Lady Taylor PhD Case Problem 41 Coats Decision LG2 LG4

For Lady Taylor Phdcase Problem41coatess Decisionlg2lg4on Januar

Analyze the investment decisions and scenarios presented involving Dave Coates's investment options, assessing their acceptability, risk, and return characteristics using present value techniques, IRR calculations, and risk premiums. Compare and contrast the investments under different discount rates, estimate IRRs, and recommend the best choice. Additionally, evaluate the growth of the extra $50 savings over time and discuss decision implications considering risk and investment horizon factors.

Paper For Above instruction

The case involving Dave Coates's investment decisions presents a comprehensive scenario in which key financial concepts such as present value analysis, internal rate of return (IRR), and risk premium assessment are central to evaluating investment choices. Coates's objective is to select between two long-term investments, A and B, each costing $1,050 and expected to generate income over ten years, with additional money allocated to a savings account earning 3% interest. The critical analytical tasks involve estimating the present value of each investment's income streams, calculating the IRR for both options, and understanding the implications of risk premiums on discount rates and valuation.

Initially, assuming both investments are equally risky, the appropriate discount rate is 4%, reflecting the relatively certain stream of income from investment A. Using the present value technique, the acceptability of each investment can be identified by discounting future income streams at 4%. For a typical annuity or stream of cash flows, the present value is calculated by summing the discounted income over the 10-year period. When these calculations are performed, the investment with the higher present value or IRR exceeding 4% is deemed more favorable. If investment A's IRR exceeds 4%, it indicates a profitable opportunity, whereas B's IRR below 4% would suggest otherwise. Under the assumption of equal risk, these calculations offer a straightforward comparison and recommendation.

Second, recognizing that investment B is riskier, a risk premium of 4% is added, making the effective discount rate for A 4% and for B 8%. Reapplying the present value analysis under these new rates adjusts the valuation process to account for perceived increased risk. Typically, the higher discount rate diminishes the present value of the income stream from B more significantly than from A, likely making B less attractive despite potentially higher returns. The recalculated IRRs in this revised risk scenario can be compared to the discount rates—if the IRRs are above the respective discount rates, the investments still remain acceptable; if below, they become less attractive.

Estimating the IRR involves solving for the discount rate at which the present value of income streams equals the initial investment. This requires iterative calculation or financial calculator use. If, in the initial scenario, IRR for A surpasses 4%, and for B surpasses 8%, it indicates that both investments provide returns exceeding their discount thresholds. Conversely, if the IRRs are below these rates, the investments are less desirable. The IRRs serve as internal measures of profitability, independent of the discount rates used for external valuation.

Based on the calculated IRRs, a recommendation for Dave hinges on comparing these to his required return thresholds. If investment A’s IRR exceeds 4% and is higher than B’s IRR, and B’s IRR exceeds 8%, then A is the preferred choice, especially if risk considerations are uniform or favor the less risky investment. Alternatively, if both IRRs are below their respective discount rates, neither investment may be appealing, urging consideration of other options. Bob’s extra investment remains in savings earning 3%, which can be compared to the IRRs to decide if reallocating funds makes sense.

Finally, analyzing the growth of the surplus $50 investment at 3% over the period from 2017 to 2026 involves compound interest calculations. Using the future value formula FV = PV * (1 + r)^n, with PV = $50, r = 3%, n = 10 years, the future value can be calculated, showing how much the extra savings will grow over time. This demonstration clarifies the compounding effect of the savings account, illustrating the value of even small extra investments when compounded over long durations.

In conclusion, the combined analysis employing present value techniques, IRR assessments, and risk premium adjustments provides a structured framework for evaluating long-term investments. The decision criteria demonstrate the importance of comparing internal profitability measures with external discount rates reflecting risk and return expectations. It also underscores the significance of managing risk and optimizing returns through appropriate discounting and reinvestment strategies, ultimately guiding Dave toward an informed investment choice that aligns with his risk appetite and financial goals.

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