Chapter 6

# Chapter 6 - Discount Cash Flow Valuation - Chapter 6 Yihui...

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Discount Cash Flow Valuation -- Chapter 6 Yihui Wang Discount Cash Flow Valuation

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Main Issues • Compound Interest Rate APRs and EARs Compounding • Value additivity • Shortcut to special cash flows Annuity Perpetuity Discount Cash Flow Valuation 2
Comparing Rates: APR and EAR • Typically compound interest is quoted using an annual percentage rate (APR) with an associated di i l compounding interval. APR = period rate * the number of periods per year f ti A l R t AR) i th t l t id ( Effective Annual Rate (EAR) is the actual rate paid (or received) after accounting for compounding that curs during the year. occurs during the year. • To compare cash flows with different compounding period, use EAR, not APR! Discount Cash Flow Valuation 3

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Comparing Rates: Example eet Bank offers a one ar CD compounded Fleet Bank offers a one-year CD compounded semiannually, paying a 6% APR. If you invest \$10,000, how much money would you have at the end of one year? What is the actual annual rate of interest you earn? Quoted APR of 6% is not the “true” annual rate. It is only used to compute the 6-month interest rate (6%)(1 / 2) = 3% ti \$10 000 t th d f h Investing \$10,000, at the end of one year you have: 10,000(1+.03)(1+.03) = 10 , 000(1 . 0609) = 10 , 609 he “true” annual rate, AR is = (1+.03) 2 - = 6 % Discount Cash Flow Valuation The true annual rate, EAR , is r (1 .03) 1 6 . 09% 4
Computing EARs • Let APR be the annual percentage rate and m be the number of compounding intervals per year. One ll i d d i ld d ll i PR dollar invested today yields dollars in one year. AR i i b m m APR ) 1 ( + AR APR • EAR is given by ) 1 ( ) 1 ( EAR m m + = + m APR AR or 1 ) 1 ( + = m EAR Discount Cash Flow Valuation 5

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Computing EARs – Example 1 • Suppose if you put your money in an bank account and you earn 3% per quarter. hat is the APR? What is the APR? How much are you effectively earning, or EAR? Discount Cash Flow Valuation 6
Computing EARs – Example 2 • You are looking at two savings accounts. One pays 5.25%, with daily compounding. The other pays 3% i h i l di Whi h 5.3% with semiannual compounding. Which account should you use? Why? Discount Cash Flow Valuation 7

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Computing APRs • If you have an effective rate, how can you compute the APR? Rearrange the EAR equation and you get: 1 + = 1 - EAR) (1 m APR m Discount Cash Flow Valuation 8
Computing APRs - Example • Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay? Discount Cash Flow Valuation 9

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Present Value with Daily Compounding • You need \$15,000 in 3 years for a new car. If you can deposit money into an account that pays an APR 5 5% b d d il di h h of 5.5% based on daily compounding, how much would you need to deposit?
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## This note was uploaded on 02/16/2011 for the course ACCT 233 taught by Professor 123 during the Spring '11 term at CUHK.

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Chapter 6 - Discount Cash Flow Valuation - Chapter 6 Yihui...

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