Expert answer:Financial decision making and the law of one price
Answer & Explanation:IMPORTANT NOTE: The questions must be addressed in its full context. These questions are an opportunity to go outside the box to demonstrate your analytical, integrative, problem- solving and critical thinking skills using the knowledge acquired in your readings. As a result, it is very important to pay close attention to the questions and be able to conduct your discussions in the context of your question. – Please keep this in mind when you complete this assignment.You must expand your ideas further. Analysis must be deep and very instructive. ANSWER THE FOLLOWING QUESTIONS. Each question should be answered in at least 300 words. Quality of content and use of course and outside-of-course resources to support your position or analysis. The answers should not be in the form of essay, just straight to the point- Work must be original and cite your sources.Please be sure to answer the question completely but specifically in well-written complete sentences. Use the attached lecture to help you answer these questions, and conduct your own research1. From the Chapter 7 discussion question you have settled upon one of the two proposed projects. Now you need to understand the requirements associated with capital budgeting for this project as you move forward. Based upon your study of material in Chapter 8, what are the major steps involved in the capital budgeting process?2. In your study of the capital budgeting process it is obvious that you need to understand the concept of free cash flow related to the project selected. Discuss the adjustments that will need to be made to the estimated free cash flow in your evaluation of the selected project. Include in your discussion comments as to the roll that salvage value of equipment would play in your estimate of free cash flow.financial_decision_making_and_the_law_of_one_price.docx
financial_decision_making_and_the_law_of_one_price.docx
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Financial Decision Making and the
Law of One Price
I
N MID-2007, MICROSOFT DECIDED TO ENTER A BIDDING WAR with competitors Google and Yahoo! for a stake
in the fast-growing social networking site, Facebook. How did Microsoft’s managers decide that this was a good decision?
Every decision has future consequences that will affect the value of the firm. These consequences will generally include both
benefits and costs. For example, after raising its offer, Microsoft ultimately succeeded in buying a 1.6% stake in Facebook, along
with the right to place banner ads on the Facebook Web site, for $240 million. In addition to the upfront cost of $240 million,
Microsoft also incurred ongoing costs associated with software development for the platform, network infrastructure, and
international marketing efforts to attract advertisers. The benefits of the deal to Microsoft included the revenues associated with the
advertising sales, together with the appreciation of its 1.6% stake in Facebook. In the end, Microsoft’s decision appeared to be a
good one—in addition to advertising benefits, by the time of Facebook’s IPO in May 2012, the value of Microsoft’s 1.6% stake had
grown to over $1 billion.
More generally, a decision is good for the firm’s investors if it increases the firm’s value by providing benefits whose value
exceeds the costs. But comparing costs and benefits is often complicated because they occur at different points in time, may be in
different currencies, or may have differ- ent risks associated with them.To make a valid comparison, we must use the tools of
finance to express all costs and benefits in common terms. In this chapter, we introduce a central principle of finance, which we
name the Valuation Principle, which states that we can use current market prices to determine the value today of the costs and
benefits associated with a decision.This principle allows us to apply the concept of net present value (NPV) as a way to compare
the costs and benefits of a project in terms of a common unit—namely, dollars today. We will then be able to evaluate a decision by
answering this question: Does the cash value today of its
CHAPTER
3
NOTATION
59
NPV net present value
rf risk-free interest rate
PV present value
59
60 Chapter 3 Financial Decision Making and the Law of One Price
benefits exceed the cash value today of its costs? In addition, we will see that the NPV indicates the net amount by which the
decision will increase wealth.
We then turn to financial markets and apply these same tools to determine the prices of securities that trade in the market. We
discuss strategies called arbitrage, which allow us to exploit situations in which the prices of publicly available invest- ment
opportunities do not conform to these values. Because investors trade rapidly to take advantage of arbitrage opportunities, we argue
that equivalent investment opportunities trading simultaneously in competitive markets must have the same price.This Law of One
Price is the unifying theme of valuation that we use throughout this text.
3.1 Valuing Decisions
A financial manager’s job is to make decisions on behalf of the firm’s investors. For example, when
faced with an increase in demand for the firm’s products, a manager may need to decide whether to raise
prices or increase production. If the decision is to raise production and a new facility is required, is it
better to rent or purchase the facility? If the facility will be purchased, should the firm pay cash or
borrow the funds needed to pay for it?
