# Lecture4 - Chapter 5 00:52 Time-Varying Rates of Return In...

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1 Time-Varying Rates of Return In this chapter, we assume perfect markets , so we assume four market features: 1. No differences in opinion. 2. No taxes. 3. No transaction costs. 4. No big sellers/buyers. Important: You need your calculator! Scan Chp. 5.1 – 5.3 and lecture notes before class. 07/13/11 00:52 References Corporate Finance: An Introduction (Welch, 2009, Prentice Hall) Chapter 5

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2 Time-Varying Rates of Returns Important: All earlier formulas hold . The only difference is that (1 + r 0,T ) ≠ (1 + r ) T , because r is not the same in each period. • The main complication is that we are now in subscript hell. We need one subscript (well, two) for each period. • For example ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 3 , 2 2 , 1 1 , 0 3 2 , 1 1 , 0 2 1 , 0 1 0 3 , 0 3 2 , 0 2 1 , 0 1 0 3 , 2 2 , 1 1 , 0 3 , 0 r r r C r r C r C C r C r C r C C NPV r r r r + + + + + + + + + = + + + + + + = + + + = + 5-1A, 1C
3 Annualized Rates of Returns The rate of return over the entire time period ( r 0,T ) is called the holding period rate of return. It is how much you earn over the period for which you hold an investment. Comparing holding rates of return is often difficult. Which is better: 10% over 5 years, 15% over 10 years, or 17% over 12.2 years? The annualized rate of return is an easy and quick way to compare different investments. Ex. Suppose an investment earns 15% over three years. The annualized rate of return return r is: (1+r)*(1+r)*(1+r) = 1.15 → r = 1.15^(1/3) – 1 = .048 General formula: r ANN = (1+ r 0,T )^(1/T) - 1 5-1A, 1C

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Important: Almost all interest rates are quoted as annualized. Q4: If the interest rate is 8% in year 1 and 4% in year 2, what is the annualized interest rate? Q2: If the four-year holding period rate of return is 20%, what is the annualized interest rate? What if the six-year holding period rate of return is 32%? Q3:
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## This document was uploaded on 11/04/2011 for the course FINANCE 0901 at Brown College.

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Lecture4 - Chapter 5 00:52 Time-Varying Rates of Return In...

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