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Samenvatting Finance for Pre-MasterHoofdstuk 3 Financial Decision Making and the Law of One price
3.1 Valuing Decisions
A financial manager’s job is to make decisions on behalf of the firm’s investors. 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. 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 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 management
structure
- Strategy: to predict a competitor’s response to a price increase
- Operations: to estimate the cost savings from a plat modernization
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. Je moet ervoor zorgen dat je de kosten kan vergelijken ->
uitdrukken in hoeveel € het waard is vandaag of op moment van tekenen.
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 of gold to dollars. We did not concern ourselves with whether the jeweler thought that the
price was fair of whether the jeweler would use the silver of gold. 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 prices determines the cash value
of the good. As long as a competitive market exists, the value of the good will not depend on the
views of preferences of the decision maker. Wanneer een goed tegen dezelfde prijs gekocht als
verkocht kan worden, is er sprake van een competitieve markt en doet de mening van de
verkopen/koper er niet toe.
Thus, by evaluating costs and benefits using competitive market prices, we can determine 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 principle 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 the 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.
,3.2 Interest Rated and the Time Value of Money
For most financial decisions, unlike in the example presented so far, costs and benefits occur at
different points in time.
The Time Value of Money
Consider an investment opportunity with the following certain cash flows:
- Costs €100.000,- today
- Benefit €105.000,- in one year
Because both are expressed in dollar terms, it might appear that the costs and benefit are directly
comparable so that the project’s net value is €5.000,-. But this calculation ignores the timing of the
costs and benefits, and it treats money today as equivalent tot money in 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 an exchange rate allows us to convert
from one currency to another, the interest rate allows us to convert from one point in time to
another. In essence, an interest rate is like an exchange rate across time. 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 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
borrowing.
Value of Investment in One Year
Cost (€100.000,- today) X (€1,07 in one year/ € today)
= €107.000 in one year
Now can compare:
Costs €107.000,-
Benefit €105.000,-
Loss €2.000,-
In other words, we could earn €2.000,- more in one year by putting the €100.000,- in the bank rather
than making this investment.
Value of Investment Today
The other way around we can also calculate what the €105.000,- would be worth today. We find this
amount by dividing by the interest rate factor:
Benefit = (€105.000,- ) / (€1,07/ € todag)
= €105.000 X (1/1,07)
= €98.130,84 today
This is also the amount the bank would lend to us today if we promised to repay €105.000,- in one
year. Thus, it is the competitive market price at which we can ‘buy’ or ‘sell’ €105.000,- in one year.
,Now we are ready to compute the net value of the investment:
€98.130,84 - €100.000,- = -€1.869,16 today.
Once again, the negative result indicates that we should reject the investment.
Present Versus Future Values
This calculation demonstrates that our decision is the same whether we express the value of the
investment in terms of € in one year of € today: we should reject the investment.
When we express the value in terms of € today, we call it the Present Value (PV) of the investment. If
we express it in terms of € in one year, 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 is its price reflects a discount. Because it provides the discount at which we
can purchase money in the future, the amount +r is called the one-year discount factor. The risk-
free rate is also referred to as the discount-rate for a risk-free investment.
3.3 Present Value and the NPV Decision Rule
In this section we apply the Valuation Principle to derive the concept of the Net Present Value, of
NPV, and define the ‘golden rule’ of financial decision making, the NPV Rule.
Net Present Value
When we compute the value of a cost or benefit in terms of cash today, we refer to it as the present
value (PV). Smilarly, we define the Net Present Value (NPV) of a project or investment as the
difference between the present value of its benefits and the present value of its costs:
NPV = PV (benefits) – PV (costs)
If we use positive cash flows to represent benefits and negative cash flows to represent costs, and
calculate the present value of multiple cash flows as the sum of present values for individual cash
flows, we can also write this definition as:
NPV = PV (all project cash flows)
That is, the NPV is the total of the present values of all project cash flows.
€500 today, €550 in one year, risk-free interest rate 8%
PV (benefit) = €550 in one year / (€1,08 in one year/€ today)
= €509,25 today
This PV is the amount we would need to put in the bank today to generate €550,- in one year
(€509,26 *1,08 = €550). In other words, the present value is the cash cost today of doing it yourself –
it is the amount you need to invest at the current interest rate to recreate the cash flow.
, NPV = €509,26 - €500 = €9,26 today
But what if your firm doesn’t have the €500,- needed to cover the initial cost of the project? Does the
project still have the same value? Because we computed the value using competitive market prices, it
should not depend on your tastes or the amount of cash your firm has in the bank. If your firm
doesn’t have the €500,-, it could borrow €509,26 from the bank at the 8% interest rate and then take
the project. What are your cash flows in this case?
Today: €509,26 (loan) - €500 (investment) = €9,26
In one year: €550 (project) - €509,26 * 1,08 = €0
This transaction leaves you with exactly €9,26 extra cash today and no future net obligations. So,
taking the project is like having an extra €9,26 in cash up front. Thus, the NPV expresses the value of
an investment decision as an amount of cash received today. As long as your NPV is positive, the
decision increases the value of the firm and is a good decision regardless of your current cash
needs or preferences regarding when to spend the money.
The NPV Decision Rule
Because NPV is expressed in terms of cash today, it simplifies decision making. As long as we have
correctly captured all of the costs and benefits of the project, decisions with a positive NPV will
increase the wealth of the firm and its investors. We capture this logic in the NPV Decision Rule:
When making an investment decision, take the alternative with the highest NPV. Choosing this
alternative is equivalent to receiving its NPV in cash today.
Accepting or rejecting a project:
A common financial decision is whether to accept or reject a project. Because rejecting the project
generally has NPV = 0 (there are no new costs of benefits from not doing the project), the NPV
decision rule implies what we should:
- Accept those projects with positive NPV because accepting them is equivalent to receiving
their NPV in cash today, and
- Reject those projects with negative NPV; accepting them would reduce the wealth of
investors, whereas not doing them has no costs (NPV=0)
NPV and Cash Needs
When we compare projects with different patterns of present and future cash flows, we may have
preferences regarding when to receive the cash. Some may need cash today; others may prefer to
save for the future. -> regardless of our preferences for cash today versus cash in the future, we
should always maximize NPV first. We can then borrow or lend to shift cash flows through time
and find our most preferred pattern of cash flows.
3.4 Arbitrage and the Law of One Price
So far, we have emphasized the importance of using competitive market prices to compute the NPV.
But is there always only one such price?
Arbitrage
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