chapter 7: principles of asset valuation

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FinanceFinance School of Management School of Management

ObjectiveExplain the principles of

asset evaluation

Chapter 7: Principles of Asset Chapter 7: Principles of Asset ValuationValuation

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Chapter 7 ContentsChapter 7 Contents

The relationship between an asset’s value & price

Value maximization & financial decisions

Accounting measures of value

How information is reflected in security prices

The efficient markets hypothesis

The law of one price & arbitrage

Interest rates & the law of one price

Exchange rates & triangular arbitrage

Valuation using comparables

Valuation Models

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The Role of Asset ValuationThe Role of Asset Valuation The process of estimating how much an asset is worth. At the heart of much of financial decision making:

– Investing in securities

– Investing in real estate

– Wealth (value) maximization

– Venture capital

– Financing

– Mergers and acquisition (M&A)

– Others

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The Principle of Asset ValuationThe Principle of Asset Valuation Arbitrage & Law of One Price: The prices of

equivalent assets must be the same. Use information about one or more comparables

whose market prices we know. Market price & fundamental value: The price of

well-informed investors must pay for it in a free and competitive market.

Value maximization and irrelevance of risk preference, consumption and expectations.

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Market Value & Book ValueMarket Value & Book Value You buy a house for

$100,000 on January 1, 19X0 and rent it out to make a profit.

You finance the purchase with $20,000 of your own money (equity financing) and an $80,000 mortgage loan from a bank (debt financing).

On January 2, someone makes you a bona fide offer of $150,000, which is the market value.

AssetsLand $25,000Building 75,000LiabilitiesMortagage Loan 80,000Owner’s Equity (Net Worth) 20,000

ABC Realty Balance Sheet

January 1, 19X0

AssetsLand & Building $150,000LiabilitiesMortagage Loan 80,000Owner’s Equity (Net Worth) 70,000

ABC Realty Market-Value Balance Sheet

January 2, 19X0

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Market Price & Fundamental ValueMarket Price & Fundamental Value — — QRS Pharmaceuticals CorporationQRS Pharmaceuticals Corporation

How is the stock market reacting to the information?

– Announcements of good news: QRS’ research scientists have just discovered a drug that can cure the common cold.

– Announcements of bad news: A judge has just ruled against QRS Pharmaceuticals in a lawsuit involving the payment of millions of dollars in compensation to customers who bought one of its products.

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Efficient Market Hypothesis (EMH)Efficient Market Hypothesis (EMH)

An asset’s current price fully reflects all

publicly available information about

future economic fundamentals affecting

the asset’s value.

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How Does the Market Pool the Information PiecesHow Does the Market Pool the Information Pieces — — A typical analyst-investor’s decision makingA typical analyst-investor’s decision making

– Collecting the information or ‘facts’– Determining the best estimate (expectation)

– Determining the extent of dispersion around the

estimate (risk) – Risk-return trade-off, budget limitation and

investment decision or recommendation

1P(0)

(1)Pr

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– Differing abilities to access and process the information– The total demand for shares of a company– The ‘votes’ cast with dollars:

The market price of the stock will reflect the weighted

average of analysts’ opinions with heavier weights on

the opinions of those analysts with control of more than

the average amount of money and with better than

average amounts of information.

— AggregationAggregation of all analysts’ estimatesof all analysts’ estimates How Does the Market Pool the Information PiecesHow Does the Market Pool the Information Pieces

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How Does the Market Price Approach the How Does the Market Price Approach the

Fundamental ValueFundamental Value – The consequences of consistently overestimating the

accuracy of one’s estimates– The enormous rewards to anyone who can consistently

beat the average– The relative ease of entry into the analyst business

Precisely because professional analysts compete with each other, the market price becomes a better and better estimate of “fair value”, and it becomes more difficult to find profit opportunities.

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Arbitrage: The Price of GoldArbitrage: The Price of Gold

The price of gold in New York City is $300 per ounce.

Suppose that the price of gold in Los Angeles was only $250.

It takes a day to ship the gold by air from Los Angels to New York.

The transaction costs of buying gold in Los Angels and selling it in New York include the costs of shipping, handling, insuring, and broker fees, which account for $2 per ounce.

