Financial environment interest rate

An Assignment of Business Finance
Course Code: FIN -2101

Submitted To:
Md. Monzur Morshed Bhuiya
Associate Professor
Department of Finance
Jagannath University, Dhaka.

Submitted By:
Md. Mazharul Islam.
Group Representative of Finance Interface
B.B.A, 3rd Batch (2nd Year, 1st Semester)
Session: 2008-2009
Department of Finance
Jagannath University, Dhaka.

Date of Submission: 25-10-2010

Department of Finance Jagannath University 1|Page

1
Sl. No. Name Roll No.
01. Md. Mazharul Islam. (Group Representative) 091541
02. Khadizatuz Zohara. 091526


Table of Contents

Sl. No. Contents Page No.
Problems
2-1 Yield Curves 5
2-2 Yield Curves 6
2-3 Inflation and Interest Rate 7
2-4 Rate of Interest 9
2-5 Real Risk-Free Rate, MRP and DRP 10
Exam-Type Problems
2-6 Expected Inflation Rate 12
2-7 Expected Rate of Interest 13
2-9 Interest Rate 14
2-10 Interest Rate 15
Ending Part
Formula and Necessary Illustration for Calculation 17
Summary of the Assignment 18


The Financial Environment: Interest Rates

Problems 2-1:

Suppose you and most other investors expect the rate of inflation to be 7 percent next year, to fall to 5
percent during the following year, and then to remain at a rate of 3 percent thereafter. Assume that the real
risk-free rate, k*, is 2 percent and that maturity risk premium on treasury securities rise from zero on very
short-term bonds ( those that mature in few days) by 0.2 percentage points for each year to maturity, up to
a limit of 1.0 percentage point on five year or longer-term T-bonds.

a. Calculate the interest rate on one, two, three, four, five, 10 and 20 year Treasury securities, and Plot
the yield curve.
b. Now suppose IBM, a highly rated company, had bonds with the same- maturities as the Treasury
bonds. As an approximation, plot a yield curve for IBM on the same graph with the Treasury bond
yield curve, (Hint: Think about the default risk premium on IBM’s long-term versus its short-term
bonds.)
c. Now plot the approximate yield curve of Long Island Lighting Company (LILCO), a risky nuclear
utility.

Solution 2-1:

Requirement ‘a’:

Expected Average
Real Average Expected Inflation
Annual Nominal
Bond Type Risk-free Rate or Inflation Premium
Inflation Interest Rate
Rate (k*) (IP)
Rate 𝑘 𝑅𝐹 = k* + IP
1st year bond 7% 2% 𝐼𝑃1 = 7% 1 =7% 9%
2nd year bond 5% 2% 𝐼𝑃2 = (7%+5%) ∕2 = 6% 8%
3rd year bond 3% 2% 𝐼𝑃3 = (12%+3%) ∕3 = 5% 7%
4th year bond 3% 2% 𝐼𝑃4 = (15%+3%) ∕4 =4.5% 6.5%
5th year bond 3% 2% 𝐼𝑃5 =(18%+3%) ∕5 = 4.2% 6.2%
10th year bond 3% 2% 𝐼𝑃10 =(21%+3%×5) ∕10=3.6% 5.6%
20th year bond 3% 2% 𝐼𝑃20 =(36%+3%×10) ∕20=3.3% 5.3%

Bond Type Maturity Risk Premium (MRP)
1st year bond 0.2%
2nd year bond 0.2%+0.2% =0.4%
3rd year bond 0.4%+0.2% =0.6%
4th year bond 0.6%+0.2% =0.8%
5th year bond 0.8%+0.2% =1.0%
10th year bond 1.0%
20th year bond 1.0%


And

Bond Type 𝑘 𝑅𝐹 + 𝑀𝑅𝑃 Interest Rate (k)
1st year bond 9% + 0.2% 9.2%
2nd year bond 8% + 0.4% 8.4%
3rd year bond 7% + 0.6% 7.6%
4th year bond 6.5% + 0.8% 7.3%
5th year bond 6.2% + 1.0% 7.2%
10th year bond 5.6% + 1.0% 6.6%
20th year bond 5.3% + 1.0% 6.3%

The yield Curve:

10.5
Yield Curve
10.0

9.5

9.0

8.5
Yield (%)

8.0
LILCO
7.5
IBM
7.0

6.5
T - Bonds - Bonds
T
6.0

5.5

5.0
0 2 4 6 8 10 12 14 16 18 20
Yield of Maturity

Requirement ‘b’:

The interest rate on the IBM bonds has the same components as the Treasury securities, except that the
IBM bonds have default risk, so a default risk premium must be included. Therefore,

𝐾 𝐼𝐵𝑀 = 𝑘* + IP + MRP + DRP

For a strong company such as IBM, 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 IBM bonds will rise above the yield curve for
the Treasury securities. In the graph, the default risk premium was assumed to be 1.2 percentage points on
the 20-year IBM bonds. The return should equal 6.3% + 1.2% = 7.5%.


