Financial Decision Making and the Law of One Price. Chapter 3

1. BEE1006 Introduction to Finance Chapter 3: Financial Decision Making and the Law of One Price

Dr Weihan Ding
Spring Term 2022

2.

Chapter Outline
3.1 Valuing Decisions
3.2 Interest Rates and the Time Value of Money
3.3 Present Value and the NPV Decision Rule
3.4 Arbitrage and the Law of One Price
3.5 No-Arbitrage and Security Prices

3.

Learning Objectives
1. Assess the relative merits of two-period projects using net
present value.
2. Define the term “competitive market,” give examples of
markets that are competitive and some that aren’t, and
discuss the importance of a competitive market in
determining the value of a good.
3. Explain why maximizing NPV is always the correct decision
rule.

4.

Learning Objectives (cont'd)
4. Define arbitrage, and discuss its role in asset pricing. How
does it relate to the Law of One Price?
5. Calculate the no-arbitrage price of an investment
opportunity.
6. Show how value additivity can be used to help managers
maximize the value of the firm.
7. Describe the Separation Principle.

5.

Motivation: Why this Chapter?
• This Chapter discusses some very important principles that are
foundations for the incoming chapters (this is probably an incomplete
list):
• Valuation Principle
• Time Value of Money
• NPV Decision Rule
• Arbitrage and the Law of One Price
• Value Additivity

6.

3.1 Valuing Decisions
Identify Costs and Benefits
Financial managers should made decisions where the
benefits exceed the costs
We need to evaluate benefits and costs in the same unit
before we could compare them
Suppose a jewelry manufacturer has the opportunity to trade 400
ounces of silver and receive 10 ounces of gold today.
To compare the costs and benefits, we first need to convert them
to a common unit.

7.

Analyzing Costs and Benefits
• If the current market price for gold is $1300 per ounce, then
the 10 ounces of gold we receive has a cash value of
(10 ounces of gold) X ($1300/ounce) = $13,000 today
• Suppose silver can be bought and sold for a current market
price of $17 per ounce. Then the 400 ounces of silver we
give up has a cash value of
(400 ounces of silver) X ($17/ounce) = $6,800 today

8.

Analyzing Costs and Benefits
• Therefore, the jeweller's opportunity has a benefit of
$13,000 today and a cost of $6,800 today. In this case, the
net value of the project today is
$13,000 – $6,800 = $6,200 today
• Because the net value is positive, the benefits exceed the
costs, and the jeweller should accept the trade.
• By accepting the trade, the jeweller will be richer by $6200

9.

Using Market Prices to Determine Cash Values
• Competitive Market
• A market in which goods can be bought and sold at the
same price.
• In evaluating the jeweller'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 jeweller
thought that the price was fair or whether the jeweller
would use the silver or gold.

10.

Using Market Prices to Determine Cash Values
• We know the market value of 10 ounces of gold is $13000
• What if the jeweller do not need gold at all?
• She will still value the gold at $13000
• As she can sell the gold at $13000 in the market
• She will not sell it at a lower price
• What if the jeweller really, really want the gold?
• She will still value the gold at $13000
• As she can buy the gold at $13000 in the market
• She will not buy it a higher price

11.

Textbook Example 3.1

12.

Textbook Example 3.1

13.

3.1 Valuation Principle
The previous example illustrates the point that we can determine
whether a decision will make the firm and its investors wealthier
This is called 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.

14.

3.2 Interest Rates and the Time Value of Money
Consider an investment opportunity with the following certain cash
flows.
Cost: $100,000 today
Benefit: $105,000 in one year
Cannot simply compare 1$ today and 1$ tomorrow
For example, if you invest 1$ today, most likely you will get more
than 1$ tomorrow
The difference in value between money today and money in the
future is due to the time value of money.

15.

The Interest Rate: An Exchange Rate Across Time
The rate at which we can exchange money today for money in the
future is determined by the current interest rate.
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),