Concept explainers
a.
To identify: The interest on Treasury securities, and yield curve.
Yield:
Yield is the percentage of securities at which the return is provided by the company to its investors. Yield can be there in the form of dividend and interest.
Yield Curve:
The graphical representation of the expected return, provided by the company to its investors during the years is known as the yield curve.
a.
Answer to Problem 18P
The items required for the calculation of interest rate are the real risk-free rate, inflation rate, and maturity risk premium.
Explanation of Solution
Given,
The risk free rate is 2% or 0.02.
Inflation rate for the first year is 7% or 0.07.
The inflation rate of second year is 5% or 0.05.
The inflation rate after two years is 3% or 0.03.
The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.
Formula to calculate the interest rate,
Where,
- r is the corporate bond yield.
- r* is the risk free rate.
- IP is the inflation premium.
- MRP is the maturity risk premium.
Statement to show the calculation of interest rate
Maturity |
Real Risk-Free Rate (%) (r*) |
Inflation Rate (%) (IP) |
Maturity Risk Premium (MRP) |
Interest Rate on Treasury Bond
|
1 | 2 | 7 | 0.2 | 9.20 |
2 | 2 | 5 | 0.4 | 7.40 |
3 | 2 | 3 | 0.6 | 5.60 |
4 | 2 | 3 | 0.8 | 5.80 |
5 | 2 | 3 | 1 | 6 |
10 | 2 | 3 | 1 | 6 |
20 | 2 | 3 | 1 | 6 |
Table (1)
The yield curve of the given data
Fig 1
- The x-axis represents the maturity.
- The y-axis represents the interest rate.
- The interest rates with their respective time period can be shown from the graph.
Hence, the interest of 1-year treasury securities is 9.20%, at 2-year treasury securities is 7.60%, 3-year treasury securities is 5.60%, 4-year treasury securities is 5.80% and thereafter is 6%.
b.
To identify: The interest rate on AAA rated securities, and the yield curve.
b.
Answer to Problem 18P
The items required for the calculation of interest rate are real risk-free rate, inflation rate, and maturity risk premium.
Explanation of Solution
Explanation:
Given,
The risk free rate is 2% or 0.02.
Inflation rate for the first year is 7% or 0.07.
The inflation rate of second year is 5% or 0.05.
The inflation rate after two years is 3% or 0.03.
The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.
The default risk premium is 1% which increases
Formula to calculate the interest rate,
Where,
- r is the corporate bond yield.
- r* is the risk free rate.
- IP is the inflation premium.
- MRP is the maturity risk premium.
- DRP is the default risk premium.
Statement to show the calculation of interest rate
Maturity |
Real Risk-Free Rate (%) (r*) |
Inflation Rate on Treasury Bond (%) (IP) |
Maturity Risk Premium (%) (MRP) |
Interest Rate on Treasury Bond
|
Default Risk Premium (%) (DRP) |
Interest Rate on AAA rated Bonds
|
1 | 2 | 7 | 0.2 | 9.20 | 1 | 10.20 |
2 | 2 | 5 | 0.4 | 7.40 | 2 | 9.40 |
3 | 2 | 3 | 0.6 | 5.60 | 2 | 7.60 |
4 | 2 | 3 | 0.8 | 5.80 | 3 | 8.80 |
5 | 2 | 3 | 1 | 6 | 4 | 10 |
10 | 2 | 3 | 1 | 6 | 5 | 11 |
20 | 2 | 3 | 1 | 6 | 5 | 11 |
Table (2)
The yield curve of the given data
Fig 2
- The x-axis represents the maturity.
- The y-axis represents the interest rate.
- The interest rates of treasury securities and AAA bonds with their respective time period can be shown from the graph.
Hence, the interest of 1-year AAA bond is 10.20%, at 2-year AAA bond is 9.40%, 3-year AAA bond is 7.60%, 4-year AAA bond is 8.80% 5-year AAA bond is 10% and thereafter it is 11%.
c.
