Comm298-Week4-Discounted_cash_flow_valuation-wit

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

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

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

Page1 / 26

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online