Requirement ‘c’:

Long Island Lighting Company (LILCO) bonds would have significantly more default risk than either
Treasury securities or IBM 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 one-year LILCO bonds and 2.0 percentage points on the 20-year bonds. The 20-year return should
equal 6.3% + 2% = 8.3%.

-------------

Problem 2-2:

The following yield on U.S. Treasury securities were taken from The Wall Street Journal on January 7,
2004:
Term Rate
6 months 1.0%
1 year 1.2%
2 year 1.6%
3 year 2.5%
4 year 2.9%
5 year 3.7%
10 year 4.6%
20 year 5.1%
30 year 5.3%

Plot a yield curve based on these data. Discuss how each term structure theory mentioned in the chapter
can explain the shape of the yield curve you plot.

Solution 2-2:

Yield Curve
5.35
5.30
5.25
5.20
Yield (%)

5.15
5.10
5.05
5.00
4.95
4.90
4.85
0 5 10 15 20 25 30
Maturity (years)

-------------


Problem 2-3:

Inflation currently is about 2 percent. Last year the Fed took actions to maintain inflation at this level.
However, the economy is showing signs that it might be growing too quickly, and reports indicate that
inflation is expected to increase during the next five year. Assume that at the beginning of 2005, the rate of
inflation expected for the year is 4 percent; for 2006, it is expected to be 5 percent; for 2007, it is expected
to be 7 percent; and, for 2008 and every year thereafter, it is expected to settle at 4 percent.

a. What is the average expected inflation rate over the five year period 2005-2009?
b. What average nominal interest would, over the five-year period, be expected to produce a 2 percent
real risk-free rate of return on five-year Treasury securities?
c. Assuming a real risk-free rate of 2 percent and a maturity risk premium that starts at 0.1 percent
and increases by 0.1 percent each year, estimate the interest rate in January 2005on bond that
mature in one, two, five, 10 and 20 years and draw a yield curve based on these data.
d. Describe the general economic conditions that could be expected to produce an upward-sloping
yield curve.
e. If the consensus among investors in early 2005 is that the expected rate of inflation for every future
year is 5 percent ( 𝐼 𝑡 = 5% for t = 1 to ∞), what do you think the yield curve would look like?
Consider all the factors that are likely to affect the curve. Does your answer here make you
question the yield curve you drew in part c?

Solution 2-3:

Requirement ‘a & b’:

Expected Average
Annual Nominal
Rate (k*) (IP)
1st year bond 4% 2% 𝐼𝑃1 = 4% 1 =4% 6%
2nd year bond 5% 2% 𝐼𝑃2 = (4%+5%) ∕2 = 4.5% 6.5%
3rd year bond 7% 2% 𝐼𝑃3 = (9%+7%) ∕3 = 5.33% 7.33%
4th year bond 4% 2% 𝐼𝑃4 = (16%+4%) ∕4 =5% 7%
5th year bond 4% 2% 𝐼𝑃5 =(20%+4%) ∕5 = 4.8% 6.8%
10th year bond 4% 2% 𝐼𝑃10 =(24%+4%×5) ∕10=4.4% 6.4%
20th year bond 4% 2% 𝐼𝑃20 =(44%+2%×5) ∕20=4.2% 6.2%


1st year bond 0.1%
2nd year bond 0.1%+0.1% =0.2%
3rd year bond 0.2%+0.1% =0.3%
4th year bond 0.3%+0.1% =0.4%
5th year bond 0.5%+0.1% =0.5%
10th year bond 0.5%+(0.1%×5) =1.0%
20th year bond 1.0%+(0.1%×10) =2.0%


And
Estimated Interest Rate
Bond Type 𝑘 𝑅𝐹 + 𝑀𝑅𝑃
(k)
1st year bond 6% + 0.1% 6.1%
2nd year bond 6.5% + 0.2% 6.7%
5th year bond 6.8% + 0.5% 7.3%
10th year bond 6.4% + 1.0% 7.4%
20th year bond 6.2% + 2.0% 8.2%

