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**Lecture-1 Financial Decision Making and the Law of one Price**

Berk, De Marzo Chapter 3

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Valuing Decisions Competitive Market: A market in which goods can be bought and sold at the same price. The Valuing decision making is to identify the costs and benefits of a decision. In order to compare the costs and benefits, we need to evaluate them in the same terms (cash today). It’s may need help from other areas in identifying the relevant costs and benefits. Such as, Marketing, Economics, Organizational Behavior, Strategy, Operations Valuing Principle: The value of an asset to the firm or its investors is determined by its competitive market price. The benefits and costs of a decision should be evaluated using these market prices, and when the value of the benefits exceeds the value of the costs, the decision will increase the market value of the firm. CF:723G28:L01

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**Interest Rates and the Time Value of Money**

Time Value of Money: Consider an investment opportunity with the following certain cash flows. For example; Cost: $100,000 today , Benefit: $105,000 in one year. The difference in value between money today and money in the future is due to the time value of money. Interest Rate: The rate at which we can exchange money today for money in the future is determined by the current interest rate. For Example; Suppose the current annual interest rate is 7%. By investing or borrowing at this rate, we can exchange $1.07 in one year for each $1 today. Risk–Free Interest Rate (Discount Rate), rf: The interest rate at which money can be borrowed or lent without risk. Interest Rate Factor = 1 + rf Discount Factor = 1 / (1 + rf)

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**Present Value and NPV Decision Rule**

Present Versus Future Value: When we express the value in terms of dollars today, we call it the present value (PV) of the investment. If we express it in terms of dollars in the future, we call it the future value of the investment. The net present value (NPV) of a project or investment is the difference between the present value of its benefits and the present value of its costs. When making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today. Decision: Accept those projects with positive NPV because accepting them is equivalent to receiving their NPV in cash today. Reject those projects with negative NPV because accepting them would reduce the wealth of investors. CF:723G28:L01

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Example 01: NPV . CF:723G28:L01

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**Arbitrage and the Law of One Price**

Arbitrage: The practice of buying and selling equivalent goods in different markets to take advantage of a price difference. An arbitrage opportunity occurs when it is possible to make a profit without taking any risk or making any investment. A competitive market in which there are no arbitrage opportunities. Law of One Price: If equivalent investment opportunities trade simultaneously in different competitive markets, then they must trade for the same price in both markets. In a normal market, the NPV of buying or selling a security is zero.

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**No-Arbitrage Price and Security Prices**

Unless the price of the security equals the present value of the security’s cash flows, an arbitrage opportunity will appear. If we know the price of a risk-free bond, we can use to determine what the risk-free interest rate must be if there are no arbitrage opportunities.

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**Arbitrage and Financial Decision Making**

Separation Principle: We can evaluate the NPV of an investment decision separately from the decision the firm makes regarding how to finance the investment or any other security transactions the firm is considering. Value additivity. The price of X (security) equal to the price of the portfolio, which is the combined price of Y (security) and Z(Security). Price(X) = Price(Y+Z) = Price(Y) + Price(Z) Value of the firm: The total value of the assets is equal to the sum of the debt and equity, no matter what. So we can use the principle to make the valuation. Value of the firm = Value of Equity + Value of Debt Impact of Risk on Valuation: When cash flows are risky, we must discount them at a rate equal to the risk-free interest rate plus an appropriate risk premium. The appropriate risk premium will be higher the more the project’s returns tend to vary with overall risk in the economy.

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Example 2: Arbitrage Consider a security that pays its owner $2,000 today and $3,000 in one year, without any risk. Suppose the risk-free interest rate is 6%. What is the no-arbitrage price of the security today (before the $2,000 is paid)? If the security is trading for $4,950, what arbitrage opportunity is available? Answer 01: We need to compute the present value of the security’s cash flows. The present value of the first cash flow is $2,000 since it is received today. The present value of the second cash flow of $3,000 received in one year is: $3,000 / (1.06) = $2,830.19 We can then use $2,000 of the sale proceeds to replace the $2,000 we would have received from the security today and invest $2, of the sale proceeds at 6% to replace the $3,000 we would have received in one year. The remaining $4,950 - $2,000 - $2, = $ is an arbitrage profit. CF:723G28:L01

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**Example 3: Investing and Financing**

CF:723G28:L01

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