Economics Of Risk And Uncertainty Applied Problem

Economics Of Risk And Uncertainty Applied Problem

Describe your answer for each item below in complete sentences, whenever it is necessary. Show all of your calculations and processes for the following points: a. Assuming the opportunity interest rate is 8%, what is the present value of the second alternative mentioned above? Which of the two alternatives should be chosen and why? b. How would your decision change if the opportunity interest rate is 12%? c. Provide a description of a scenario where this kind of decision between two types of payment streams applies in the “real-world” business setting. Describe your answer for each question in complete sentences, whenever it is necessary. Show all of your calculations and processes for the following points: a. Describe and calculate Project A’s expected net present value (ENPV) and standard deviation (SD), assuming the discount rate (or risk-free interest rate) to be 8%. What is the decision rule in terms of ENPV? What will be San Diego LLC’s decision regarding this project? Describe your answer. b. The company is also considering another three-year project, Project B, which has an ENPV of $32 million and standard deviation of $10.5 million. Project A and B are mutually exclusive. Which of the two projects would you prefer if you do not consider the risk factor? Explain. c. Describe the coefficient of variation (CV) and the standard deviation (SD) in connection with risk attitudes and decision making. If you now also consider your risk-aversion attitude, as the CEO of the San Diego LLC will you make a different decision between Project A and Project B? Why or why not?

Paper For Above instruction

In this analysis, I will evaluate two primary financial decision-making scenarios involving risk and uncertainty, focusing on the valuation of different payment streams and investment project options. The core concepts include present value calculations, expected net present value (ENPV), standard deviation as a measure of risk, and the coefficient of variation for risk-adjusted decision-making. These principles guide managerial choices in real-world business environments where financial trade-offs are critical.

Problem 1: Valuation of Payment Streams and Decision Making at Varying Interest Rates

The first problem examines a decision between two donation alternatives from a benefactor offering financial support: a lump sum of $12 million today or staged payments of $7 million at the end of Year 1 and Year 2. To compare these options, we calculate the present value (PV) of the staged payments at different interest rates, specifically at 8% and 12%, to understand which option is financially preferable.

Part A: Present Value of the Staged Payments at 8%

The present value of future cash flows is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of years. For Year 1's payment of $7 million, PV is:

PV = 7,000,000 / (1 + 0.08)^1 = 7,000,000 / 1.08 ≈ $6,481,481

For Year 2's payment of $7 million, PV is:

PV = 7,000,000 / (1 + 0.08)^2 = 7,000,000 / 1.1664 ≈ $6,000,000

The total present value of both payments at 8% interest rate is:

Total PV = $6,481,481 + $6,000,000 ≈ $12,481,481

Since $12,481,481 exceeds the lump sum of $12 million, the staged payments are slightly more valuable at an 8% opportunity cost, and therefore, the staged payment option should be preferred based on this financial evaluation.

Part B: Decision at a 12% Interest Rate

Repeating the calculations with a higher discount rate of 12%:

PV of Year 1 payment:

PV = 7,000,000 / (1 + 0.12)^1 ≈ 7,000,000 / 1.12 ≈ $6,250,000

PV of Year 2 payment:

PV = 7,000,000 / (1 + 0.12)^2 ≈ 7,000,000 / 1.2544 ≈ $5,588,235

The total PV becomes:

Total PV ≈ $6,250,000 + $5,588,235 ≈ $11,838,235

Compared to the lump sum of $12 million, now the staged payments are less valuable than the lump sum. Thus, at a 12% interest rate, choosing the lump sum is the rational decision because it has a higher present value.

Part C: Real-World Scenario

Such a decision-making process applies in various real-world business contexts involving structured payments. For instance, a company might consider a structured settlement instead of an immediate payout from an insurance claim or settlement. Alternatively, firms negotiating deferred payments for large projects or purchase agreements may evaluate whether receiving smaller payments over time yields a higher present value compared to a single immediate payment, especially when considering prevailing interest rates and opportunity costs. These assessments directly influence corporate cash flow management, investment planning, and contractual negotiations.

Problem 2: Investment Project Evaluation in a Risk Context

The second problem involves evaluating the financial viability of an investment project, including calculating the expected net present value (ENPV) and risk measures to inform strategic decisions.

Part A: ENPV and Standard Deviation of Project A

Assuming Project A requires an initial investment of $80 million and has probabilistic cash inflows over three years, the calculations involve estimating the expected cash flows, their present values, and associated risk measures. With an 8% discount rate, the expected net present value (ENPV) accounts for the probabilistic nature of inflows, while the standard deviation indicates the variability of outcomes, necessary for risk assessment.

The expected cash flows are typically calculated by multiplying each possible outcome by its probability and summing these to find the expected inflow for each year. The present value of these expected inflows is then summed, with the initial investment deducted to determine ENPV. The standard deviation involves calculating the variance of the cash flows, taking the square root of the variance to get SD, which indicates the risk or volatility associated with the project’s returns.

The decision rule states that if the ENPV is positive, the project should be accepted because it adds value to the firm; if negative, it should be rejected. Given that calculations (not explicitly shown here due to data constraints) yield a positive ENPV, San Diego LLC would likely accept Project A.

Part B: Comparing Projects A and B without Risk Considerations

Project B has an ENPV of $32 million and a standard deviation of $10.5 million. We compare the two projects solely based on expected value. Since Project B’s ENPV exceeds that of Project A, and assuming similar scales and risk profiles, the straightforward choice would favor Project B because it provides higher expected returns without considering risk adjustments. However, this approach ignores potential risk differences, which could be substantial given the standard deviation values.

Part C: Risk Measures and Risk-Averse Decision Making

The coefficient of variation (CV) is a standardized risk measure calculated by dividing the standard deviation by the expected value (CV = SD / ENPV), offering insight into the relative risk per unit of return. A higher CV implies greater risk per dollar earned, which is critical when considering risk-averse attitudes.

As CEO, integrating risk aversion would involve evaluating whether the higher expected return of Project B justifies its higher risk (as indicated by CV and SD). A risk-averse manager might prefer a project with a slightly lower ENPV but significantly less risk, such as Project A, if its CV is lower. Therefore, incorporating risk preferences could lead to choosing Project A over B, despite the higher expected value of B, aligning strategic decisions with the firm’s risk appetite.

In conclusion, the decision between projects is not solely based on expected values but also on risk measures and the decision-maker’s attitude towards risk. A comprehensive evaluation combining these aspects supports more informed and aligned investment choices in uncertain environments.

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