CHAPTER 7
PRINCIPLES OF ASSET VALUATION
Objectives
?Understand why asset valuation is important in finance.
?Explain the Law of One Price as the principle underlying all asset-valuation procedures.
?Explain the meaning and role of valuation models.
?Explain how information gets reflected in security prices.
Outline
7.1 The Relation Between an Asset’s Value and Its Price
7.2 Value Maximization and Financial Decisions
7.3 The Law of One Price and Arbitrage
7.4 Arbitrage and the Prices of Financial Assets
7.5 Exchange Rates and Triangular Arbitrage
7.6 Interest Rates and the Law of One Price
7.7 Valuation Using Comparables
7.8 Valuation Models
7.9 Accounting Measures of Value
7.10 How Information Gets Reflected in Security Prices
7.11 The Efficient Markets Hypothesis
Summary
?In finance the measure of an asset’s value is the price it would fetch if it were sold in a competitive market. The ability to accurately value assets is at the heart of the discipline of finance because many personal and corporate financial decisions can be made by selecting the alternative that maximizes value.
?The Law of One Price states that in a competitive market, if two assets are equivalent they will tend to have the same price. The law is enforced by a process called arbitrage, the purchase and immediate sale of equivalent assets in order to earn a sure profit from a difference in their prices.
?Even if arbitrage cannot be carried out in practice to enforce the Law of One Price, unknown asset values can still be inferred from the prices of comparable assets whose prices are known.
?The quantitative method used to infer an asset’s value from information about the prices of comparable assets is called a valuation model. The best valuation model to employ varies with the information available and the intended use of the estimated value.
?The book value of an asset or a liability as reported in a firm’s financial statements often differs from its current market value.
?In making most financial decisions, it is a good idea to start by assuming that for assets that are bought and sold in competitive markets, price is a pretty accurate reflection of fundamental value. This assumption is generally warranted precisely because there are many well-informed professionals looking for mispriced assets who profit by eliminating discrepancies between the market prices and the fundamental values of assets. The proposition that an asset’s current price fully reflects all publicly-available information about future economic fundamentals affecting the asset’s value is known as the Efficient Markets Hypothesis.
?The prices of traded assets reflect information about the fundamental economic determinants of their value.
Analysts are constantly searching for assets whose prices are different from their fundamental value in order to buy/sell these “bargains.” In deciding the best strategy for the purchase/sale of a “bargain,” the analyst has to evaluate the accuracy of her information. The market price of an asset reflects the weighted average of all analysts opinions with heavier weights for analysts who control large amounts of money and for those analysts who have better than average information.
Solutions to Problems at End of Chapter
Law of One Price and Arbitrage
1. IBX stock is trading for $35 on the NYSE and $33 on the Tokyo Stock Exchange. Assume that the costs of buying and selling the stock are negligible.
a. How could you make an arbitrage profit?
b. Over time what would you expect to happen to the stock prices in New York and Tokyo?
c. Now assume that the cost of buying or selling shares of IBX is 1% per transaction. How does this affect
your answer?
SOLUTION:
a. Buy IBX stock in Tokyo and simultaneously sell them in NY. Your arbitrage profit is $2 per share.
b. The prices would converge.
c. Instead of the prices becoming exactly equal, there can remain a 2% discrepancy between them, roughly $.70 in
this case.
2. Suppose you live in the state of Taxachusetts which has a 16% sales tax on liquor. A neighboring state called Taxfree has no tax on liquor. The price of a case of beer is $25 in Taxfree and it is $29 in Taxachusetts. a. Is this a violation of the Law of One Price?
b. Are liquor stores in Taxachusetts near the border with Taxfree going to prosper?
SOLUTION:
a. This is not a violation of the Law of One Price because it is due to a tax imposed in one state but not in the other.
