In Chapter 2, van der Wijst covers what he terms are the basic, fundamental concepts and techniques for finance.  His aim is to provide mechanisms by which even somewhat qualitative aspects of decision making can be made quantitative so that a rational decision can be made in such a fashion that another person, consuming the same facts and following the same algorithms would arrive at.  For example, if we want to be able to understand whether or not we should be investing profits from a business in one way or another, we first need to have a sense of how much a particular investment is going to cost and how to weigh pursuing that investment versus other investments (i.e., opportunity cost). 

To these ends he provides three basic suites or types of tools:

  1. Time Value of Money: A method for comparing costs widely separated time so that an apples-to-apples comparison can be made in terms of monetary value
  2. Assigning Monetary Value: A method for deciding what aspects of a business are relevant and then for subsequently quantifying the value of all these relevant pieces, including tangible assets and liabilities along with intangible ones (like reputation or brand recognition)
  3. Picking Between Alternatives: A method for being able to calculate marginal utility for the investment compared with others a firm might make (i.e., the firm as a single economic actor)

Time Value of Money

van der Wijst starts by discussing the time value of money defined as the notion that a dollar today has a greater value than it will tomorrow and less than it had yesterday.  He cites two reasons for this effect.  The first reason is the observation that immediate enjoyment is worth more to almost all people than the delay of their gratification.  An individual can only be enticed into foregoing consumption by the payment of a premium that compensates for both the loss of the immediate gratification but also hedges against the risk that the opportunity may not be there in the future.  The second reason is what he calls productive investments in which the original amount of money is put to use to generate a greater amount in the future.  As an example, van der Wijst gives the concept of grain or livestock that can be consumed for a given amount in the present or cultivated to bring a larger harvest are some passage of time.  Nowhere in these two reasons is reckoned inflation since inflation reflects the expansion of the money supply within an economy in ways that are independent of the other two. 

The premium to be paid for deferring immediate consumption is summarized entirely in what is called the risk-free interest rate, denoted by r.  To compare amounts of money in two distinct times one can either ‘move’ the current money forward (called compounding) or ‘move’ the future money backwards (call discounting).  In both cases, the future value (FV) is related to the present value (PV) by the well-known formula

FVT = PV (1 + r)T

where T is the elapsed time (in years, months, etc.) between the two epochs.

Since it's more common to speak of compounding when investing or saving in a bank, most people think of it that way and call it compound interest.  Note that the risk-free rate r is difficult to pin down quantitatively in practice since actual interest rates offered by financial institutions take into account inflation but the general rule is that U.S. government bonds (typically 3-month T-bills) set the value of r.

van der Wijst spends some time showing that it, while the formulas are mathematically simple, the thinking associated with using them isn’t trivial.  He does this by examining annuities, which are defined as specific fixed payments that are done on an annual or periodic basis and he offers the following question to ponder:

Suppose you just inherited €1 million from a distant relative. The accountancy firm that handles the estate suggests to make the money available over a longer period of time, so that you are not tempted to spend it all at once. They offer to pay out in fifteen amounts of €100,000, one now and one after each of the following fourteen years. If the interest rate is 10 per cent, is this a fair offer?

Even though the absolutely value of the money is €1.5 million, by properly accounting for the time value of money (with r=0.1) the actual present value is PV = 836,670 and so the offer isn’t fair.  Fairness (or perhaps the correct term should be equity) is achieved when the annuity payments are €119,520 or about 20% larger than what has been proposed by the accountancy firm.

Assigning Monetary Value

Once it is clear how to move quantities of money forward in time by compounding or backwards in time by discounting, the next step is to use a standard process by which a firm or business can be assigned a monetary value.  At the heart of this approach, van der Wijst says that a firm's accounting system is meant to record two things. The first is the flows of goods and money through the firm and the effect those flows have on the firm's assets. The second is the claims by various parties against the firm.  In essence, this is the standard accounting formula that says

assets = liabilities + equity

with one variation, only a subset of what an accountant cares about is considered when assigning a monetary value for the purposes of finance.  Things like amortization and depreciation are largely ignored because these things impact questions of taxes and so only indirectly impact the money available.  In addition, intangible assets (such as reputation) and illiquid assets (such as buildings) are left out of the financial representation because they lack a monetary value (reputation) or have an accounting book value that is different from the market value and that the market value is hard to find and/or achieve (buildings).   Monetary value is assigned by mining the balance sheet, the income statement, the statement of cash flows and the statement of stockholders/business equity (alternatively names the statement of retained earnings) to produce a financial (as opposed to accounting) representation of the firm.  Typically, this financial representation is summarized as:

net working capital = current assets - current liabilities

van der Wijst gives a tangible example in this style of investment analysis by posing the question as to whether a fictitious company, that he calls ZX Co., should contemplate a potential upgrade in certain purification installations.  He goes through a simplified accounting representation (balance sheet, income statement, cash flows, and statement of equity) and a set of costing assumptions associated with the potential upgrade:

  • 3-year length of applicability
  • estimate sales over this period
  • cash outlay for construction
  • internal investment in labor and parts
  • tax rates
  • time-value of money rate (including both risk-free and inflation and risk premiums)

At the end of a straightforward but lengthy analysis, van der Wijst shows that the net present value (NPV) is €15.7 million and therefore the financial investment is sound in so far as it will earn money, not lose it.  To decide whether this is the best investment opportunity, we have to turn to the third and final consideration.

Picking Between Alternatives

van der Wijst closes by examining the role of utility and risk aversion should play in making a quantitative financial decision.  Of the two of these, he considers utility as less useful in making financial decisions but, despite that initial statement, he starts there and he spends a fair amount of space talking about the mathematical ways to represent utility.  Using three basic assumptions:

  1. People always prefer more of a good
  2. Marginal utility
  3. Preferences are well-behaved
    1. preferences can be clearly ranked (A is preferred over B means B is not preferred over A)
    2. preferences are transitive (if A is preferred over B and B over C then A is preferred over C)

van der Wijst then shows how either the natural logarithm U(W) = ln(W) or a negative curvature quadratic U(W) = a + b W - c W2 can serve as mathematical tools provided certain cautions are observed if we can assign a quantitative value W (called wealth) to the preference.  He then uses these tools to express risk aversion in terms of two distinct ratios between the curvature (second derivative) and slope (first derivative), called the Arrow-Pratt absolute risk aversion coefficient

ARA(W) = U''(W) U'(W)

or the relative risk aversion coefficient

RRA(W) = -W U''(W) U'(W)

He further notes that each of these suffers from the fact that they increase with W in contrast to the fact that most people become less risk averse as their wealth increases.  However, he only touches upon these points and doesn’t elaborate how to assign utility and, subsequently, risk to a financial situation – perhaps deferring it to later chapters.

The final tool leveraged on the idea of utility is the notion of an indifference curve, which is essentially a contour or level curve in utility space where U(W) takes on a constant value.  The curve tells us which combinations of good or services (say apples and bananas) provides us with the same utility.  Since marginal utility is always decreasing (adding 1 apple to a stack of 2 may be fine but adding it to a stack of 100 is useless), the indifference curve helps to pick between combinations all with the same utility. 

In Closing

In closing, I found that Chapter 2 of his book lacked the clear narrative focus of Chapter 1 and that the treatment was uneven with some areas explored deeply while others were barely touched.  I was hoping for a focused case study for ZX Co. where utility and risk would help select between all investment opportunities with positive NPV.  I assume that this will come further in the book.