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FNCE 2P91 (13)
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FNCE+2P91-Corporate+Finance-Notes-Chapter+Five+Continued+and+Chapter+Six.docx

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Department
Finance
Course
FNCE 2P91
Professor
Clarke Melville
Semester
Winter

Description
FNCE 2P91 - Section 05 Winter 2011 - Duration 03 18.01.11 FNCE 2P91: Corporate Finance-Notes-Chapter Five Continued and Chapter Six Notes Formula from Last Class: Question: How much would you have to save on your 30 birthday to have one million dollars when you retire at age 60? Assuming you can ear 8% compounding interest. Answer: Question: Compare Bobby and Brady’s saving plans th Bobby saves $1000 on his 20 birthday for retirement at age 60. th Brady will wait until age 30 then save $1000 and deposit $2000 at age 40 and $3000 on his 50 and save until age 60. Both can earn 10% interest. What has the greater future value at age 60? Answer: Therefore Bobby’s future value is greater than Brady’s future value. Question: What is the future value at the end of 10 years of $1000 invested today, $2000 in one year and $5000 invested in 5 years. You can earn 10% for the first 2 years then 8% from years 3 to 5 and 6% thereafter. Answer: INTEREST RATES: APRS AND EARS Can compound more than one per year Example: 10% compounding twice str year Investing $10 000 on January 1 on July you take the ( ) st On December 31 ( ) So effectively you earned FNCE 2P91 - Section 05 Winter 2011 - Duration 03 EFFECTIVE ANNUAL RATE Question: APR (annual percentage rate) or the quoted rate and calculate EAR (effective annual rate) 10% compounding semi-annually Formula: ( ) Where: m = the number of compounding periods Answer: ( ) Question Part Two: What is the effective annual rate of 8% compounding quarterly? Answer Part Two: ( ) APR (ANNUAL PERCENTAGE RATE)  Rate per period and number of periods = APR Question: So the APR of 1% per month = 12% APR Answer: ( ) USE EAR TO COMPARE DIFFERENT OPTIONS BANK A BANK B BANK C APR 16% 15% 15.5% Compounding Once Daily Quarterly EAR 16% ( ) ( ) Therefore Bank C has the highest effective rate USING EAR IN FV OR PV CASH ANALYSIS: Question: What is the FV of $1000 invested today for 2 years at 8% interest compounding semi-annually? FNCE 2P91 - Section 05 Winter 2011 - Duration 03 Answer: Method One: Calculate the EAR ( ) Method Two: Compounding 4 times at 4%: 4 times at 4% because every 6 months it is 4% (8% in one year), 2 years = 4 times CONTINUOUS COMPOUNDING: Formula: ( ) Where m ∞ If we have 10%: COMPOUNDS NUMBER OF TIMERS PER YEAR EAR Once 1 10% Twice 2 10.25% Quarterly 4 10.3818% Monthly 12 10.4713% Daily 365 10.51558% Minutely 525 000 10.51709% EXPRESSION OR CONTINUOUS COMPOUNDING: Question: EAR of 10% compounding continuously Answer: NOW WE CAN FLIP BETWEEN RATES: Question: What rate compounding semi-annually is equal to 8% compounding quarterly? FNCE 2P91 - Section 05 Winter 2011 - Duration 03 Answer: Make ( ) ( ) ( ) ( ) Therefore, be indifferent between 8.08% semi-annually and 8% quarterly Question: What is the present value of the following series of cash flows? Year 1 $500 Year 2 ($100) Year 3 ($500) Year 4 $1000 Interest is 12% daily compounding Answer: ( ) ANNUITIES Question: FV of $1000 each year for 3 years at 10% rate Answer: Definition: have to have a set or equal amount of cash flows (in example above $1000), have to have a set number of periods (years) and set interest rate (10%), and has to be finite (it has to end) If you have these things you have annuity. Annuities are golden in business. Examples: rent, cell phone bills, insurance, student loan, mortgage, “$1000 Weeks for Life” lottery, etc. Question: What is the FV of $1000 deposited each year for 10 years at 10% interest? FNCE 2P91 - Section 05
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