In this book, our objective is to explain how to make decisions that increase the value of the firm to its
investors. In principle, the idea is simple and intuitive: For good decisions, the benefits exceed the costs.
Of course, real-world opportunities are usually complex and so the costs and benefits are often difficult
to quantify. The analysis will often involve skills from other management disciplines, as in these
examples:
Marketing : to forecast the increase in revenues resulting from an advertising campaign
Accounting : to estimate the tax savings from a restructuring
Economics: to determine the increase in demand from lowering the price of a product
Organizational Behavior: to estimate the productivity gains from a change in manage- ment structure
Strategy: to predict a competitor’s response to a price increase Operations: to estimate the cost savings
from a plant modernization
For the remainder of this text, we assume that the analysis of these other disciplines has been completed
to quantify the costs and benefits associated with a decision. With that task done, the financial manager
must compare the costs and benefits and determine the best decision to make for the value of the firm.
Analyzing Costs and Benefits
The first step in decision making is to identify the costs and benefits of a decision. The next step is to
quantify these costs and benefits. In order to compare the costs and benefits, we need to evaluate them in
the same terms—cash today. Let’s make this concrete with a simple example.
Suppose a jewelry manufacturer has the opportunity to trade 400 ounces of silver for 10 ounces of gold
today. Because an ounce of gold differs in value from an ounce of silver,
it is incorrect to compare 400 ounces to 10 ounces and conclude that the larger quantity is better. Instead,
to compare the costs and benefits, we first need to quantify their values in equivalent terms.
Consider the silver. What is its cash value today? Suppose silver can be bought and sold for a current
market price of $15 per ounce. Then the 400 ounces of silver we give up has a cash value of1
(400 ounces of silver today) * ($15/ounce of silver today) = $6000 today If the current market price for
gold is $900 per ounce, then the 10 ounces of gold we
receive has a cash value of
(10 ounces of gold today) * ($900/ounce of gold today) = $9000 today
Now that we have quantified the costs and benefits in terms of a common measure of value, cash today,
we can compare them. The jeweler’s opportunity has a benefit of $9000 today and a cost of $6000 today,
so the net value of the decision is $9000 – $6000 = $3000 today. By accepting the trade, the jewelry firm
will be richer by $3000.
Using Market Prices to Determine Cash Values
In evaluating the jeweler’s decision, we used the current market price to convert from ounces of silver or
gold to dollars. We did not concern ourselves with whether the jeweler thought that the price was fair or
whether the jeweler would use the silver or gold. Do such considerations matter? Suppose, for example,
that the jeweler does not need the gold, or thinks the current price of gold is too high. Would he value the
gold at less than $9000? The answer is no—he can always sell the gold at the current market price and
receive $9000 right now. Similarly, he would not value the gold at more than $9000, because even if he
really needs the gold or thinks the current price of gold is too low, he can always buy 10 ounces of gold
for $9000. Thus, independent of his own views or preferences, the value of the gold to the jeweler is
$9000.
This example illustrates an important general principle: Whenever a good trades in a competitive
market—by which we mean a market in which it can be bought and sold at the same price—that price
determines the cash value of the good. As long as a competi- tive market exists, the value of the good
will not depend on the views or preferences of the decision maker.
3.1 Valuing Decisions 61
Competitive Market Prices Determine Value
Problem
You have just won a radio contest and are disappointed to find out that the prize is four tickets to the Def Leppard reunion tour (face val
each). Not being a fan of 1980s power rock, you have no intention of going to the show. However, there is a second choice: two tickets
favorite band’s sold-out show (face value $45 each). You notice that on eBay, tickets to the Def Leppard show are being bought and sol
apiece and tickets to your favorite band’s show are being bought and sold at $50 each. Which prize should you choose?
EXAMPLE 3.1
1
You might worry about commissions or other transactions costs that are incurred when buying or selling gold, in addition to the
market price. For now, we will ignore transactions costs, and discuss their effect in the appendix to this chapter.
62
Chapter 3 Financial Decision Making and the Law of One Price
Solution
Competitive market prices, not your personal preferences (nor the face value of the tickets), are relevant here:
Four Def Leppard tickets at $30 apiece = $120 market value
market value
Two of your favorite band’s tickets at $50 apiece = $100
Instead of taking the tickets to your favorite band, you should accept the Def Leppard tickets, sell them on eBay, and use
the proceeds to buy two tickets to your favorite band’s show. You’ll even have $20 left over to buy a T-shirt.
