Carl Forster, a trainee at an investment-banking
firm, is trying to get an idea of what real rate of return investors are
expecting in todayâ€™s marketplace. He has looked up the rate paid on 3-month
U.S. Treasury bills and found that it to be 5.5%. He has decided to use the
rate of change in the Consumer Price Index as a proxy for the inflationary
expectation of investors. That annualized rate now stands at 3%. On the basis
of the information that Carl has collected, what estimate can he make of the
real rate of return?
A firm wishing to evaluate interest rate
behavior has gathered yield data on five U.S. Treasure securities, each having
a different maturity and all measured at the same point in time. The summarized
U.S. Treasure security
Time to maturity
a. Draw the yield curve associated with
b. Describe the resulting yield curve in
part a, and explain the general expectations embodied in it.
A recent study of inflationary expectations has
revealed that the consensus among economic forecasters yields the following
average annual rates of inflation expected over the period noted. (Note: Assume
that the risk that future interest rate movements will affect longer maturities
more than shorter maturities is zero; that is, there is no maturity risk.)
Average annual rate of inflation
If the real rate of interest is currently 2.5%,
find the nominal rate of interest on each of the following U.S. Treasure
issues: 20-year bond, 3-month bill, 2-year note, and 5-year bond.
If the real rate of interest suddenly dropped to
2% without any change in inflationary expectation, what effect, if any, would
this have on your answers in part a? Explain.
Using your findings in parts a, draw a yield
curve for U.S. Treasury securities. Describe the general shape and expectation
reflected by the curve.
What would a follower of the liquidity
preference theory say about how the preferences of lender and borrowers tend to
affect the shape of the yield curve drawn in the part c? Illustrate that effect
by placing on your graph a dotted line that approximates the yield curve
without the effect of liquidity preference.
What would a follower of the market segmentation
theory say about the supply and demand for long-term loans versus the supply
and demand for short-term loans given the yield curve constructed for the part
c of this problem?
The real rate of interest is currently 3%; the
inflation expectation and risk premium for a number of securities follow.
a. Find the risk-free rate of interest, .png”>, that is applicable to each
b. Although not noted, what factor must be
the cause of the differing risk-free rates found in part a?
c. Find the nominal rate of interest for
Assume that the financial Management
Corporationâ€™s $1,000-par-value bond had a 5.700% coupon, matured on May 15,
2020, had a current price quote of 97.708, and had a yield to maturity (YTM) of
6.034%. Given this information, answer the following questions:
a. What was the dollar price of the bond?
b. What is the bondâ€™s current yield?
c. Is the bond selling at par, at a
discount, or at a premium? Why?
d. Compare the bondâ€™s current yield
calculated in part b to its YTM and explain why they differ.
Using the information provided in the following
table, find the value of each asset.
End of year
Appropriate required return
1 through ∞
1 through 5
Pecos Manufacturing has just issued a 15-year,
12% coupon interest rate, $1,000-par bond that pays interest annually. The
required return is currently 14%, and the company is certain it will remain at
14% until the bond matures in 15 years.
a. Assuming that the required return does
remain at 14% until maturity, find the value of the bond with (1) 15 years, (2)
12 years, (3) 9 years, (4) 6 years, (5) 3 years, and (6) 1 year to maturity.
b. Plot your findings on a set of â€œtime to
maturity (x axis) â€“ market value of bond (y axis)â€ axes constructed similarly
to Figure 6.5 on page 246.
c. All else remaining the same, when the
required return differs from the coupon interest rate and is assumed to be
constant to maturity, what happens to the bond value as time moves toward
maturity? Explain in light of the graph in part b.
The Salem Company bond currently sells for $955,
has a 12% coupon interest rate and a $1,000 par value, pays interest annually,
and has 15 years to maturity.
a. Calculate the yield of maturity (YTM) on
b. Explain the relationship that exists
between the coupon interest rate and yield to maturity and the par value and
market value of bond.