Comm298-Week4-Discounted_cash_flow_valuation-wit

# Comm298-Week4-Discounted_cash_flow_valuation-wit - Com298:...

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Com298: Week 4 Discounted Cash Flow Valuation Learning Objectives: Focus on the following: Effects of multiple compounding. EAR and APR. Ordinary annuities and annuities due. Applications of FVA and PVA. Perpetuities. Multiple Compounding Multiple compounding: when interest is 1

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compounded m times a year. Products with different compounding periods: Virtually all bonds pay interest semi-annually. Most stocks pay dividends quarterly. Most mortgages, student loans and car loans require monthly payments. Compounding involves 3 types of interest rates: Quoted rates r (or the APR) Periodic rates (or the r/m) Effective annual rates (EAR) Multiple Compounding When the quoted rate is compounded m times, we use the following equation: FV = PV(1 + r/m) mt 2
r = quoted rate or annual percentage rate (APR) m = frequency of compounding Example: An investment of \$1 compounded quarterly at a quoted rate of 12% for 1 year (t): FV = 1 (1 + 0.12/4) 4 FV = 1 (1 + 0.03) 4 = 1.12551 This implies that the interest payment every quarter is equal to 3%. And this quarterly rate of 3% is compounded every quarter to give you an annual rate of 12.551% Multiple Compounding within 1 Year (t) FV = PV( 1 + r ) mt m r = 12% m = frequency of compounding Semi 3

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Annual FV = PV(1 + r/2) 2 = 1.1236 (m = 2) Quarterly FV = PV(1 + r/4) 4 = 1.1255 (m = 4) Monthly FV = PV(1 + r/12) 12 = 1.1268 (m = 12) Daily FV = PV(1 + r/365) 365 = 1.1275 (m = 365) Synchronization i.e. if you divide the r by m, then the exponent for the year t should be multiplied by m. Effective Annual Rate (EAR) EAR = (1 + r ) mt - 1 m r = 12% m = frequency of compounding Semi Annual EAR = (1 + r/2) 2 - 1 = 12.36 % (m = 2) Quarterly EAR = (1 + r/4) 4 - 1 = 12.55 % (m = 4) 4
Monthly EAR = (1 + r/12) 12 - 1 = 12.68 % (m = 12) Daily EAR = (1 + r/365) 365 - 1 = 12.7475 % (m = 365) Infinity EAR = e q – 1 where q = 0.12 = 12.7497 % EAR and Multiple Compounding EAR is the annual rate after accounting for the compounding of the periodic rate m times per year. EAR = (1 + r/m) mt - 1 EAR = (1 + APR/m) mt - 1 r = quoted rate or annual percentage rate (APR) r/m = periodic rate 5

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The EAR allows us to compare two alternative investments with different compounding periods. EAR for quarterly compounding can now be compared with the EAR for monthly compounding. Student Exercise EAR = (1 + APR/m) mt - 1 Find the EAR for each of the following: APR m EAR 7% quarterly 7.18 18% monthly 19.56 10% daily 10.52 14% infinity 15.02 (EAR = e q – 1) 6
Calculator Approach: 4 (x, y) 7 2 nd EFF = 7.1859% 12 (x, y) 18 2 nd EFF = ________ 365 (x, y) 10 2 nd EFF = _______ Annual Percentage Rate (APR) Banking regulations: Banking regulations require that the quoted rate or the APR must be disclosed by the lenders in all consumer loans. APR = the quoted rate.

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## This note was uploaded on 01/27/2011 for the course COMM 298 taught by Professor L during the Spring '10 term at Capilano.

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Comm298-Week4-Discounted_cash_flow_valuation-wit - Com298:...

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