a market yield increases, the Macaulay duration -(Select:declines/increases) . If the duration of the portfolio from Part a is equal to the desired investment horizon the portfolio from Part b is -(Select: no longer/still) perfectly immunized. Only typed answerGiven the following spot rates, calculate the value of a 3-year, 6% annual-coupon bond. Spot rates: 1-year: 5% 2-year: 5% 3-year: 6% A. $1,001.56 B. $1,044.73 C. $1,094.56 D. $1,114.29 Clear my choice2) You have a liability of 1,000 at the end of year 1 and another liability of L at the end of year 2. You create a portfolio of assets that exactly match your liabilities using the following available bonds with annual coupons: Term of bond Coupon Rate Yield Rate 3% 6% 1-year 2-year 5% 8% Find L if you invested 932 to purchase the 1-year bond.
- You have a bond with the following features: - Semi-annual coupon payments. - Coupon rate 7.60%. - Face value $1,000. - 3.5 years to maturity. - Current market price $1,130. Requirements (A, B, and C are independent): 1. Calculate the duration and modified duration for this bond. Duration ___ Mduration ___ 2. Now, let’s assume the modified duration of this bond is 3 years. If the yield increases by 30 bps (basis points), what will the new price of the bond using modified duration? 3. If the yield drops by 75 bps, what is the actual new price of the bond?A bond pays 10% semi-annual coupons with a face and redemption value of 1000. The bond can be redeemed on an coupon date between 12 and 15 years (inclusive) from the issue date. 1. Find the price payed at issue if investment has a minimum annual effective yield of 8%. Use P = Fr an i + Cv^n Show workConsider a 10-year bond with a face value of $1,000 that has a coupon rate of 5.5%, with semiannual payments. a. What is the coupon payment for this bond? b. Draw the cash flows for the bond on a timeline