Economics Of Risk And Uncertainty Applied Problems

Economics of Risk and Uncertainty Applied Problems

A generous university benefactor has agreed to donate a large amount of money for student scholarships. The money can be provided in one lump-sum of $10 million, or in parts, where $5.5 million can be provided in year 1, and another $5.5 million can be provided in year 2. Assuming the opportunity interest rate is 6%, what is the present value of the second alternative? Which of the two alternatives should be chosen and why? How would your decision change if the opportunity interest rate was 12%? Please, show all your calculations.

An angel investor is considering investing in one of two start-up businesses and is evaluating the expected returns along with the risk of each option in order to choose the better alternative.

- Business 1 is an innovative protein energy drink, which has ENPV of $100,000 with a standard deviation of $40,000.

- Business 2 is a unique chicken wings dipping sauce with an ENPV of $60,000 and a standard deviation of $25,000.

a) Apply the coefficient-of-variation decision criterion to these alternatives to find out which is preferred by the angel investor, assuming that he/she is risk-averse.

b) Apply the maximin criterion, assuming that the worst outcome in Business 1 is to lose $5,000, whereas the worst outcome in Business 2 is to make only $5,000 in profit.

c) If you were the angel investor, what is your certainty equivalent for these two projects? Are you risk-averse, risk-neutral, or risk-lovers?

Paper For Above instruction

The evaluation of proposed financial decisions in uncertain environments requires meticulous analysis of present value calculations, risk assessment, and decision-making criteria. This paper explores these concepts through two applied problems: the valuation of an installment donation and the investment assessment of start-up ventures by an angel investor. Each problem demonstrates the application of financial theories such as discounted cash flows, coefficient of variation, maximin criterion, and certainty equivalents in real-world scenarios.

Part 1: Valuation of a Sequential Donation

The first problem involves a university benefactor considering two donation options: a single lump sum of $10 million or split donations of $5.5 million each in two consecutive years. Using the concept of present value (PV), we compare these options based on the opportunity interest rate, which affects the time value of money. For an interest rate of 6%, the present value of the second option is calculated by discounting the future donation in year 2 back to the present:

PV of Year 2 donation = $5.5 million / (1 + 0.06)^2 = $5.5 million / 1.1236 ≈ $4.89 million.

The total present value of the split donations = $5.5 million + $4.89 million ≈ $10.39 million, which exceeds the lump sum of $10 million. Therefore, at a 6% discount rate, the second alternative is financially more advantageous.

If the opportunity interest rate increases to 12%, the present value of the second donation becomes:

PV of Year 2 donation = $5.5 million / (1 + 0.12)^2 = $5.5 million / 1.2544 ≈ $4.39 million.

Thus, the total PV of split donations = $5.5 million + $4.39 million ≈ $9.89 million, which is now less than the lump sum of $10 million. Consequently, at a 12% discount rate, donating the lump sum immediately is more favorable.

This analysis illustrates how the choice between lump-sum or staggered donations depends heavily on the prevailing discount rate, influencing present value calculations and decision-making.

Part 2: Investment Decision Analysis

The second problem involves an angel investor evaluating two start-ups based on their expected net present value (ENPV) and associated risks, measured via standard deviation. The decision-making criteria include the coefficient of variation and the maximin strategy, as well as personal risk preferences as indicated by the certainty equivalent.

Coefficient of Variation Analysis

The coefficient of variation (CV) is calculated as the ratio of standard deviation to ENPV:

• Business 1: CV = $40,000 / $100,000 = 0.4
• Business 2: CV = $25,000 / $60,000 ≈ 0.4167

The lower CV indicates less relative risk per unit of expected return. Since Business 1 has a lower CV, a risk-averse investor would prefer Business 1 as it offers a higher expected return with comparatively less relative risk.

Maximin Criterion

The maximin principle involves selecting the alternative with the best worst-case outcome. The worst outcomes are given as losses of $5,000 in Business 1 and gains of $5,000 in Business 2. Comparing these, the investor would prefer Business 2, as it guarantees a positive minimum profit while Business 1’s worst case involves a loss.

Certainty Equivalent and Risk Profile

The certainty equivalent (CE) reflects the guaranteed amount an investor considers equivalent to a risky prospect, directly linked to their risk preferences. For risk-averse investors, CE ENPV. Given the risk measures and preferences expressed, the investor likely exhibits risk aversion, valuing safer, more predictable outcomes over higher but riskier returns.

Assuming a risk-averse stance, the CE for Business 1 would be somewhat less than its ENPV (say, around $80,000), whereas for Business 2, it might be closer to its ENPV (around $55,000), reflecting a slight risk-adjusted reduction. These values reinforce the preference for less volatile investments aligning with risk-averse behavior.

Conclusion

Financial decision-making under risk involves evaluating both quantitative measures such as present value and coefficient of variation, as well as qualitative factors like risk appetite. The analysis of donation options demonstrates the importance of discount rates in valuation, while the investment scenario highlights the significance of risk measures and personal preferences. A comprehensive understanding of these concepts aids investors and organizations in making informed choices that align with their financial goals and risk tolerance.

References

• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
• Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
• Ross, S. A., Westerfield, R., & Jaffe, J. (2013). Corporate Finance. McGraw-Hill Education.
• Brealey, R. A., Myers, S. C., & Allen, F. (2014). Principles of Corporate Finance. McGraw-Hill Education.
• Sharpe, W. F., & Alexander, G. J. (1990). Modern Corporate Finance. Prentice Hall.
• Peterson, P. P., & Fabozzi, F. J. (2002). Foundations of Financial Markets and Institutions. Pearson.
• Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2014). Modern Portfolio Theory and Investment Analysis. Wiley.
• Copeland, T., Weston, J., & Shastri, K. (2005). Financial Theory and Corporate Policy. Pearson.
• Kahn, B. (2011). The Essentials of Risk Management. Wiley.
• Hull, J. C. (2018). Risk Management and Financial Institutions. Wiley.