The Yield Curve:

9.0 Yield Curve
8.0
7.0
6.0
Yield (%)

5.0
4.0
3.0
2.0
1.0
0.0
0 2 4 6 8 10 12 14 16 18 20
Years to Maturity

Requirement ‘d’:

The ―normal‖ yield curve is upward sloping because, in ―normal‖ times, inflation is not expected to trend
either up or down, so IP is the same for debt of all maturities, but the MRP increases with years, so the
yield curve slopes up. During a recession, the yield curve typically slopes up especially steeply, because
inflation and consequently short-term interest rates are currently low, yet people expect inflation and
interest rates to rise as the economy comes out of the recession.

Requirement ‘e’:

If inflation rates are expected to be constant, then the expectations theory holds that the yield curve should
be horizontal. However, in this event it is likely that maturity risk premiums would be applied to long-term
bonds because of the greater risks of holding long-term rather than short-term bonds:

Yield (%)

Actual yield curve

Maturity risk

premium

Pure expectations yield curve

Years to Maturity

If maturity risk premiums were added to the yield curve in part e above, then the yield curve would be
more nearly normal—that is, the long-term end of the curve would be raised.
-------------

Problem 2-4:
Assume that the real risk-free rate of return, k*, is 3 percent, and it will remain at that level far into the
future. Also assume that maturity risk premiums on Treasury Bonds increase from zero for bonds that
mature in one year or less to a maximum of 2 percent, and MRP increases by 0.2 percent for each year to
maturity that is greater than one year – that is, MRP equals 0.2 percent for a two-year bond, 0.4 percent for
a three year bond, and so forth. Following are the expected inflation rates for the next five years:
Year Inflation Rate (%)
2005 3
2006 5
2007 4
2008 8
2009 3

a. What is the average expected inflation rate for a one, two, three, four and five year bond?
b. What should be the MRP for a one, two, three, four and five year bond?
c. Compute the interest rate for a one, two, three, four and five year bond?
d. If inflation is expected to equal 2 percent every year after 2009, what should be the interest rate for
a 10 and 20 year bond?
e. Plot the yield curve for the interest rates you computed in parts c and d.

Solution 2-4:

Expected Average
Annual Nominal
Rate (k*) (IP)
1st year bond 3% 3% 𝐼𝑃1 = 3% 1 =3% 6%
2nd year bond 5% 3% 𝐼𝑃2 = (3%+5%) ∕2 = 4% 7%
3rd year bond 4% 3% 𝐼𝑃3 = (8%+4%) ∕3 = 4% 7%
4th year bond 8% 3% 𝐼𝑃4 = (12%+8%) ∕4 =5% 8%
5th year bond 3% 3% 𝐼𝑃5 =(20%+3%) ∕5 = 4.6% 7.6%
10th year bond 2% 3% 𝐼𝑃10 =(23%+2%×5) ∕10=3.3% 6.3%
20th year bond 2% 3% 𝐼𝑃20 =(33%+2%×5) ∕20=2.65% 5.65%

1st year bond 0%
2nd year bond 0%+0.2% =0.2%
3rd year bond 0.2%+0.2% =0.4%
4th year bond 0.4%+0.2% =0.6%
5th year bond 0.6%+0.2% =0.8%
10th year bond 0.8%+(0.2%×5)=1.8%
20th year bond 2%


Requirement ‘c & d’:

Bond Type 𝑘 𝑅𝐹 + 𝑀𝑅𝑃 Interest Rate (k)
1st year bond 6% + 0% 6%
2nd year bond 7% + 0.2% 7.2%
3rd year bond 7% + 0.4% 7.4%
4th year bond 8% + 0.6% 8.6%
5th year bond 7.6% + 0.8% 8.4%
10th year bond 6.3% + 1.8% 8.1%
20th year bond 5.65% + 2% 7.65%

Requirement ‘e’:

Yield Curve
9.0
8.5
8.0
Yield (%)

7.5
7.0
6.5
6.0
5.5
5.0
0 2 4 6 8 10 12 14 16 18 20
Years to Maturity

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Problem 2-5:

Today’s edition of The Wall Street Journal reports that the yield on Treasury bills maturing in 30 days is
3.5 percent, the yield on Treasury bills maturing in 10 years is 6.5 percent, and the yield on a bond issued
by Nextel Communications that matures in six years is 7.5 percent. Also, today the Federal Reserve
announced that inflation is expected to be 2 percent during the next 12 months. There is a maturity risk
premium (MRP) associated with all bonds with maturities equal to one year or more.

a. Assume that the increase in the MRP each year is the same and the total MRP is the same for
bonds with maturities equal to 10 years and greater that is, MRP is at its maximum for bonds with
maturities equal to 10 years and greater. What is the MRP per year?
b. What is default risk premium associated with Nextel’s bond?
c. What is the real risk-free rate of return?

