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Two 1000 bonds redeemable at par at the end of the same period are bought to yield 4% convert- ible semiannually. One bond costs $1,136.78, and has a coupon rate of 5% payable semiannually. The other bond has a coupon rate of 2.5% payable semiannually. Find the price of the second bond. Hint: Write two bond price equations (use the basic formula) and from the first equation

Two 1000 bonds redeemable at par at the end of the same period are bought to yield 4% convert- ible semiannually. One bond costs $1,136.78, and has a coupon rate of 5% payable semiannually. The other bond has a coupon rate of 2.5% payable semiannually. Find the price of the second bond. Hint: Write two bond price equations (use the basic formula) and from the first equation

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two 1000 bonds redeemable at par at the end of the same period are bought to yield 4% convert- ible semiannually. One bond costs $1,136.78, and has a coupon rate of 5% payable semiannually. The other bond has a coupon rate of 2.5% payable semiannually. Find the price of the second bond. Hint: Write two bond price equations (use the basic formula) and from the first equation solve for u. Use this to solve for the price P in the second equation. (d) A is priced at 1,158.47 to yield an annual nominal rate of 6% compounded semiannually. Calculate the re- demption value of the bond. Hint: Multiply the basic formula by (1 + i)". II. Bond Amortization (a) Find the (negative) amortization of discount in period 4 for the bond in problem I.(a). (b) A 10,000 par value 10-year bond with 8% annual coupons is bought at a premium to yield an annual effective rate of 6%. Calculate the interest portion of the 7th coupon. (c) A 10,000 par value 5 year bond with 8% semiannual coupons was bought to yield 7.5% convertible semiannually. Determine the amount of premium amortized in the sixth coupon payment. (d) A P 100,000 par value two-year 8% bond with semiannual coupons is bought to yield 10% con- vertible semiannually. (i) Create an amortization schedule for this transaction. (ii) Find the book values of the bond using the straight line method. Hint: In this method, the book values are linear, grading from Bo = P to Bn = C. The principal adjustment on each time period t is constant, P₁ = PC for t = 1, 2, ..., n. Therefore, B₁ = Bt-1 – Pt. n (e) Do the previous problem assuming it was bought at a yield rate III. Book Value between Two Coupon Dates (a) A 10 year bond with semi-annual coupons has a book value immediately after the 5th coupon of 90,000. The flat price 5 months later using the theoretical method is 94,591. Calculate the semi-annual yield on the bond. Hint: You are being asked for the yield rate i; k = 5/6. (b) A 10 year bond with a par value of 100,000 and semi-annual coupons 2,500 is bought at a discount to yield 6% convertible semi-annually. (i) Calculate the book value immediately after the 5th coupon. (ii) Using the theoretical method, calculate the flat price, accrued coupon and market price 4 months after the 5th coupon.
Transcribed Image Text:Two 1000 bonds redeemable at par at the end of the same period are bought to yield 4% convert- ible semiannually. One bond costs $1,136.78, and has a coupon rate of 5% payable semiannually. The other bond has a coupon rate of 2.5% payable semiannually. Find the price of the second bond. Hint: Write two bond price equations (use the basic formula) and from the first equation solve for u. Use this to solve for the price P in the second equation. (d) A is priced at 1,158.47 to yield an annual nominal rate of 6% compounded semiannually. Calculate the re- demption value of the bond. Hint: Multiply the basic formula by (1 + i)". II. Bond Amortization (a) Find the (negative) amortization of discount in period 4 for the bond in problem I.(a). (b) A 10,000 par value 10-year bond with 8% annual coupons is bought at a premium to yield an annual effective rate of 6%. Calculate the interest portion of the 7th coupon. (c) A 10,000 par value 5 year bond with 8% semiannual coupons was bought to yield 7.5% convertible semiannually. Determine the amount of premium amortized in the sixth coupon payment. (d) A P 100,000 par value two-year 8% bond with semiannual coupons is bought to yield 10% con- vertible semiannually. (i) Create an amortization schedule for this transaction. (ii) Find the book values of the bond using the straight line method. Hint: In this method, the book values are linear, grading from Bo = P to Bn = C. The principal adjustment on each time period t is constant, P₁ = PC for t = 1, 2, ..., n. Therefore, B₁ = Bt-1 – Pt. n (e) Do the previous problem assuming it was bought at a yield rate III. Book Value between Two Coupon Dates (a) A 10 year bond with semi-annual coupons has a book value immediately after the 5th coupon of 90,000. The flat price 5 months later using the theoretical method is 94,591. Calculate the semi-annual yield on the bond. Hint: You are being asked for the yield rate i; k = 5/6. (b) A 10 year bond with a par value of 100,000 and semi-annual coupons 2,500 is bought at a discount to yield 6% convertible semi-annually. (i) Calculate the book value immediately after the 5th coupon. (ii) Using the theoretical method, calculate the flat price, accrued coupon and market price 4 months after the 5th coupon.
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