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Chapter 4
Discounted Cash Flow Valuation
4A1
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 ±
nancial
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.
The line
AB
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
available.
We will use the letter
r
to denote the interest rate—the equilibrium rate—in this market.
The rate is riskfree because we assume that no default can take place. Look at point
A
on
the vertical axis of Figure 4A.1. Point
A
is a height of:
A
5
$60,000
1
[$50,000
3
(1
1
r
)]
For example, if the rate of interest is 10 percent, then point
A
would be:
A
5
$60,000
1
[$50,000
3
(1
1
0.1)]
5
$60,000
1
$55,000
5
$115,000
Point
A
is the maximum amount of wealth that this person can spend in the second year.
He gets to point
A
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
of $115,000.
Appendix 4A
Figure 4A.1
Intertemporal
Consumption
Opportunities
www.mhhe.com/rwj
Consumption next year
Slope = – (1 +
r
)
C
Y
D
B
$115,000
$71,000
$60,000
$49,000
$40,000
$60,000
$50,000
Consumption this year
Borrowing
Lending
A
$104,545
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View Full Document 4A2
Part II
Valuation and Capital Budgeting
Now let’s take a look at point
B.
Point
B
is a distance of:
B
±
$50,000
²
[$60,000
±
(1
²
r
)]
along the horizontal axis. If the interest rate is 10 percent, point
B
will be:
B
±
$50,000
²
[$60,000
±
(1
²
0.1)]
±
$50,000
²
$54,545
±
$104,545
(We have rounded off to the nearest dollar.)
Why do we divide next year’s income of $60,000 by (1
²
r
), or 1.1 in the preceding
computation? Point
B
represents the maximum amount available for this person to consume
this year. To achieve that maximum he would borrow as much as possible and repay the
loan from the income, $60,000, that he was going to receive next year. Because $60,000
will be available to repay the loan next year, we are asking how much he could borrow this
year at an interest rate of
r
and still be able to repay the loan. The answer is:
$60,000
±
(1
²
r
)
because if he borrows this amount, he must repay it next year with interest. Thus, next year
he must repay:
[$60,000
±
(1
²
r
)]
³
(1
²
r
)
±
$60,000
no matter what the interest rate,
r
, is. In our example we found that he could borrow
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This note was uploaded on 06/22/2009 for the course ECON 134a taught by Professor Lim during the Spring '08 term at UCSB.
 Spring '08
 Lim

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