Thus, by evaluating cost and benefits using competitive market prices, we can deter- mine whether a
decision will make the firm and its investors wealthier. This point is one of the central and most powerful
ideas in finance, which we call the Valuation 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.
The Valuation Principle provides the basis for decision making throughout this text. In the remainder of
this chapter, we first apply it to decisions whose costs and benefits occur at different points in time and
develop the main tool of project evaluation, the Net Present Value Rule. We then consider its
consequences for the prices of assets in the market and develop the concept of the Law of One Price.
Applying the Valuation Principle
Problem
You are the operations manager at your firm. Due to a pre-existing contract, you have the oppor- tunity to acquire 200 barrels
3000 pounds of copper for a total of $12,000. The cur- rent competitive market price of oil is $50 per barrel and for copper is
pound. You are not sure you need all of the oil and copper, and are concerned that the value of both commodities may fall in
Should you take this opportunity?
Solution
To answer this question, you need to convert the costs and benefits to their cash values using market prices:
(200 barrels of oil) * ($50/barrel of oil today) = $10,000 today
(3000 pounds of copper) * ($2/pound of copper today) = $6000 today
The net value of the opportunity is $10,000 + $6000 – $12,000 = $4000 today. Because the net value is positive, you should ta
value depends only on the current market prices for oil and copper. Even if you do not need all the oil or copper, or expect th
to fall, you can sell them at current market prices and obtain their value of $16,000. Thus, the opportunity is a good one for th
will increase its value by $4000.
EXAMPLE 3.2
3.2 Interest Rates and the Time Value of Money 63
When Competitive Market Prices Are Not Available
Competitive market prices allow us to calculate the value of a decision without worrying about the tastes or opinions of the
maker. When competitive prices are not available, we can no longer do this. Prices at retail stores, for example, are one sid
can buy at the posted price, but you cannot sell the good to the store at that same price. We cannot use these one-sided pric
determine an exact cash value. They determine the maximum value of the good (since it can always be purchased at that pr
indi- vidual may value it for much less depending on his or her preferences for the good.
Let’s consider an example. It has long been common for banks to entice new depositors by offering free gifts for opening a
account. In 2012, ThinkForex offered a free
iPad 3 for individuals opening a new account. At the time, the retail price of that model iPad was $539. But because there i
competitive market to trade iPads, the value of the iPad depends on whether you were going to buy one or not.
If you planned to buy the iPad anyway, then the value to you is $539, the price you would otherwise pay for it. But if you d
want or need the iPad, the value of the offer would depend on the price you could get for the iPad. For example, if you cou
iPad for $450 to your friend, then ThinkForex’s offer is worth $450 to you. Thus, depending on your preferences, ThinkFo
is worth somewhere between $450 (you don’t want an iPad) and $539 (you definitely want one).
CONCEPT CHECK
3.2
1. In order to compare the costs and benefits of a decision, what must we determine? 2. If crude oil trades in a competitive market,
would an oil refiner that has a use for the
oil value it differently than another investor?
Interest Rates and the Time Value of Money
For most financial decisions, unlike in the examples presented so far, costs and benefits occur at different
points in time. For example, typical investment projects incur costs upfront and provide benefits in the
future. In this section, we show how to account for this time difference when evaluating a project.
The Time Value of Money
Consider an investment opportunity with the following certain cash flows:
Cost: $100,000 today Benefit: $105,000 in one year
Because both are expressed in dollar terms, it might appear that the cost and benefit are directly
comparable so that the project’s net value is $105,000 – $100,000 = $5000. But this calculation ignores
the timing of the costs and benefits, and it treats money today as equivalent to money in one year.
In general, a dollar today is worth more than a dollar in one year. If you have $1 today, you can invest it.
For example, if you deposit it in a bank account paying 7% interest, you will have $1.07 at the end of one
year. We call the difference in value between money today and money in the future the time value of
money.
The Interest Rate: An Exchange Rate Across Time
By depositing money into a savings account, we can convert money today into money in the future with
no risk. Similarly, by borrowing money from the bank, we can exchange money in the future for money
today. The rate at which we can exchange money today for money in the future is determined by the
current interest rate. In the same way that
64 Chapter 3 Financial Decision Making and the Law of One Price
an exchange rate allows us to convert money from one currency to another, the interest rate allows us to
convert money from one point in time to another. In essence, an inter- est rate is like an exchange rate
across time. It tells us the market price today of money in the future.
