Financial Environment and Interest Rate and Inflation

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 01. Md. Mazharul Islam. (Group Representative) 02. Khadizatuz Zohara. Roll No. 091541 091526 Department of Finance Jagannath University 2|PageTable of Contents Sl. No. 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 2-10 2-11 Contents Problems Yield Curves Yield Curves Inflation and Interest Rate Rate of Interest Real Risk-Free Rate, MRP and DRP Exam-Type Problems Expected Inflation Rate Expected Rate of Interest Expected Rate of Interest Interest Rate Interest Rate Expected Rate of Interest Ending Part Formula and Necessary Illustration for Calculat ion Summary of the Assignment Page No. 5 6 7 9 10 12 13 14 14 15 16 17 18 Department of Finance Jagannath University 3|Page 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. .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 bon d 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 Annual Inflation Rate 7% 5% 3% 3% 3% 3% 3% Real Risk-free Rate (k*) 2% 2% 2% 2% 2% 2% 2% Average Expected Inflation Rate or Inflation Premium (IP) = 7% 1 =7% 2 = (7%+5%) ? 2 = 6% 3 = (12%+3%) ? 3 = 5% 4 = (15%+3%) ? 4 =4. 5% 5 =(18%+3%) ? 5 = 4. 2% 10 =(21%+3%? 5) ? 10=3. 6% 20 =(36%+3%? 10) ? 20=3. 3% Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond Average Nominal Interest Rate = k* + IP 9% 8% 7% 6. 5% 6. 2% 5. 6% 5. 3%Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond Maturity Risk Premium (MRP) 0. 2% 0. 2%+0. 2% =0. 4% 0. 4%+0. 2% =0. % 0. 6%+0. 2% =0. 8% 0. 8%+0. 2% =1. 0% 1. 0% 1. 0% Department of Finance Jagannath University 4|Page And Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond The yield Curve: + 9% + 0. 2% 8% + 0. 4% 7% + 0. 6% 6. 5% + 0. 8% 6. 2% + 1. 0% 5. 6% + 1. 0% 5. 3% + 1. 0% Interest Rate (k) 9. 2% 8. 4% 7. 6% 7. 3% 7. 2% 6. 6% 6. 3% 10. 5 10. 0 9. 5 9. 0 8. 5 Yield (%) 8. 0 7. 5 7. 0 6. 5 6. 0 5. 5 5. 0 0 2 4 6 8 Yield Curve LILCO IBM T – Bonds – Bonds T 10 12 14 16 18 20 Yield of MaturityRequirement ‘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, = * + 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 yiel d 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%. Department of Finance Jagannath University 5|Page 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: 5. 35 5. 30 5. 25 Yield (%) 5. 20 5. 15 5. 10 5. 05 5. 00 4. 95 4. 90 4. 85 0 5 Yield Curve 10 15 20 Maturity (years) 25 30 ———— Department of Finance Jagannath University 6|Page 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. . If the consensus among investors in early 2005 is that the expected rate of inflation for every future year is 5 percent ( = 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 Annual Inflation Rate 4% 5% 7% 4% 4% 4% 4% Real Risk-free Rate (k*) 2% 2% 2% 2% 2% 2% 2% Average Expected Inflation Rate or Inflation Premium (IP) 1 = 4% 1 =4% 2 = (4%+5%) ? 2 = 4. 5% 3 = (9%+7%) ? 3 = 5. 33% 4 = (16%+4%) ? =5% 5 =(20%+4%) ? 5 = 4. 8% 10 =(24%+4%? 5) ? 10=4. 4% 20 =(44%+2%? 5) ? 20=4. 2% Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond Average Nominal Interest Rate = k* + IP 6% 6. 5% 7. 33% 7% 6. 8% 6. 4% 6. 2% Requirement ‘c’: Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond Department of Finance Maturity Risk Premium (MRP) 0. 1% 0. 1%+0. 1% =0. 2% 0. 2%+0. 1% =0. 3% 0. 3%+0. 1% =0. 4% 0. 5%+0. 1% =0. 5% 0. 5%+(0. 1%? 5) =1. 0% 1. 0%+(0. 1%? 10) =2. 0% Jagannath University 7|PageAnd Bond Type 1st year bond 2nd year bond 5th year bond 10th year bond 20th year bond The Yield Curve: 9. 0 8. 0 7. 0 6. 0 5. 0 4. 0 3. 0 2. 0 1. 0 0. 0 0 2 4 + 6% + 0. 1% 6. 5% + 0. 2% 6. 8% + 0. 5% 6. 4% + 1. 0% 6. 2% + 2. 0% Estimated Interest Rate (k) 6. 1% 6. 7% 7. 3% 7. 4% 8. 2% Yield Curve Yield (%) 6 8 10 12 14 Years to Maturity 16 18 20 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 o f the greater risks of holding long-term rather than short-term bonds: Yield (%) Actual yield curveMaturity risk premium Pure expectations yield curve Years to Maturity Department of Finance Jagannath University 8|Page 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. 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 Inflat ion Rate (%) 2005 3 2006 5 2007 4 2008 8 2009 3 a. b. c. d. What is the average expected inflation rate for a one, two, three, four and five year bond? What should be the MRP for a one, two, three, four and five year bond? Compute the interest rate for a one, two, three, four and five year bond?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: Requirement ‘a’: Expected Annual Inflation Rate 3% 5% 4% 8% 3% 2% 2% Real Risk-free Rate (k*) 3% 3% 3% 3% 3% 3% 3% Average Expected Inflation Rate or Inflation Premium (IP) 1 = 3% 1 =3% 2 = (3%+5%) ? 2 = 4% 3 = (8%+4%) ? 3 = 4% 4 = (12%+8%) ? 4 =5% 5 =(20%+3%) ? 5 = 4. 6% 10 =(23%+2%? 5) ? 10=3. 3% 20 =(33%+2%? 5) ? 20=2. 65%Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond Requirement ‘b†™: Average Nominal Interest Rate = k* + IP 6% 7% 7% 8% 7. 6% 6. 3% 5. 65% Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond Maturity Risk Premium (MRP) 0% 0%+0. 2% =0. 2% 0. 2%+0. 2% =0. 4% 0. 4%+0. 2% =0. 6% 0. 6%+0. 2% =0. 8% 0. 8%+(0. 2%? 5)=1. 8% 2% Department of Finance Jagannath University 9|Page Requirement ‘c & d’: Bond Type 1st year bond 2nd year bond 3rd year bond 4th year bond 5th year bond 10th year bond 20th year bond 6% + 0% 7% + 0. 2% 7% + 0. 4% 8% + 0. 6% 7. 6% + 0. 8% 6. 3% + 1. 8% 5. 65% + 2% Interest Rate (k) 6% 7. 2% 7. 4% 8. 6% 8. 4% 8. 1% 7. 65% Requirement ‘e’: Yield Curve 9. 0 8. 5 Yield (%) 8. 0 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 ————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 m aturing 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 0 | P a g e Solution 2-5: Requirement ‘a’: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%. Requirement ‘b’: 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. % ? 6) ? 7. 5% = 3. 5% + DRP + 1. 8% ? DRP = 7. 5% ? 3. 5% ? 1. 8% ? DRP = 2. 2% Requirement ‘c’: Now real risk-free rate of return k* = 3. 5% – IP = 3. 5% – 2. 0% = 1. 5% ————- 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 ( ). The one-y ear bond matures one year from today, the two-year bond matures two year from today and so forth.