Illegal arbitrage will probably occur, with lawbreakers buying large quantities of liquor in Taxfree and selling it in Taxachusetts without paying the tax.
b. It is likely that liquor stores will locate in Taxfree near the border with Taxachusetts. Residents of both states
will buy their liquor in the stores located in Taxfree, and liquor stores in Taxachusetts will go out of business.
Triangular Arbitrage
3. Suppose the price of gold is 155 marks per ounce.
a. If the dollar price of gold is $100 per ounce, what should you expect the dollar price of a mark to be?
b. If it actually only costs $0.60 to purchase one mark, how could one make arbitrage profits?
SOLUTION:
a. $100 buys the same amount of gold (1 ounce) as 155 DM, so 1 DM should cost 100/155 or $.645.
b. The marks are “cheaper ” than they should be, so the arbitrage transaction requires you to buy marks at the
cheap price, use them to purchase gold, and sell the gold for dollars.
Example:
1. Start with $1 million, which you borrow for only enough time to carry out the arbitrage transaction.
2. Use the million dollars to buy 1,666,667 marks (1,000,000 / 0.60)
3. Buy 10,752.69 ounces of gold (1,666,667 / 155)
4. Sell the gold for $1,075,269 (10752.69 x 100)
Your risk-free arbitrage profit is $75,269.
4. You observe that the dollar price of the Italian lira is $0.0006 and the dollar price of the yen is $0.01. What must be the exchange rate between lira and yen for there to be no arbitrage opportunity?
SOLUTION:
lira
/Y en 06.Y en /$01.lira
/$0006.
5. Fill in the missing exchange rates in the following table:
Valuation Using Comparables
6. Suppose you own a home that you purchased four years ago for $475,000. The tax assessor’s office has just informed you that they are increasing the taxable value of your home to $525,000.
a.How might you gather information to help you appeal the new assessment?
b.Suppose the house next door is comparable to yours except that it has one fewer bedroom. It just sold for
$490,000. How might you use that information to argue your case? What inference must you make about the value of an additional bedroom?
SOLUTION:
a.You should retrieve as much information as you can about recent sales of comparable homes. If you can
convince the assessor’s office that your home is comparable (and the market value of the recent sales is less than $525,000) you should have a good case. You can gather the information about home sales from a real estate broker.
b.The difference between your house’s assessed value and the actual market value of the home next door is
$35,000 ($525,000 - $490,000). If you can convince the tax assessor’s office that the value of a bedroom is less than $35,000, then the assessor must agree that your home is worth less than $525,000. For example, if comparable sales figures show that one additional bedroom (all else reasonably equivalent) is worth only $10,000, then you should be able to argue that your home is worth $500,000 rather than $525,000.
7. The P/E ratio of ITT Corporation is currently 6 while the P/E ratio of the S&P 500 is 10. What might account for the difference?
SOLUTION:
There are several possible reasons:
?ITT may be riskier than the S&P500 either because it is in a relatively risky industry or has a relatively higher debt ratio.
?ITT’s reported earnings may be higher than they are expected to be in the future, or they may be inflated due to special accounting methods used by ITT.
8. Suppose you are chief financial officer of a private toy company. The chief executive officer has asked you to come up with an estimate for the company’s price per share. Your company’s earnings per share were $2.00 in the year just ended. You know that you should look at public company comparables, however, they seem to fall into two camps. Those with P/E ratios of 8x earnings and those with P/E ratios of 14x earnings. You are perplexed at the difference until you notice that on average, the lower P/E companies have higher leverage than the higher P/E group. The 8x P/E group has a debt/equity ratio of 2:1. The 14x P/E group has a debt/equity ratio of 1:1. If your toy company has a debt/equity ratio of 1.5:1, what might you tell the CEO about your company’s equity value per share?
SOLUTION:
It would be reasonable to apply a P/E of 11x earnings (= (8 + 14) / 2) because your leverage is midway between the two groups. Hence, your company’s price per share would be: 11x $2.00 = $22.00 per share.