To identify: The interest rate on lower rated bonds, and the yield curve.
c.
Answer to Problem 18P
The items required for the calculation of interest rate are the inflation rate, real risk-free rate, and maturity risk premium.
Explanation of Solution
Given,
The risk free rate is 2% or 0.02.
Inflation rate for the first year is 7% or 0.07.
The inflation rate of second year is 5% or 0.05.
The inflation rate after two years is 3% or 0.03.
The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.
The default risk premium is 1% which increases
Formula to calculate the interest rate,
Where,
- r is the corporate bond yield.
- r* is the risk free rate.
- IP is the inflation premium.
- MRP is the maturity risk premium.
- DRP is the default risk premium.
Statement to show the calculation of interest rate on AAA rated bonds
Maturity |
Real Risk-Free Rate (%) (r*) |
Inflation Rate on Treasury Bond (%) (IP) |
Maturity Risk Premium (%) (MRP) |
Default Risk Premium (%) (DRP) |
Interest Rate
|
1 | 2 | 7 | 0.2 | 1 | 10.20 |
2 | 2 | 5 | 0.4 | 2 | 9.40 |
3 | 2 | 3 | 0.6 | 2 | 7.60 |
4 | 2 | 3 | 0.8 | 3 | 8.80 |
5 | 2 | 3 | 1 | 4 | 10 |
10 | 2 | 3 | 1 | 5 | 11 |
20 | 2 | 3 | 1 | 5 | 11 |
Table (3)
Statement to show the calculation of interest rate on lower rated bonds
Maturity |
Real Risk-Free Rate (%) (r*) |
Inflation Rate on Treasury Bond (%) (IP) |
Maturity Risk Premium (%) (MRP) |
Default Risk Premium on Lower rated Bonds (%) (DRP) |
Interest Rate (%)
|
1 | 2 | 7 | 0.2 | 2 | 11.2 |
2 | 2 | 5 | 0.4 | 3 | 10.40 |
3 | 2 | 3 | 0.6 | 4 | 9.60 |
4 | 2 | 3 | 0.8 | 5 | 10.80 |
5 | 2 | 3 | 1 | 5 | 11 |
10 | 2 | 3 | 1 | 6 | 12 |
20 | 2 | 3 | 1 | 7 | 13 |
Table (4)
The yield curve of the given data
Fig 2
- The x-axis represents the maturity.
- The y-axis represents the interest rate.
- The interest rates of Treasury securities, AAA bonds and lower rated bonds with their respective time period can be shown from the graph.
Hence, the interest of 1-year lower rated bond is 11.20%, at 2-year lower rated bond is 10.40%, 3-year lower rated bond is 9.60%, 4-year lower rated bond is 10.80% 5-year lower rated bond is 11%, 10-year lower rated bond is 12% and thereafter is 13%.
Want to see more full solutions like this?
