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Finance

FNCE 2P91

Clarke Melville

Winter

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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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