Solution to Homework Problems for Chapter 6

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SOLUTION TO HOMEWORK PROBLEMS FOR CHAPTER 6

1.  Given the following information that the real, risk-free rate of return is 2% and annual inflation expected next year is 3%, what should be the interest rate on a 1-year U.S. T-Bill?

U.S. T-Bill DRP=0, LP=0 , MRP= 0 rRF = 2+3=5%

2.  a. Average annual inflation premium (IP) for 1 year = 4%

b. Average annual inflation premium (IP) for 2 years = (4+4.25)/2=4.125%

c. Average annual inflation premium (IP) for 3 year = [4+(2*4.25)]/3=4.1667%

d. Average annual inflation premium (IP) for 4 years =[4+(3*4.25)]/4=4.1875%

e Average annual inflation premium (IP) for 5 years =[4+(4*4.25)]/5=4.2000%

f. Average annual inflation premium (IP) for 7 years =[4+(4*4.25)+(2*4.5)]/7=4.2857%

g. Average annual inflation premium (IP) for 10 years ==[4+(4*4.25)+(5*4.5)]/10=4.3500%

3.  MRP = 0.1 *(t-1)%, where t=# of years to maturity

a.  0.1*(1-1)=0%

b.  0.1(2-1)=0.1%

c.  0.1*(8-1)=0.7%

d.  0.1*(15-1)=1.4%

e.  0.1*(20-1)=1.9%

f.  0.1*(30-1)=2.9%

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4.  You are given the following information about interest rates and risk-premiums:

The real, risk-free rate of return is 2.5%. The average annual inflation expected over the next 10, 20 and 30 years are, respectively, 3.5%, 4.5% and 5% The Default Risk Premium for AA+ rated corporate bonds is 1.5% The Liquidity Premium for AA+ rated corporate bonds is 1% Maturity Risk Premium is found from

MRPt = 0.1 * (t-1)%, where t=# of years to maturity

Remember that U.S. Treasury securities have no default or liquidity risk.

What should be the interest rate on :

a.  10-year U.S. Treasury bond? DRP =0; LP=0 r=2.5+3.5+0.9= 6.9%

b.  20-year U.S. Treasury bond? DRP =0; LP=0 r=2.5+4.5+1.9=8.9%

c.  30-year U.S. Treasury bond? DRP =0; LP=0 r=2.5+5.0+2.9=10.4%

d.  10-year corporate bond? DRP =1.5%; LP=1%

r= 2.5+3.5+1.5+1+0.9=9.4%

e.  20-year corporate bond? DRP =1.5%; LP=1%

r= 2.5+4.5+1.5+1+1.9=11.4%

f.  30-year corporate bond? DRP =1.5%; LP=1%

r= 2.5+5.0+1.5+1+2.9=12.9%