ECN437
Peter J Wilcoxen The Maxwell School Economics and Public Administration Syracuse
University
Present Value 2: Combined Forms
The fundamental equations for present value (see “Present Value 1: Fundamentals”) can
be combined to analyze more complex cash flows. Here are a couple of important special
cases. In all examples, the interest rate is given by R.
Infinite stream with a delayed start
Suppose an infinite stream of equal payments of B dollars begins in year T+1. The cash
flow diagram would be:
The present value can be computed in two steps. First, the infinite stream is converted to
an equivalent lump sum in the year before the first payment arrives—in this case, year T.
That’s easy because from year T’s perspective, the stream of payments is very simple: the
payment at T+1 occurs 1 year in the future, the payment at T+2 is 2 years in the future,
and so on. Thus, from period T’s perspective it’s an infinite stream with payments
beginning in one year in the future:
From period T’s perspective, therefore, the value of that stream is B/R. Thus, the original
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 Spring '12
 PeterWilcoxen
 Economics, Net Present Value, Summation

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