6. You are considering an investment in a one-year government debt
security with a yield of 5 percent or a highly liquid corporate debt
security with a yield of 6.5 percent. The expected inflation rate for
the next year is expected to be 2.5 percent.
a. What would be your real rate earned on either of the two
investments?
b. What would be the default risk premium on the corporate
debt security?
a. Real rate on return
Government Debt Security=5%-2.5%=2.5%
CD=6.5%-2.5%=4%
b. risk premium
6.5%-5%=1.5%
Adjustment for inflation
1.5%-2.5%= -1%
a. To calculate the real rate earned on either of the two investments, we need to adjust the nominal rate of return for inflation. The real rate of return is calculated as the nominal rate of return minus the inflation rate.
For the government debt security:
Real rate earned = Nominal rate - Inflation rate
Real rate earned = 5% - 2.5%
Real rate earned = 2.5%
For the corporate debt security:
Real rate earned = Nominal rate - Inflation rate
Real rate earned = 6.5% - 2.5%
Real rate earned = 4%
b. The default risk premium on the corporate debt security is the additional return an investor requires to compensate for the risk of default by the issuer. It represents the difference in yield between the corporate debt security and the risk-free government debt security.
Default risk premium = Yield on corporate debt security - Yield on government debt security
Default risk premium = 6.5% - 5%
Default risk premium = 1.5%
To calculate the real rate earned on the investments, as well as the default risk premium on the corporate debt security, we need to consider the following:
a. Real Rate Earned:
The real rate earned is the return on investment after adjusting for inflation. To calculate the real rate earned on either investment, we can use the formula:
Real Rate = Nominal Rate - Inflation Rate
For the one-year government debt security with a yield of 5 percent and an expected inflation rate of 2.5 percent:
Real Rate = 5% - 2.5% = 2.5%
For the highly liquid corporate debt security with a yield of 6.5 percent and an expected inflation rate of 2.5 percent:
Real Rate = 6.5% - 2.5% = 4%
Therefore, the real rate earned on the one-year government debt security is 2.5%, and the real rate earned on the highly liquid corporate debt security is 4%.
b. Default Risk Premium:
The default risk premium is the additional yield investors expect to earn for taking on the risk of default by the corporation. To calculate the default risk premium on the corporate debt security, we can subtract the risk-free rate (the yield on the government debt security) from the yield on the corporate debt security.
Default Risk Premium = Yield on Corporate Debt Security - Yield on Government Debt Security
Using the given yields, the default risk premium on the corporate debt security is:
Default Risk Premium = 6.5% - 5% = 1.5%
Therefore, the default risk premium on the corporate debt security is 1.5%.