9. Assume that you have operated your business for 15 years. Sales for the most recent fiscal year were $12,000,000. Net income for the most recent fiscal year was $1,000,000. Your book value is $10,500,000. A similar company recently sold for the following statistics:
Multiple of Sales: 0.8x
Multiple of Net Income 12x
Multiple of Book Value 0.9x
a.What is an appropriate range of value for your company?
b.If you know that your company has future investment opportunities that are far more profitable than the
company above, what does that say about your company’s likely valuation?
SOLUTION:
a.Multiple of Sales: .8x = $12 million x .8 = $9.6 million
Multiple of Net Income 12x = $1 million x 12 = $12 million
Multiple of Book Value .9x = $10.5 million x .9 = $9.45 million
An appropriate range might be 9 to 12 million
b.Higher end of the range
Efficient Markets Hypothesis
10. The price of Fuddy Co. stock recently jumped when the sudden unexpected death of its CEO was announced. What might account for such a market reaction?
SOLUTION:
Investors may believe that the company’s future prospects look better (i.e., either higher earnings or less risky) without the deceased CEO.
11. Your analysis leads you to believe that the price of Outel’s stock should be $25 per share. Its current market price is $30.
a. If you do not believe that you have access to special information about the company, what do you do?
b. If you are an analyst with much better than average information, what do you do?
SOLUTION:
a.If you believe that the market for Outel stock is an informationally efficient one then the $30 market price
(which is a weighted average of the valuations of all analysts) is the best estimate of the stock’s true value. You should question whether your own analysis is correct.
b.You sell the stock because you think you have superior information.
Real Interest Rate Parity
12. Assume that the world-wide risk-free real rate of interest is 3% per year. Inflation in Switzerland is 2% per year and in the United States it is 5% per year. Assuming there is no uncertainty about inflation, what are the implied nominal interest rates denominated in Swiss francs and in US dollars?
SOLUTION:
Switzerland: (1.03 x 1.02) =1.0506 hence nominal interest rate = 5.06%
US: (1.03 x 1.05) = 1 .0815 hence nominal interest rate = 8.15%
Integrative Problem
13.Suppose an aunt has passed away and bequeathed to you and your siblings (one brother, one sister) a variety of assets. The original cost of these assets follows:
ITEM COST WHEN PURCHASED
Jewelry $500 by Grandmother 75 years ago
House 1,200,000 10 years ago
Stocks and Bonds 1,000,000 3 years ago
Vintage (used) Car 200,000 2 months ago
Furniture 15,000 various dates during last 40 years
Because you are taking a course in finance, your siblings put you in charge of dividing the assets fairly among the three of you. Before you start, your brother approaches you and says: “I’d really like the car for myself, so when you divide up the assets, just give me the car and deduct the $200,000 from my share.”
Hearing that, your sister says: “That sounds fair, because I really like the jewelry and you can assign that to me and deduct the $500 from my share.”
You have always loved your aunt’s house and its furnishings, so you would like to keep the house and the furniture.
a. How do you respond to your brother and sister’s requests? Justify your responses.
b. How would you go about determining appropriate values for each asset?
SOLUTION:
a.Because the market price of the car is close to the what your brother is willing to give up for it, your brother’s
request is reasonable. It is, however, quite possible (even likely), that the antique jewelry is worth much more today than what your relative’s grandmother paid for it in the past. Assigning only its acquisition cost to your sister’s share is quite likely a gross miscalculation. If she wants the jewelry, she should be “charged” an amount equal to today’s market value. It does not matter that your sister does not want to sell the jewelry for a profit, because the jewelry has VALUE even if you do not sell it. Fairness is all about equal VALUE.
b.You would probably have to hire a professional appraiser for the furniture and the jewelry. You can look up the
value of the stocks and bonds in a financial newspaper. You can estimate the value of the house by inquiring for how much similar houses in the same neighborhood have recently been sold. The car was purchased only two months ago, so it is probably reasonable to assume that the current market price is very close to what your distant relative paid for the car.