# SEC03 - UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL...

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UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL LECTURE NOTES FNCE 601 FINANCIAL ANALYSIS Franklin Allen Fall 2003 QUARTER 1 - WEEK 2 (part 2) Th: 9/11/03 Copyright 2003 by Franklin Allen

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FNCE 601 - Section 3 - Page 1 Section 3: Calculating Present Values Read Chapter 3 BM Motivation Calculation of PV The first question that is usually asked is whether it is necessary to understand where the formulas that you use to calculate PV come from. The answer is that you don’t need to but it’s helpful if you do. Essentially a large part of what we’ll be doing in the coming weeks is discounting streams of cash flows. You can always use a basic formula but this can be tedious and having short-cut formulas can save time and effort. Often it’s quicker to derive a formula than to solve a problem using the basic formula - you’ll see an example of this in the homework problems. Also knowing where the formulas come from help you understand the standard assumptions about the timing of cash flows. In the last section we used the formula r 1 C PV 1 + = In this section we’re first going to look at how to calculate more complicated PV’s when there are many periods and hence many cash flows to consider. Similarly to the one-period case, if we have a cash flow C 2 two periods from now then its present value is given by 2 2 ) r 1 ( C PV + = We can go on doing this for three or more years. It follows that for t years
FNCE 601 - Section 3 - Page 2 t t ) r 1 ( C PV + = Note that 1/(1+r) t is called the discount factor . In other words, t ) r 1 ( 1 %) r , years t ( DF + = Now, present values are all measured in dollars today. What do we know about \$100 today plus \$60 today? It is equal to \$160. In other words, we can sum present values. Time-varying discount rates In the expression above we are implicitly assuming that the interest rate and hence the discount rate is the same in every period. However, there is no reason why this should be so. The discount rate can vary over time. The graph of interest rates for different periods against the periods is known as the yield curve . It is usually upward sloping as shown. ) r + (1 C + ... + ) r + (1 C + ) r + (1 C + r + 1 C = PV T T 3 3 2 2 1 ) r + (1 C = t t T 1 = t

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FNCE 601 - Section 3 - Page 3 The determinants of the shape of the yield curve such as inflation expectations are considered in macroeconomics courses. For the moment what we are interested in is the relationship between rates for different periods. There are two different but equivalent ways of thinking about what happens when interest rates are different for different periods of time. Method 1 : One possibility is to think in terms of the reinvestment rate . Suppose you are investing for two periods, for the first one you invest at r 1 and for the second one you invest at r 1,2 . t
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SEC03 - UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL...

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