Chapter 6 Solutions
Bundle: Fundamentals of Financial Management, 14th + MindTap Finance, 1 term (6 months) Printed Access Card
- Suppose the inflation rate is expected to be 7% next year, 5% the followingyear, and 3% thereafter. Assume that the real risk-free rate, r*, will remain at 2% and thatmaturity risk premiums on Treasury securities rise from zero on very short-term bonds(those that mature in a few days) to 0.2% for 1-year securities. Furthermore, maturity riskpremiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer termT-bonds.a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities andplot the yield curve.b. Suppose a AAA-rated company (which is the highest bond rating a firm can have)had bonds with the same maturities as the Treasury bonds. Estimate and plot whatyou believe a AAA-rated company’s yield curve would look like on the same graphwith the Treasury bond yield curve. (Hint: Think about the default risk premium on itslong-term versus its short-term bonds.)c. On the same graph, plot the approximate yield curve of a much riskier…arrow_forwardThe real risk-free rate is 2.25%. Inflation is expected to be 2.5% this year and 4.25% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?arrow_forwardSuppose the real risk-free rate of interest is r=4% and it is expected to remain constant over time. Inflation is expected to be 1.60% per year for the next two years and 3.90% per year for the next three years. The maturity risk premium is 0.1 x (t-1) %, where t is number of years to maturity, a liquidity premium is 0.45%, and the default risk premium for a corporate bond is 1.40%, The average inflation during the first 4 years is What is the yield on a 4-year Treasury bond? O 6.75% O 8.90% O 4.30% O 7.05% What is the yield on a 4-year BBB-rated bond? O 7.50% O 7.05 % O 8.45% 8.90% If the yield on a 5-year Treasury bond is 7.38% and the yield on a 6-year Treasury bond is 7.83%, the expected inflation in 6 years is (Hint: Do not round intermediate calculations.)arrow_forward
- The real risk-free rate is 2.25%. Inflation is expected to be 2.5%this year and 4.25% during the next 2 years. Assume that the maturity risk premium iszero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasurysecurities?arrow_forwardThe real risk-free rate is 3%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium risk is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?arrow_forwardAssume that the real risk-free rate of return, k*, is 3%, and it will remain at that level far into the future. Also assume that maturity risk premiums (MRP) increase from zero for bonds that mature in one year or less to a maximum of 1%, and MRP increases by 0.2% for each year to maturity that is greater than one year-that is, MRP equals 0.2% for two-year bond, 0.4% for a three-year bond, and so forth. Following are the expected inflation rates for the next five years: Year Inflation Rate (%) 2017 5 2018 6 2019 7 2020 8 2021 9 a) Compute the interest rate for a one-, two-, three-, four-, and five-year bond. b) If inflation is expected to equal 9% every year after 2021, what should be the interest rate for a 10- and 20-year bond? c) Plot the yield curve for the interest rates you computed in part [a] and [b]. d) Based on the curve (in part c), interpret your findings.arrow_forward
- The risk free rate of interest is 2.0%. Inflation is expected to be 8.0% this year, 6.5% next year and 2.5% in each of the following years. Assume the liquidity premium is fixed at 0.5%; maturity riskpremium is calculated to be .1% x (t-1); and default risk premium is fixed at 1.5% for years 1-5 and 2% for years 6-20. Calculate the rate for the following:a) A 9 year bond?b) A 2 year bond? Please do it in excel show the fomulas pleasearrow_forwardThe real risk-free rate is 2 percent, and inflation is expected to be 3 percent next year and 6 percent for the following 3 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? a. 8.00% b. 6.50% c. 2.00% d. 5.00% e. 11.00%arrow_forwardThe real risk-free rate is 2% which is projected to be constant indefinitely. The expected inflation for year 1 is 1%, for year 2 is 2%, and it will increase by 1% each year after. Liquidity Premium is 1% and the default risk premium is 2.5%. Maturity Risk premium for long-term securities is computed as estimated to be 0.5%(t - 1), where the variable “t” is an independent variable that shows the years of maturity of the bond. How much is the difference between the nominal rate of a 7-year long-term government issued bond and 7-year long-term corporate issued bond? a. 3.5% b. 1.5% c. 3.3% d. 5.5%arrow_forward
- The real risk-free rate of interest is 4%. Inflation is expected to be 2% thisyear and 4% during each of the next 2 years. Assume that the maturity riskpremium is zero. What is the yield on 2-year Treasury securities? What is theyield on 3-year Treasury securities?arrow_forwardThe real risk-free rate is 2.05%. Inflation is expected to be 3.05% this year, 4.75% next year, and 2.3% thereafter. The maturity risk premium is estimated to be 0.05 × (t − 1)%, where . What is the yield on a 7-year Treasury note?arrow_forwardThe real risk-free rate is 4.19%. Inflation is expected to be 2.1% this year and 4.75% during the next 4 years. Assume that the maturity risk premium is zero. What is the yield on 4-year treasury securities? State your answer as a percentage to 2 decimal places. Do not include the % symbol.arrow_forward
- Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage LearningEBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENT