BUS FPX 4070 Assessment 4 Evaluating Returns and Cash Flow Streams

Student Name

Capella University

BUS-FPX4070 Foundations in Finance

Prof. Name:

Date

Problem 1: Portfolio Required Return

As the manager of a $10 million investment fund consisting of four stocks, it is essential to determine the required rate of return. Given the market’s required rate of return at 12% and a risk-free rate of 4%, we can calculate the fund’s required rate of return using the individual stock betas and their respective investments. The formula for portfolio beta is as follows:

[ \text{Portfolio Beta} = \left(\text{Investment in Stock A} \times \text{Beta of Stock A}\right) + \left(\text{Investment in Stock B} \times \text{Beta of Stock B}\right) + \left(\text{Investment in Stock C} \times \text{Beta of Stock C}\right) + \left(\text{Investment in Stock D} \times \text{Beta of Stock D}\right) ]

Substituting the given values:

[ \text{Portfolio Beta} = (0.30 \times 1.50) + (0.10 \times -0.50) + (0.20 \times 1.25) + (0.40 \times 0.75) = 0.95 ]

Next, the required rate of return is calculated using the following formula:

[ \text{Required Rate of Return} = \text{Risk-Free Rate} + \left(\text{Portfolio Beta} \times \left(\text{Market Rate of Return} – \text{Risk-Free Rate}\right)\right) ]

Substituting the values:

[ \text{Required Rate of Return} = 0.04 + (0.95 \times (0.12 – 0.04)) = 0.04 + 0.076 = 0.116 ]

Therefore, the required rate of return for the portfolio is 11.6%.

Problem 2: Required Rate of Return for Stocks

In this scenario, we are tasked with determining the required rate of return for two individual stocks based on a market-required return of 14% and a risk-free rate of 6%.

Stock R Calculation:

The required return for Stock R is calculated using the formula:

[ \text{Stock R’s Required Return} = \text{Risk-Free Rate} + \left(\text{Beta of Stock R} \times (\text{Required Market Return} – \text{Risk-Free Rate})\right) ]

Substituting the given values:

[ \text{Stock R’s Required Return} = 0.06 + (1.5 \times (0.14 – 0.06)) = 0.06 + 0.12 = 0.18 ]

Stock S Calculation:

Similarly, the required return for Stock S is calculated as:

[ \text{Stock S’s Required Return} = 0.06 + (0.75 \times (0.14 – 0.06)) = 0.06 + 0.06 = 0.12 ]

The difference in the required returns between Stock R and Stock S is:

[ 0.18 – 0.12 = 0.06 \quad \text{(or 6%)} ]

References

Borad, S. B. (2022, April 16). eFinance Management. Present value of uneven cash flow – all you need to know. Retrieved from https://efinancemanagement.com/investmentdecisions/present-value-of-uneven-cash-flows

Brigham, E. F., & Houston, J. F. (2019). Fundamentals of Financial Management. Retrieved from https://capella.vitalsource.com/reader/books/9780357088562/epubcfi/6/36[%3Bvnd.vst.id ref%3DM18]!/4/204/9:237[at%20%2Csho]

Geler, B. (2022, January 12). Smart Asset. What is the present value of an annuity. Retrieved from https://smartasset.com/retirement/present-value-of-annuity