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1. A particular securitys equilibrium rate of return is 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. The securitys liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the securitys default risk premium. (1.65%)

2. A 2-year Treasury security currently earns 1.94 percent. Over the next two years, the real risk-free rate is expected to be 1.00 percent per year and the inflation premium is expected to be 0.50 percent per year. Calculate the maturity risk premium on the 2-year Treasury security. (0.44%)

3. Tom and Sues Flowers, Inc.s 15-year bonds are currently yielding a return of 8.25 percent. The expected inflation premium is 2.25 percent annually and the real risk-free rate is expected to be 3.50 percent annually over the next 15 years. The default risk premium on Tom and Sues Flowerss bonds is 0.80 percent. The maturity risk premium is 0.75 percent on five-year securities and increases by 0.04 percent for each additional year to maturity. Calculate the liquidity risk premium on Tom and Sues Flowers, Inc.s 15-year bonds. (0.55%)

4. Nikki Gs Corporations 10-year bonds are currently yielding a return of 6.05 percent. The expected inflation premium is 1.00 percent annually and the real risk-free rate is expected to be 2.10 percent annually over the next 10 years. The liquidity risk premium on Nikki Gs bonds is 0.25 percent. The maturity risk premium is 0.10 percent on 2-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the default risk premium on Nikki Gs 10-year bonds. (2.20%)

5. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

1R1 = 6%, E(2r1) = 7%, E(3r1) = 7.5%, E(4r1) = 7.85%

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve. (₁R₁ = 6%

₁R₂ = [(1 + 0.06)(1 + 0.07)]^1/2 - 1 = 6.499%

₁R₃ = [(1 + 0.06)(1 + 0.07)(1 + 0.075)]^1/3 - 1 = 6.832%

₁R₄ = [(1 + 0.06)(1 + 0.07)(1 + 0.075)(1 + 0.0785)]^1/4 - 1 = 7.085%)

6. Suppose we observe the three-year Treasury security rate (1R3) to be 12 percent, the expected one-year rate next year E (2r1)to be 8 percent, and the expected one-year rate the following year E (3r1)to be 10 percent. If the unbiased expectations theory of the term structure of interest rates

holds, what is the one-year Treasury security rate? (₁R₁ = 0.1826 = 18.26%)

7. The Wall Street Journal reports that the rate on four-year Treasury securities is 5.60 percent and the rate on five-year Treasury securities is 6.15 percent. According to the unbiased expectations theory, what does the market expect the one-year Treasury rate to be four years from today, E (5r1)? (E(₅r₁) = 8.379%)

8. Based on economists forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:

1R1 = 5.65%

E (2r1) = 6.75% L 2 = 0.05%

E (3r1) = 6.85% L 3 = 0.10%

E (4r1) = 7.15% L 4 = 0.12%

Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (₁R₁ = 5.65%

₁R₂ = [(1 + 0.0565)(1 + 0.0675 + 0.0005)]^1/2 - 1 = 6.223%

₁R₃ = [(1 + 0.0565)(1 + 0.0675 + 0.0005)(1 + 0.0685 + 0.0010)]^1/3 - 1 = 6.465%

₁R₄ = [(1 + 0.0565)(1 + 0.0675 + 0.0005)(1 + 0.0685 + 0.0010)(1 + 0.0715 + 0.0012)]^1/4 - 1 = 6.666%)

9. Suppose we observe the following rates: 1R1 = 10%, 1R2 = 14%, and E (2r1) = 18%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? (L₂ = 0.00145 = 0.145%)

If you note the following yield curve in The Wall Street Journal, what is the one-year forward rate for the period beginning one year from today, 2f1 according to the unbiased expectations theory? (7.51%)

Maturity Yield

One day 2.00%

One year 5.50

Two years 6.50

Three years 9.00

10. On March 11, 20XX, the existing or current (spot) one-year, two-year, three-year, and four-year zero-coupon Treasury security rates were as follows:

1R1 = 4.75%, 1R2 = 4.95%, 1R3 = 5.25%, 1R4 = 5.65%

Using the unbiased expectations theory, calculate the one year forward rates on zero-coupon Treasury bonds for years two, three, and four as of March 11, 20XX.

(₂f₁ = [(1 + ₁R₂)²/(1 + ₁R₁)] 1 = [(1 + 0.0495)²/(1 + 0.0475)] 1 = 5.15%

₃f₁ = [(1 + ₁R₃)³/(1 + ₁R₂)²] 1 = [(1 + 0.0525)³/(1 + 0.0495)²] 1 = 5.85%

₄f₁ = [(1 + ₁R₄)⁴/(1 + ₁R₃)³] 1 = [(1 + 0.0565)⁴/(1 + 0.0525)³] 1 = 6.86%)

11. Assume the current interest rate on a one-year Treasury bond (1R1) is 4.50 percent, the current rate on a two-year Treasury bond (1R2) is 5.25 percent, and the current rate on a three-year Treasury bond (1R3) is 6.50 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year interest rate expected on Treasury bills during year 3 (E(3r1) or 3f1)? (₁R₁ = 4.5%

₁R₂ = 5.25% = [(1 + 0.045)(1 + ₂f₁)]^1/2 - 1 => ₂f₁ = 6.01%

₁R₃ = 6.50% = [(1 + 0.045)(1 + 0.0601)(1 + ₃f₁)]^1/3 - 1 => ₃f₁ = 9.04%)

12. Calculate the future value of the following annuity streams:

a. $5,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.

b. $5,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.

c. $5,000 received each year for 5 years on the first day of each year if your investments pay 6 percent compounded annually.

d. $5,000 received each quarter for 5 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.

(a. FV = $5,000{[(1 + 0.06)⁵ -1]/0.06} = $5,000 (5.637092) = $28,185.46

b. FV = $5,000{[(1 + 0.015)²⁰ -1]/0.015} = $5,000 (23.123667) = $115,618.34

c. FV = $5,000{[(1 + 0.06)⁵ -1]/0.06}(1 + 0.06) = $5,000 (5.637092)(1 + .06) = $29,876.59

d. FV = $5,000{[(1 + 0.015)²⁰ -1]/0.015}(1 + 0.015) = $5,000 (23.123667)(1.015) = $117,352.61)