Department of Finance Jagannath University 10 | P a g e

Solution 2-5:


Since MRP associated with all bonds with maturities equal to one year or more, so with Treasury bills
maturing in 30 days, 0% MRP is associated, then

k = k* + IP
⇒ 3.5% = k* + 2%
⇒ k* = 3.5% − 2%
∴ k* = 1.5%
At the 10 year bond:
k = k* + IP + MRP
⇒ 6.5% = 1.5% + 2% + MRP
⇒ MRP = 6.5% − 1.5% − 2%
∴ MRP = 3%
As MRP at 10 year bond is 3%. So MRP per year is (3÷10) = 0.3%.


Since 30 days T-bond and 10 years T-bond fulfills the equations:- K = k* +IP +MRP,
We have to calculate DRP from 6 years Nextel Bond:

k = k* +IP +DRP +MRP
⇒ 7.5% = 1.5% + 2% + DRP + (0.3% × 6)
⇒ 7.5% = 3.5% + DRP + 1.8%
⇒ DRP = 7.5% − 3.5% − 1.8%
∴ DRP = 2.2%


Now real risk-free rate of return
k* = 3.5% – IP
= 3.5% - 2.0%
= 1.5%

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Exam-Type Problems 2-6:

According to The Wall Street Journal, the interest rate on one-year Treasury bonds is 2.2 percent, The rate
on two-year Treasury bonds is 3.0 percent, and the rate on three-year Treasury bonds is 3.6 percent. These
bonds are considered risk free, so the rates given here are risk free rates (𝐾 𝑅𝐹 ). The one-year bond matures
one year from today, the two-year bond matures two year from today and so forth. The real risk-free rate
(k*) for each year is 2 percent. Using the expectations theory, compute the expected inflation rate for the
next 12 months (Year 1) and (Year 2).


Solution 2-6:

Here, for one-year treasury bonds-
𝑘 𝑅𝐹1 = 2.2%
k* = 2%
∴ 𝐼𝑃1 = 𝑘 𝑅𝐹1 − k*
= 2.2% −2%
= 0.2%
For one-year Treasury bond 𝐼𝑃1 = 𝐼𝑛𝑓𝑙1 = 0.2%
As average 𝑘 𝑅𝐹 for two-year bond is 3%, thus annual 𝑘 𝑅𝐹 for two-year bond is ,
𝑘 𝑅𝐹1 + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
𝑘 𝑅𝐹2 =
2
2.2% + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
⇒ 3% =
2
⇒ 6% = 2.2% + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
⇒ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 6% − 2.2%
∴ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 3.8%

Since 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 3.8% and k* = 2%.
∴ 𝐼𝑃2 = 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 – k*
= 3.8% – 2%
= 1.8%

For two-year Treasury bond 𝐼𝑃2 is 1.8% ,
so 𝐼𝑛𝑓𝑙2 ={(1.8% × 2) – 0.2%)
= (3.8% – 0.2%)
= 3.4%
-------------


Suppose the annual yield on a two-year Treasury bond id 11.5 percent, while that on a one-year bond is 10
percent, k* is 3 percent, and the maturity risk premium is zero.

a. Using the expectation theory, forecast the interest rate on one-year bond during the second year.
(Hint: Under the expectation theory, the yield on a two-year bond is equal to the average yield on
one-year bonds in Year 1 and Year 2.)
b. What is the expected inflation rate in Year 1 and Year 2?


