a. Calculate the leverage-adjusted duration gap of an FI that has assets of $2.3 million invested in 30-year, 9 percent semiannual coupon Treasury bonds selling at par and whose duration has been estimated at 10.07 years. It has liabilities of $1,030,000 financed through a two-year, 6.00 percent semiannual coupon note selling at par with a duration of 1.9143. b. What is the impact on equity values if all interest rates fall 10 basis points-that is, AR/(1+R/2) = -0.0010?

a. Calculate the leverage-adjusted duration gap of an FI that has assets of $2.3 million invested in 30-year, 9 percent semiannual coupon Treasury bonds selling at par and whose duration has been estimated at 10.07 years. It has liabilities of $1,030,000 financed through a two-year, 6.00 percent semiannual coupon note selling at par with a duration of 1.9143. b. What is the impact on equity values if all interest rates fall 10 basis points-that is, AR/(1+R/2) = -0.0010?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Assume the first-year, second-year, third-year, and fourth-year hazard rates are 1.5%, 2%, 2.5%, and 3%, respectively. Compute the expected loss on a 4-year $100 par value 6% coupon rate payable annually bond. Please use a recovery rate of 40%.
Assume you have the following asset and liability in your Balance Sheet:Asset - Bond AModified Duration = 2.6 yearsValue= RM1.5 millionLiability - Bond BModified Duration = 3.1 yearsValue= RM1.0 million duration gap is 0.53 years, net worth reduce by 8000. What should or could you to achieve immunized balance sheet?
FIXY has assets of $2 million invested in a 25-year, 6 percent annual coupon Treasury bond selling at par. The assets are financed with equity and a $ 1700000, 4-year, 3 percent annual coupon capital note selling at par. What is the leverage adjusted duration gap of FIXY? What is the impact on equity value if the relative change in all market interest rates is AR/(1+R /2)=0.003?
A firm has liabilities of $98 in one year, $100 in two years, and $107 in three years. The firm exactly matches its liabilities by purchasing the following zero or annual coupon bonds redeemable at par: Bond Maturity Par Value Coupon Rate Effective Yield A 1 year 100 5% 3% B 2 years 100 0% 4% C 3 years 100 4% 5% Find the number of units of Bond A that must be purchased to match the liabilities exactly. (A) 0.894 (B) 0.897 (C) 0.913 (D) 0.933 (E) 0.959
(c) Re-calculate the prices of the bonds if the required return falls to 9%.(d) Explain how underwriters use the overallotment option in IPOs.
Suppose your firm issues a €100,000,000 5-year bond with a coupon rate of 8% per annum (assume annual compounding). The bond will sell at face value to investors. The underwriting spread is an up-front fee of 2%. What is the actual cost of this debt? Please enter your answer as % -- e.g. if your answer is 2.34% type in 2.34.
i. Calculate the value of Macaulay’s duration for a 10-year, $1000 par value bond purchased today at a yield to maturity of 14% and a coupon rate of 10%. ii. From the answer in (i) calculate the modified duration of the bond assuming the prevailing interest rate is still 14%.iii. Now suppose the market interest rate on comparable bonds falls to 13 percent. What will be the approximate percentage change in the bond price.? (Hint: use the modified duration for your computation in (ii))
29. Which of the following has the greatest interest rate (price) risk?a. A 10-year, $1,000 face value, 10 percent coupon bond with semiannualinterest payments.b. A 10-year, $1,000 face value, 10 percent coupon bond with annualinterest payments.c. A 10-year, $1,000 face value, zero coupon bond.d. A 10-year $100 annuity.e. All of the above have the same price risk since they all mature in 10years.
A firm's bonds have a maturity of 12 years with a $1,000 face value, have an 11% semiannual coupon, are callable in 6 years at $1,209.43, and currently sell at a price of $1,365.89. What are their nominal yield to maturity and their nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places. YTM: % YTC: % What return should investors expect to earn on these bonds? I. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM. II. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM. III. Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC. IV. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.
A firm's bonds have a maturity of 12 years with a $1,000 face value, have an 11% semiannual coupon, are callable in 6 years at $1,211.14, and currently sell at a price of $1,370.78. What are their nominal yield to maturity and their nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places. YTM: % YTC: % What return should investors expect to earn on these bonds? Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.
A firm's bonds have a maturity of 8 years with a $1,000 face value, have an 8% semlannual coupon, are callable in 4 years at $1,048.54, and currently sell at a price of $1,094.91. What are their nominal yield to maturity and their nominal yield to call? Do not round Intermediate calculations. Round your answers to two decimal places. YTM: YTC: What return should investors expect to earn on these bonds? I. Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC. II. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC. III. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM. IV. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM. -Select-

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