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Arbitrage: The Price of GoldArbitrage: The Price of Gold

If you can

– Lock in the selling price of $300 at the same time that you buy the gold (by short selling).

– Delay paying for the gold you purchase until you receive payments from selling it (by buying on margin).

You will have engaged in a “pure”, riskless arbitrage transaction.

Gold dealers, arbitrageurs will also discover the discrepancy and buy as large as possible in Los Angels.

The force of arbitrage maintains a relatively narrow band around the price difference between the gold market in Los Angels and the one in New York.

The lower the transaction costs, the narrower the band.

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Arbitrage: The Price of GM SharesArbitrage: The Price of GM Shares

Shares of GM are traded on both the New York Stock Exchange (NYSE) and on the London Stock Exchange.

If shares of GM stock were selling for $54 a share on the NYSE at the same time they were selling for $56 on the London Stock Exchange, what would happy?

The transaction costs in the market for financial assets are much lower than those for gold.

The arbitrage opportunities can not persist for very long.

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Arbitrage: Interest RatesArbitrage: Interest Rates Competition in financial markets ensure that not only the

prices of equivalent assets are the same but also interest rates on equivalent assets are the same.

Interest rates on the U.S. treasure Bonds & World Bank dollar-denominated debt (both are free of default risk).

Interest-rate arbitrage: borrowing at the lower rate and lending at the higher rate.

The arbitrageurs’ attempts to expand their activity will bring about an equalization of interest rates.

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Arbitrage: Exchange RatesArbitrage: Exchange Rates You walk into a bank and observe three

exchange rates—$0.01/ ¥, ¥200/£, and $2.1/£.

What should you do?

– At the $/¥ window, convert $200 into ¥20,000.

– At the ¥/£ window, convert ¥20,000 into £100.

– At the $/£ window, convert £100 into $210.

Professional arbitrageurs can execute large arbitrage transactions at “windows” on their computer screens via an electronic hookup to other banks located almost anywhere in the world.

Arbitrage ensures that for any three currencies that are freely convertible in competitive markets, it is enough to know the exchange rates between any two in order to determine the third.

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Triangular ArbitrageTriangular Arbitrage

USA Japan

UK

¥100/$ or $0.01/¥

£0.005/¥ or ¥200/£ $2/£ or £0.5/$

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More generally,

RA/C = RA/B * RB/C

RA/B = 1/RB/A

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More specifically, in the example

R£/¥ = R£/$ * R$/¥ = 0.5 * 0.01 = 0.005

R¥/£ = 1/R£/¥ = 1/0.005 = 200 The other two pair follow the same form.

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Seemly Violation to the Law of One PriceSeemly Violation to the Law of One Price

If seemly identical assets were selling at different prices, we would suspect

– Something was interfering with the normal operation of the competitive market.

– There was some (perhaps undetected) difference between the two assets.

Illustrations: A dollar bill / four quarters

– Doing your laundry using washer & dryer.

– Paying for drinking at a beverage vending machine.

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Valuation Using ComparablesValuation Using Comparables

No two distinct assets are identical in all aspects.

Valuation: Finding comparable assets and making judgments about which differences have a bearing on their value to investors.

Example: Valuing your parents’ house.

Even when the force of arbitrage cannot be relied upon to enforce the Law of One Price, we still rely on its logic to value assets.

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Valuation ModelsValuation Models

The difficulties of finding equivalent assets

Valuation models: The quantitative methods used to infer an asset’s value from information about the prices of other comparable assets and market interest rates.

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Example: Valuing Shares of StockExample: Valuing Shares of Stock The Value of a Share of a Firm’s Stock = (its most recent)

Earnings Per Share (EPS) * Price/Earnings Multiple (derived

from comparable firms).

XYZ’s earnings per share are $2, and comparable firms in the same line of business have an average price/earnings multiple of 10. Thus

Estimated Value of a Share of XYZ Stock =

XYZ’s EPS * Industrial Average P/E Multiple = $2*10 = $20

Further notes on ‘Comparable’: debt/equity ratios, growth opportunities…

chapter 7: principles of asset valuation

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