Discounted Cash Flow Valuation
Net Present Value: First Principles of Finance
In this appendix, we show the theoretical underpinnings of the net present value rule. We
rst show how individuals make intertemporal consumption choices, and then we explain
the net present value (NPV) rule. The appendix should appeal to students who like a theo-
retical model. Those of you who can accept the NPV analysis contained in Chapter 4 can
skip to Chapter 5.
4A.1 Making Consumption Choices over Time
Figure 4A.1 illustrates the situation faced by a representative individual in the ±
market. This person is assumed to have an income of $50,000 this year and an income of
$60,000 next year. The market allows him not only to consume $50,000 worth of goods this
year and $60,000 next year, but also to borrow and lend at the equilibrium interest rate.
in Figure 4A.1 shows all of the consumption possibilities open to the person
through borrowing or lending, and the shaded area contains all of the feasible choices. Let’s
look at this ±
gure more closely to see exactly why points in the shaded area are
We will use the letter
to denote the interest rate—the equilibrium rate—in this market.
The rate is risk-free because we assume that no default can take place. Look at point
the vertical axis of Figure 4A.1. Point
is a height of:
For example, if the rate of interest is 10 percent, then point
is the maximum amount of wealth that this person can spend in the second year.
He gets to point
by lending the full income that is available this year, $50,000, and
consuming none of it. In the second year, then, he will have the second year’s income of
$60,000 plus the proceeds from the loan that he made in the ±
rst year, $55,000, for a total
Consumption next year
Slope = – (1 +
Consumption this year