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# chap 4 - Chapter 4 The Financial Environment Markets...

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Answers and Solutions: 4 - 1 Chapter 4 The Financial Environment: Markets, Institutions, and Interest Rates

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4-1 k* = 3%; I 1 = 2%; I 2 = 4%; I 3 = 4%; MRP = 0; k T2 = ?; k T3 = ? k = k* + IP + DRP + LP + MRP. Since these are Treasury securities, DRP = LP = 0. k T2 = k* + IP 2 . IP 2 = (2% + 4%)/2 = 3%. k T2 = 3% + 3% = 6%. k T3 = k* + IP 3 . IP 3 = (2% + 4% + 4%)/3 = 3.33%. k T3 = 3% + 3.33% = 6.33%. 4-2 k T10 = 6%; k C10 = 8%; LP = 0.5%; DRP = ? k = k* + IP + DRP + LP + MRP. k T10 = 6% = k* + IP + MRP; DRP = LP = 0. k C10 = 8% = k* + IP + DRP + 0.5% + MRP. Because both bonds are 10-year bonds the inflation premium and maturity risk premium on both bonds are equal. The only difference between them is the liquidity and default risk premiums. k C10 = 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* + IP + MRP = 6%; therefore, k C10 = 8% = 6% + 0.5% + DRP 1.5% = DRP. 4-3 k T1 = 5%; 1 k T1 = 6%; k T2 = ? k T2 = 2 6% + 5% = 5.5%. 4-4 k* = 3%; IP = 3%; k T2 = 6.2%; MRP 2 = ? k T2 = k* + IP + MRP = 6.2% k T2 = 3% + 3% + MRP = 6.2% MRP = 0.2%. Answers and Solutions: 4 - 2 SOLUTIONS TO END-OF-CHAPTER PROBLEMS
4-5 Let x equal the yield on 2-year securities 4 years from now: 7.5% = [(4)(7%) + 2x]/6 0.45 = 0.28 + 2x x = 0.085 or 8.5%. 4-6 k = k* + IP + MRP + DRP + LP. k* = 0.03. IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035. MRP = 0.0005(6) = 0.003. DRP = 0. LP = 0. k T7 = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%. 4-7 a. k 1 = 3%, and k 2 = 2 k + 3% 1 1 = 4.5%, Solving for k 1 in Year 2, 1 k 1 , we obtain 1 k 1 = (4.5% × 2) - 3% = 6%. b. For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is k n = k* + average inflation over n years. If k* = 1%, we can solve for IP n : Year 1: k 1 = 1% + I 1 = 3%; I 1 = expected inflation = 3% - 1% = 2%. Year 2: k 1 = 1% + I 2 = 6%; I 2 = expected inflation = 6% - 1% = 5%. Note also that the average inflation rate is (2% + 5%)/2 = 3.5%, which, when added to k* = 1%, produces the yield on a 2-year bond, 4.5 percent. Therefore, all of our results are consistent. Alternative solution: Solve for the inflation rates in Year 1 and Year 2 first: k RF = k* + IP.

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