FIN 301 – Porter
3/4/09
Information:
Fill in the following table reflecting which premiums are added to r* for the different types of debt.
Inflation
Maturity Risk
Default Risk
Liquidity
Premium
Premium
Premium
Premium
Short Term
X
Treasury
Long Term
X
X
Treasury
Short Term
X
X
X
Corporate
Long Term
X
X
X
X
Corporate
Equations:
r = r* + IP + MRP + DRP + LP
Problems:
1. The real risk-free rate of interest is 3 percent. Inflation is expected to be 2 percent this year and 4
percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on
3-year Treasury securities?
r = r* + IP + MRP
r = 3 + ((2+4+4)/3) + 0
r = 6.33%
2. The real risk-free rate is 2.5%. Inflation is expected to average 2.8% a year for the next 4 years, after
which time inflation is expected to average 3.75% a year. Assume that there is no maturity risk
premium. An 8-year corporate bond has a yield of 8.3%. Assume that the liquidity premium on the
corporate bond is 0.75%. What is the default risk premium on the corporate bond?
r = r* + IP + MRP + DRP + LP
8.3 = 2.5 + (((2.8 *4)+(3.75*4))/8) + 0 + .75 + DRP
DRP = 1.775%
3. The real risk free rate is 3%, and inflation is expected to be 3.5% for the next 2 years. A 2 year treasury
security yields 6.8%. What is the maturity risk premium for the 2 year security?
r = r* + IP + MRP
6.8 = 3 + 3.5 + MRP
MRP = .3
FIN 301 – Porter
3/4/09
4. The real risk free rate is 4%. Inflation is expected to be 3% this year, 4% next year, and then 2% for the
following 2 years. Assume that the maturity risk premium is 0. What is the yield on 2 year Treasury
securities? What about 4 year treasury securities?
r2 = r* + IP + MRP
r2 = 4 + ((3+4)/2) + 0
r2 = 7.5%
r4 = r* + IP + MRP
r4 = 4 + ((3+4+2+2)/4) + 0
r4 = 6.75%
5. You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5%. Your brother-in-law,
a broker at Safe and Sound Securities, has given you the following estimates of current interest rate
premiums:
Inflation premium= 3.25%
Liquidity premium= 0.6%
Maturity risk premium= 1.8%
Default risk premium= 2.15%
On the basis of these data, what is the real risk-free rate of return?
r = r* + IP
5.5 = r* + 3.25
r* = 2.25%
6. Using the information and risk free rate found in #5, what would the yield of a 30-day corporate bond
be?
r = r* + IP + DRP + LP
r = 2.25 + 3.25 + 2.15 + .6
r = 8.25%
7. 4-year corporate securities are currently yielding 5.8%. You know the following are the current interest
rate premiums. Calculate the inflation premium.
Liquidity premium= 1.2%
Maturity Risk premium= 0.75%
Default Risk premium= 1.35%
Risk Free Rate = 1.8%
r = r* + IP + MRP + DRP + LP
5.8 = 1.8 + .75 + 1.35 + 1.2 + IP
IP = .7%
FIN 301 – Porter
3/4/09
8. Interest rates on 4-year Treasury securities are currently 7%, while interest rates on 6-year Treasury
securities are currently 7.5%. If the pure expectations hypothesis is correct, what does the market
believe that 2-year securities will be yielding 4 years from now?
(1 + .075)6 = (1 + .07)4 * (1 + x)2
1.5433 = 1.3108 * (1 + x)2
Divide both sides by 1.3108
1.1774 = (1 + x)2
Take the square root of both sides to get ride of the 2
1.0851 = 1 + x
x = .0851 or 8.51%
9. Interest rates on 3-year treasury securities are currently 8%, while 6-year treasury securities are 8.5%.
If pure expectations hypothesis is correct, what does the market believe that 3-year securities will be
yielding 3 years from now?
(1 + .085)6 = (1 + .08)3 * (1 + x)3
1.6315 = 1.2597 * (1 + x)3
Divide both sides by 1.2597
1.2951 = 1 + x)3
Take both sides to the 1/3 power to get ride of the 3
1.09 = 1 + x
x = .09 or 9%
10. One-year Treasury securities yield 4.78%. The market anticipates that 1 year from now, 1-year
Treasury securities will yield 5.29%. If the pure expectation theory is correct, what should be the yield
today for 2-year Treasury securities?
(1 + x)2 = (1 + .0478) * (1 + .0529)
(1 + x)2 = 1.1032
Take the square root of both sides to get ride of the 2
1 + x = 1.0503
x = .0503 or 5.03%
11. 3-year treasury securities beginning two years from now are expected to yield 5.75%, whereas a 2-year
Treasury security is currently yielding 5%. A 2-year security is expected to yield 6.2% beginning 3 years
from now. What is the yield for a 3-year treasury security beginning today?
(1 + x)3 * (1 + .062)2 = (1 + .05)2 * (1 + .0575)3
(1 + x)3 * 1.1278 = 1.1025 * 1.1826
(1 + x)3 * 1.1278 = 1.3038
Divide both sides by 1.1278
(1 + x)3 = 1.1561
Take both sides to the 1/3 power to get ride of the 3
1 + x = 1.0495
FIN 301 – Porter
3/4/09
x = .0495 or 4.95%