Solution 2-7:


Here,
𝑘 𝑅𝐹1 = 10%
𝑘 𝑅𝐹2 = 11.5%
∴ 𝑘 𝑅𝐹2 =
2
10% + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
⇒ 11.5% =
2
⇒ 11.5% × 2 = 10% + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
⇒ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 23% − 10%
∴ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 13%


For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is 𝑘 𝑅𝐹 = k* +
IP. If k* = 3%, we can solve for IP:

For year 1:
𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 1 = 𝑘* + 𝐼𝑛𝑓𝑙1
⇒ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 1 = 3% + 𝐼𝑛𝑓𝑙1
⇒ 10% = 3% + 𝐼𝑛𝑓𝑙1
⇒ 𝐼𝑛𝑓𝑙1 = 10% − 3%
⇒ 𝐼𝑛𝑓𝑙1 = 7%

For Year 2:
𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 𝑘* + 𝐼𝑛𝑓𝑙2
⇒ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 3% + 𝐼𝑛𝑓𝑙2
⇒ 13% = 3% + 𝐼𝑛𝑓𝑙2
⇒ 𝐼𝑛𝑓𝑙2 = 13% − 3%
⇒ 𝐼𝑛𝑓𝑙2 = 10%
Here, 𝐼𝑛𝑓𝑙2 is the expected inflation.
The average inflation rate is (7% + 10%)/2 = 8.5%, which, when added to k* = 3%, produces the yield on a
2-year bond, 11.5%. Therefore, all of our results are consistent.

-------------


Assume that the real risk-free rate is 4 percent and that the maturity risk premium is zero. If the nominal
rate of interest on one-year bonds is 11 percent and that on comparable-risk two-year bonds is 13 percent,
What is the one-year interest rate that is expected for year 2? What inflation rate is expected during year 2?
Comment on why the average interest rate during the two-year period differs from the one-year interest
rate expected for year 2?

Solution 2-8:

Here,
k* = 4%
𝑘 𝑅𝐹1 = 10%
𝑘 𝑅𝐹2 = 11.5%
MRP = 0%

∴ 𝑘 𝑅𝐹2 =
2
11% + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
⇒ 13% =
2
⇒ 13% × 2 = 11% + 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2
⇒ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 26% − 11%
∴ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 15%

∴ 𝑘 𝑅𝐹 𝑖𝑛 𝑦𝑒𝑎𝑟 2 = 𝑘* + 𝐼𝑛𝑓𝑙2
⇒ 15% = 4% + 𝐼𝑛𝑓𝑙2
⇒ 𝐼𝑛𝑓𝑙2 = 15% − 4%
∴ 𝐼𝑛𝑓𝑙2 = 11%

The average interest rate during the two-year period differs from the one-year interest rate expected for Year 2
because of the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any
security is the average rate of inflation expected over the security's life.

-------------


The rate of inflation for the coming year is expected to be 3 percent and the rate of inflation in year 2 and
thereafter is expected to be constant at some level above 3 percent. Assume that the real risk-free rate, k*,
is 2 percent for all maturities, and the expectations theory fully explains the yield curve, so there are no
maturity premiums. If three-year Treasury bonds yield 2 percentage points more than one-year bonds, what
rate of inflation is expected after Year 1?


Solution 2-9:

For one-year bond,
k* = 2%
IP = 3%
MRP = 0%

∴ 𝑘1 = k* + 𝐼𝑃1
= (2% +3%)
= 5%

Since for one-year bond, 𝑘1 is 5%, So for three-year bond 𝑘3 = (5% + 2%) = 7%.
For three-year bond,
𝑘3 = k* + 𝐼𝑃3
⇒ 7% = 2% + 𝐼𝑃3
⇒ 𝐼𝑃3 = 7% − 2%
∴ 𝐼𝑃3 = 5%
We know that, 𝐼𝑛𝑓𝑙1 = 𝐼𝑃1
∴ 𝐼𝑃3 = (𝐼𝑛𝑓𝑙1 + 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 )/3
= ( 3% + 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 )/3
Again,
𝑘3 = k* + 𝐼𝑃3
⇒ 7% = 2% + ( 3% + 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 )/3
⇒ 7% − 2% = ( 3% + 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 )/3
⇒ 5% = ( 3% + 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 )/3
⇒ 15% = 3% + 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3
⇒ 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 = 15% − 3%
∴ 𝐼𝑛𝑓𝑙2 + 𝐼𝑛𝑓𝑙3 = 12%

∴ 2 year average, 2 𝐼𝑛𝑓𝑙 = 12%
⇒ 𝐼𝑛𝑓𝑙 = 12% ÷ 2
∴ 𝐼𝑛𝑓𝑙 = 6%
-------------

Today is January 1, 2005, and according to the result of a recent survey, investors expect the annual
interest rates for the years 2008-2010 to be:
Year One-Year Rate
2008 5
2009 4
2010 3

The rates given here include the risk-free rate, 𝑘 𝑅𝐹 , and appropriate risk premiums. Today a three-year
bond – that is, a bond that matures on December 31, 2007 – has an interest rate equal to 6 percent. What is
the yield to maturity for bonds that mature at the end of 2008, 2009, 2010?