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 $1 today. More generally, we define the risk-free interest rate, rf , for a given
period as the interest rate at which money can be borrowed or lent without risk over that period. We can
exchange (1 + rf ) dollars in the future per dollar today, and vice versa, without risk. We refer to (1 + rf )
as the interest rate factor for risk- free cash flows; it defines the exchange rate across time, and has
units of “$ in one year/$ today.”
As with other market prices, the risk-free interest rate depends on supply and demand. In particular, at
the risk-free interest rate the supply of savings equals the demand for bor- rowing. After we know the
risk-free interest rate, we can use it to evaluate other decisions in which costs and benefits are separated
in time without knowing the investor’s preferences.
Value of Investment in One Year. Let’s reevaluate the investment we considered ear- lier, this time taking
into account the time value of money. If the interest rate is 7%, then we can express our costs as
Cost = ($100,000 today) * (1.07 $ in one year/$ today) = $107,000 in one year
Think of this amount as the opportunity cost of spending $100,000 today: We give up the $107,000 we
would have had in one year if we had left the money in the bank. Alterna- tively, if we were to borrow
the $100,000, we would owe $107,000 in one year.
Both costs and benefits are now in terms of “dollars in one year,” so we can compare them and compute
the investment’s net value:
$105,000 – $107,000 = -$2000 in one year
In other words, we could earn $2000 more in one year by putting our $100,000 in the bank rather than
making this investment. We should reject the investment: If we took it, we would be $2000 poorer in one
year than if we didn’t.
Value of Investment Today. The previous calculation expressed the value of the costs and benefits in terms
of dollars in one year. Alternatively, we can use the interest rate fac- tor to convert to dollars today.
Consider the benefit of $105,000 in one year. What is the equivalent amount in terms of dollars today?
That is, how much would we need to have in the bank today so that we would end up with $105,000 in
the bank in one year? We find this amount by dividing by the interest rate factor:
1
Benefit = ($105,000 in one year) , (1.07 $ in one year/$ today) = $105,000 * today
This is also the amount the bank would lend to us today if we promised to repay $105,000 in one year.2
Thus, it is the competitive market price at which we can “buy” or “sell” $105,000 in one year.
2
We are assuming the bank will both borrow and lend at the risk-free interest rate. We discuss the case when these rates differ in
“Arbitrage with Transactions Costs” in the appendix to this chapter.
1.07 = $98,130.84 today
3.2 Interest Rates and the Time Value of Money 65
Now we are ready to compute the net value of the investment: $98,130.84 – $100,000 = -$1869.16 today
Once again, the negative result indicates that we should reject the investment. Taking the investment
would make us $1869.16 poorer today because we have given up $100,000 for something worth only
$98,130.84.
Present Versus Future Value. This calculation demonstrates that our decision is the same whether we
express the value of the investment in terms of dollars in one year or dol- lars today: We should reject the
investment. Indeed, if we convert from dollars today to dollars in one year,
(-$1869.16 today) * (1.07 $ in one year/$ today) = -$2000 in one year
we see that the two results are equivalent, but expressed as values at different points in time. 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 (FV) of the investment.
Discount Factors and Rates. When computing a present value as in the preceding calculation, we can
interpret the term
1
1
= = 0.93458 $ today/$ in one year 1+r 1.07
as the price today of $1 in one year. Note that the value is less than $1—money in the
future is worth less today, and so its price reflects a discount. Because it provides the discount at which we can purchase money in the future, the amount 1 is called the one- 1+r
year discount factor. The risk-free interest rate is also referred to as the discount rate for a risk-free
investment.
Comparing Costs at Different Points in Time
Problem
The cost of rebuilding the San Francisco Bay Bridge to make it earthquake-safe was approxi- mately $3 billion in 20
time, engineers estimated that if the project were delayed to 2005, the cost would rise by 10%. If the interest rate we
what would be the cost of a delay in terms of dollars in 2004?
Solution
If the project were delayed, it would cost $3 billion * (1.10) = $3.3 billion in 2005. To compare this amount to the co
billion in 2004, we must convert it using the interest rate of 2%:
$3.3 billion in 2005 , ($1.02 in 2005/$ in 2004) = $3.235 billion in 2004 Therefore, the cost of a delay of one year w
$3.235 billion – $3 billion = $235 milli …
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