Fundamentals Of Corporate FinanceTU Board 2077
Suppose the inflation rate is expected to be 7% next year, 5% the following year, and 3% thereafter. Assume that the real risk free rate, will remain at 2% and that maturity risk premium on Treasury…
10Suppose the inflation rate is expected to be 7% next year, 5% the following year, and 3% thereafter. Assume that the real risk-free rate, will remain at 2% and that maturity risk premium 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 risk premium increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-years or longer term T-bonds. a. Calculate the average expected inflation rate for 1-, 2-, 3-, 4-, 5- and 10- year treasury securities. b. Calculate the maturity risk premium for 1-, 2-, 3-, 4-, 5- and 10- years Treasury securities. c. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, and 10-year treasury securities. [3+3+4]
Answer
Solution to Question on Treasury Securities (FIN250, TU Board 2077)
Given Data:
- Inflation rates:
- Next year (Year 1): 7%
- Following year (Year 2): 5%
- Thereafter (Year 3 onwards): 3%
- Real risk-free rate (r):* 2%
- Maturity risk premium (MRP):
- 0% for very short-term bonds (negligible for our calculations).
- Increases by 0.2% per year up to a maximum of 1.0% for 5+ years.
(a) Average Expected Inflation Rate for Different-Term Treasury Securities
The average expected inflation rate for a bond is calculated as the average of the expected inflation rates over its life.
For a 1-year bond, the inflation rate is simply 7% (next year). For a 2-year bond, it is the average of 7% (Year 1) and 5% (Year 2). For 3+ years, the average includes 7% (Year 1), 5% (Year 2), and 3% (Years 3 onwards).
Calculations:
| Term (Years) | Inflation Rates (Year-wise) | Average Inflation Rate |
|---|---|---|
| 1 | 7% | 7% |
| 2 | 7%, 5% | |
| 3 | 7%, 5%, 3% | |
| 4 | 7%, 5%, 3%, 3% | |
| 5 | 7%, 5%, 3%, 3%, 3% | |
| 10 | 7%, 5%, 3% (x8) |
(b) Maturity Risk Premium (MRP) for Different-Term Treasury Securities
The MRP increases by 0.2% per year, up to a maximum of 1.0% for 5+ years.
| Term (Years) | MRP Calculation | MRP (%) |
|---|---|---|
| 1 | 0.2% (1 × 0.2) | 0.2% |
| 2 | 0.4% (2 × 0.2) | 0.4% |
| 3 | 0.6% (3 × 0.2) | 0.6% |
| 4 | 0.8% (4 × 0.2) | 0.8% |
| 5 | 1.0% (max limit) | 1.0% |
| 10 | 1.0% (max limit) | 1.0% |
(c) Interest Rate on Treasury Securities
The nominal interest rate (r) on a Treasury security is calculated using the Fisher equation:
Where:
- Inflation Premium = Average expected inflation rate (from part a).
- MRP = Maturity risk premium (from part b).
Calculations:
| Term (Years) | Inflation Premium (%) | MRP (%) | Interest Rate (r) = r + Inflation + MRP* |
|---|---|---|---|
| 1 | 7% | 0.2% | |
| 2 | 6% | 0.4% | |
| 3 | 5% | 0.6% | |
| 4 | 4.5% | 0.8% | |
| 5 | 4.2% | 1.0% | |
| 10 | 3.6% | 1.0% |
Final Answer Table (Summary of Interest Rates)
| Term (Years) | Interest Rate (%) |
|---|---|
| 1 | 9.2% |
| 2 | 8.4% |
| 3 | 7.6% |
| 4 | 7.3% |
| 5 | 7.2% |
| 10 | 6.6% |
Discussion
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