Solution 2-10:
Here,
Year One-Year Rate
2008 5
2009 4
2010 3
As, today January 1, 2005 a three-year bond that matures on December 31, 2007 has an interest rate equal
to 6%.
∴ Yield to Maturity (𝑌𝑇𝑀)2007 = 6%
∴ (𝑌𝑇𝑀)2008 = 6% × 3 + 5 /4 = 5.75%
∴ (𝑌𝑇𝑀)2009 = 6% × 3 + 5 + 4 /5 = 5.75%
∴ (𝑌𝑇𝑀)2010 = 6% × 3 + 5 + 4 + 3 /6 = 5.75%

-------------
Suppose current interest rates on Treasury securities are as follows:
Maturity Yield
1 year 5.0
2 year 5.5
3 year 6.0
4 year 5.5

Using the expectations theory, compute the expected interest rates (yields) for each security one year from
now. What will the rates be two years from today and three years from today?

Solution 2-11:
Here,
Maturity Yield
1 year 5.0
2 year 5.5
3 year 6.0
4 year 5.5

As yield to maturity is given here, we can calculate interest rate (k) from the following table:
Year Calculations Interest rate (k)
1 Year 5% 5%
2 Year 5.5% × 2 − 5% 6%
3 Year 6% × 3 − (6% + 5%) 7%
4 Year 5.5% × 4 − (7% + 6% + 5%) 4%
In one year, the bond that matures in one year will mature (die), and the other bonds will have one less
year to maturity. Given the one-year interest rates computed above, the yields on the three remaining bonds
will be:

Original Maturity Maturity After 1 Year New Yield
1 Year Matured --------
2 Year 1 Year 6%/1 = 6%
3 Year 2 Year (7% + 6%)/2 = 6.5%
4 Year 3 Year (4% + 7% + 6%)/3 = 5.7%
-------------


Formula and Necessary Illustration for Calculation

Formula:

1. 𝑘 𝑅𝐹 = k* + IP
2. 𝑘 = 𝑘 𝑅𝐹 + 𝑀𝑅𝑃
3. DRP = k + 𝑘 𝑅𝐹

Here,
k = The quoted or nominal rate of interest on a given security.
𝑘 𝑅𝐹 = The quoted risk-free free rate of return.
𝑘* = The real risk-free rate of interest.
IP = Average Expected Inflation Rate or Inflation premium.
MRP= Maturity risk premium.
DRP = Default risk premium.

Illustration:

1. Nominal Risk-Free Rate: The rate of interest on a security that is free of all risk, 𝑘 𝑅𝐹 is
proxied by the Treasury-bill rate or the Treasury-bond rate. 𝑘 𝑅𝐹 includes an inflation
premium.
2. Real Risk-Free Rate of Interest: The rate of interest that would exist on default-free
or inflation is expected to be zero.
3. Inflation Premium: A premium for expected inflation that investors add to the real
risk-free rate of return.
4. Default Risk Premium: The difference between the quoted interest rate on a
Treasury-bond and that on a corporate bond with similar maturity, liquidity, and
other features is the default risk premium.
5. Maturity risk premium: A premium that reflects interest rate risk; bonds with
longer maturities have greater interest rate risk.


Summary of the Assignment

It was a very pleasant & challenging task for us to work on the topic entitled ―The Financial
Environment: Interest Rates‖ for the course entitled ―Business Finance‖ (Fin-2101).

We are very much thankful to our course instructor Md. Monzur Morshed Bhuiya for giving us the
opportunity to analyze the cost of money in different Treasury securities which is very much
helpful for us to enrich our knowledge in the field of corporate world.

In this assignment we have tried our best to deliver the most accurate & reliable information that
we have computed through our group members.

This assignment presents that how can we calculate the interest rate, MRP, DRP, IP, forecasting,
real risk-free rate of return of Treasury securities and how can we draw a yield curve and its
illustration.

It’s truly a pleasant message for us that we are now coping with the modern business calculation
such as interest rate, MRP, DRP, IP, forecasting, real risk-free rate of return of Treasury securities
through the cost of money Calculation.

----------END---------


Financial environment interest rate

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