BECOE/Principles of Finance/Financial decision making and the law of one price.md

course, date, title

course	date	title
Finance	24-09-2024	Financial decision making and the law of one price

Tags: Time Valued Money, Arbitrage,

Financial decision making and the law of one price

Summary

This note explores the fundamental principles of financial decision making, focusing on the law of one price and related concepts such as time value of money, arbitrage, and net present value (NPV). These principles form the foundation for understanding financial markets and making informed investment decisions.

Definitions and Important Concepts

• Common Unit: A standardized measure used to compare different financial assets or investments.
• Arbitrage: The practice of taking advantage of a price difference between two or more markets, striking a combination of matching deals that capitalize upon the imbalance.
• NPV (Net Present Value): A method used to determine the current value of all future cash flows generated by a project, including the initial capital investment.
• Law of One Price: The economic theory that the price of identical goods or assets should be the same in different markets, assuming no trade restrictions and negligible transaction costs.

Financial Theories/Models

1. Time Value of Money: The concept that money available now is worth more than the same amount in the future due to its potential earning capacity.
2. Efficient Market Hypothesis: The theory that asset prices fully reflect all available information, making it impossible to consistently "beat the market."
3. Capital Asset Pricing Model (CAPM): A model that describes the relationship between systematic risk and expected return for assets.

Formulas and Calculations

• Net Present Value (NPV): NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t} - I_0 Where:
  • CF_t is the cash flow at time t
  • r is the discount rate
  • I_0 is the initial investment
  • n is the number of periods

Example: A company is considering a project with an initial investment of $100,000. The project is expected to generate cash flows of $30,000 per year for 5 years. The company's cost of capital (discount rate) is 10%. Should the company pursue this project?

Let's calculate:

• I_0 = $100,000
• CF_t = $30,000 for each year
• r = 10% = 0.10
• n = 5 years

NPV = \frac{30,000}{(1+0.10)^1} + \frac{30,000}{(1+0.10)^2} + \frac{30,000}{(1+0.10)^3} + \frac{30,000}{(1+0.10)^4} + \frac{30,000}{(1+0.10)^5} - 100,000 NPV = 27,272.73 + 24,793.39 + 22,539.45 + 20,490.41 + 18,627.64 - 100,000 NPV = 113,723.62 - 100,000 = $13,723.62

The NPV is positive, so the company should pursue this project.

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• Future Value: FV = PV \times (1 + r)^n Where:
  • FV is future value
  • PV is present value
  • r is interest rate
  • n is number of periods

Example: You invest $5,000 in a savings account that offers 3% interest per year. How much will you have after 10 years?

• PV = $5,000
• r = 3% = 0.03
• n = 10 years

FV = 5,000 \times (1 + 0.03)^{10} FV = 5,000 \times 1.3439 FV = $6,719.58

After 10 years, your investment will grow to $6,719.58.

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• Present Value: PV = \frac{FV}{(1 + r)^n} Where
  • PV = Present Value
  • FV = Future Value
  • r = Interest rate (or discount rate) per period
  • n = Number of periods

Market Applications

1. Investment Decision Making: Using NPV to evaluate and compare different investment opportunities.
2. Pricing of Financial Instruments: Applying the law of one price to ensure consistent pricing across markets.
3. Risk Management: Utilizing arbitrage principles to hedge against market risks.
4. Corporate Finance: Making capital budgeting decisions based on NPV and other time value of money concepts.

Example: You want to have $50,000 for a down payment on a house in 5 years. If you can earn 4% interest per year on your savings, how much do you need to invest today?

• $FV = $50,000
• $r = 4% = 0.04
• n = 5 years

PV = \frac{50,000}{(1 + 0.04)^5} PV = \frac{50,000}{1.2166529} PV = $41,098.97

You need to invest $41,098.97 today to have $50,000 in 5 years, assuming a 4% annual interest rate.

Case Studies or Examples

1. Currency Arbitrage: Exploiting price discrepancies in foreign exchange markets.
2. Merger Arbitrage: Taking advantage of price differences between a company's stock price and the offered acquisition price.
3. NPV in Project Evaluation: A company using NPV to decide between two competing investment projects.

Risk Considerations

• Market Inefficiencies: Temporary violations of the law of one price due to market frictions or information asymmetries.
• Transaction Costs: The impact of fees and taxes on the profitability of arbitrage opportunities.
• Regulatory Risks: Changes in laws or regulations that may affect arbitrage opportunities or investment valuations.

Questions for Analysis

1. How does the concept of time value of money influence long-term investment strategies?
2. In what situations might the law of one price not hold, and what are the implications for financial markets?
3. How can companies use NPV analysis to make better capital allocation decisions?

References

• Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance. McGraw-Hill Education.
• Bodie, Z., Kane, A., & Marcus, A. J. (2018). Investments. McGraw-Hill Education.
• Lecture notes, Date: [Financial Decision Making Principles]
• Course material: [Chapter on Time Value of Money and NPV]