SOLUTIONS TO END-OF-CHAPTER PROBLEMS
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4-1 k* = 3%; I 1 = 2%; I 2 = 4%; I 3 = 4%; MRP = 0; k T-2 = ?; k T-3 = ? k = k* + IP + DRP + LP + MRP. Since these are Treasury securities, DRP = LP = 0. k T-2 = k* + IP 2. IP 2 = (2% + 4%)/2 = 3%. k T-2 = 3% + 3% = 6%. k T-3 = k* + IP 3. IP 3 = (2% + 4% + 4%)/3 = 3.33%. k T-3 = 3% + 3.33% = 6.33%. 4-2 k T-10 = 6%; k C-10 = 8%; LP = 0.5%; DRP = ? k = k* + IP + DRP + LP + MRP. k T-10 = 6% = k* + IP + MRP; DRP = LP = 0. k C-10 = 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 C-10 = 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* + IP + MRP = 6%; therefore, k C-10 = 8% = 6% + 0.5% + DRP 1.5% = DRP. 4-4 k* = 3%; IP = 3%; k T-2 = 6.2%; MRP 2 = ? k T-2 = k* + IP + MRP = 6.2% k T-2 = 3% + 3% + MRP = 6.2% MRP = 0.2%.
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%. 4-14 a. Real Years to Risk-Free Maturity Rate (k*) IP** MRP k T = k* + IP + MRP 1 2% 7.00% 0.2% 9.20% 2 2 6.00 0.4 8.40 3 2 5.00 0.6 7.60 4 2 4.50 0.8 7.30 5 2 4.20 1.0 7.20 10 2 3.60 1.0 6.60 20 2 3.30 1.0 6.30 **The computation of the inflation premium is as follows:
Expected Average Year Inflation Expected Inflation 1 7% 7.00% 2 5 6.00 3 3 5.00 4 3 4.50 5 3 4.20 10 3 3.60 20 3 3.30 For example, the calculation for 3 years is as follows: Thus, the yield curve would be as follows: b. The interest rate on the Exxon bonds has the same components as the Treasury securities, except that the Exxon bonds have default risk, so a default risk premium must be included. Therefore, k Exxon = k* + IP + MRP + DRP.
For a strong company such as Exxon, the default risk premium is virtually zero for short-term bonds. However, as time to maturity increases, the probability of default, although still small, is sufficient to warrant a default premium. Thus, the yield risk curve for the Exxon bonds will rise above the yield curve for the Treasury securities. In the graph, the default risk premium was assumed to be 1.0 percentage point on the 20-year Exxon bonds. The return should equal 6.3% + 1% = 7.3%.
c. EXELON bonds would have significantly more default risk than either Treasury securities or Exxon bonds, and the risk of default would increase over time due to possible financial deterioration. In this example, the default risk premium was assumed to be 1.0 percentage point on the 1-year EXELON bonds and 2.0 percentage points on the
20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.
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