BUS FPX 4070 Assessment 2 Inflation and Interest Rates

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Capella University

BUS-FPX4070 Foundations in Finance

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Date

Problem 1: Real Risk-Free Rate

To determine the real risk-free rate, we begin with the yield on current 30-day Treasury bills, which is 3.5%. The accountant has provided the following interest rate premiums: an inflation premium (IP) of 1.5%, a liquidity premium (LP) of 0.6%, a maturity risk premium (MRP) of 1.8%, and a default risk premium (DFP) of 2.15%. According to Adam Hayes (2021), the real risk-free rate can be calculated by subtracting the inflation premium (IP) from the yield of the Treasury bond matching the investment duration. Therefore, the real risk-free rate is calculated as follows:

[ r^* = \text{RFR} – \text{IP} ]

[ r^* = 3.5\% – 1.5\% = 2\% ]

Thus, the real risk-free rate of return is 2%.

Problem 2: Expected Interest Rate

In this problem, we examine Treasury securities and aim to calculate the yield on 3-year Treasury securities. Given the following data: the real risk-free rate (r*) is 4%, inflation is expected to be 1.5% for the first year and 2% for the following two years, and the maturity risk premium (MRP) is 0. There is no default risk premium. To find the yield, we apply the following formula:

[ \text{Yield} = r^* + \frac{IP_1 + IP_2 + IP_3}{3} + MRP ]

[ \text{Yield} = 4\% + \frac{1.5\% + 2\% + 2\%}{3} + 0 ]

[ \text{Yield} = 4\% + \frac{5.5\%}{3} = 4\% + 1.83\% ]

Thus, the yield on 3-year Treasury securities is 5.83%.

Problem 3: Default Risk Premium

In this scenario, a 5-year Treasury bond yields 4%, while a 5-year corporate bond yields 7%. The liquidity premium (LP) on the corporate bond is 0.5%. To calculate the default risk premium (DFP), we subtract the Treasury bond yield, the inflation premium (IP), and the liquidity premium (LP) from the corporate bond yield:

[ \text{DFP} = \text{Corporate bond yield} – \text{T-bond yield} – \text{IP} – \text{LP} ]

[ \text{DFP} = 7\% – 4\% – 0 – 0.5\% = 3\% – 0.5\% = 2.5\% ]

Thus, the default risk premium on the corporate bond is 2.5%.

BUS FPX 4070 Assessment 2 Inflation and Interest Rates

Table: Key Calculations

Problem	Formula	Calculation	Result
Real Risk-Free Rate	( r^* = RFR – IP )	( r^* = 3.5\% – 1.5\% )	2%
Expected Interest Rate	( \text{Yield} = r^* + \frac{IP_1 + IP_2 + IP_3}{3} + MRP )	( \text{Yield} = 4\% + \frac{1.5\% + 2\% + 2\%}{3} + 0 )	5.83%
Default Risk Premium	( \text{DFP} = \text{Corporate yield} – \text{T-bond yield} – IP – LP )	( \text{DFP} = 7\% – 4\% – 0 – 0.5\% )	2.5%

References

Brigham. (n.d.). Fundamentals of financial management. Retrieved from https://capella.vitalsource.com/reader/books/9780357088562/epubcfi/6/36[%3Bvnd.vst.idref%3DM18]!/4/204/9:237[at%20%2Csho]

Hayes, A. (2021, August 30). Risk-free rate of return. Investopedia. Retrieved from https://www.investopedia.com/terms/r/riskfreerate.asp#:~:text=To%20calculate%20the%20real%20risk,bond%20matching%20your%20investment%20duration.