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Lecture

# Ch 5 - Economic Factors - Time Value of Money.docx

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Wilfrid Laurier University

Business

BU111

Valerie Irie

Fall

Description

Economic Factors: Financial Problems
Time value of money
• Is $1 one year from today worth the same as $1 today?
• No! Its worth less because of:
-Risk: what if something happens to ability to generate and provide dollar, always increasing element of
risk
-Inflation: eating away at what can be bought with a dollar, worth less
• Concept important to leases, mortgages, bonds, retirement contributions, stock valuation,
project selection
Single amount – FV Single period
amount accumalates, so use exponent
Single amt – FV Multiple periods
• How much money will you have in five years if you deposit $200 into an account that earns 3%
compounded annually?
FV= 200 (1+.03)^5 =$231.85
Single amount – PV Single period • How much do you have to deposit today to have $100 after one year (assuming 4% interest
compounded annually?) OR what is the present value of $100 to be received in one year
(assume a 4% discount rate).
Single amt – PV Multiple periods
• How much do you have to deposit today to have $100 after three years (assuming 4% interest
compounded annually?) OR what is the present value of $100 to be received in three years
(assume a 4% discount rate).
FV - Multiple payments & periods
• What will you have after three years if you deposit $100 each year for three years (beginning at
the end of this year) into an account that earns 4% interest compounded annually?
• As long as payments don’t start today, called an ordinary annuity
• First payment compounds only twice, second once, third none
• ****Depends on how long invested for****
Variables
R=Rate (i.e. 4%=.04)
N=Number of years (i.e. 4 years=4)
PMT=Amount of money deposited
What will you have after three years if you deposit $100 annually/Payment
each year for three years STARTING TODAY into an
account today that earns 4% interest compounded FV=Future Value
annually? PV=Present Value
• First payment compounds three times, second two, third once, etc.
Annuities
• Annuity: multiple but equal payments over equal periods of time
• Ordinary Annuity = payment does not start today • Annuity Due = payment starts today
• Ordinary does not need to start at end of year, can be at end of month, quarter, etc.
Sample problem
• How much will you have in your retirement account in 10 years if you deposit $500 per year
starting at the end of this year (assume 3% compounded annually)?
What if we began saving immediately?
• How much must we put in an account each year earning 4% if we want to have $20,000 at the
end of 10 years?
Calculating number of years
• How many years must I save to have $100,000 if I am able to save $2,000 each year in an
account the earns 2.5% compounded annually? Going to start saving today
n
(1r) 1
FV annuity dueMT r 1r
Re-arrange formula to isolate 'n' (compound periods) and use log formula to solve for exponent
PV - Multiple payments & periods
• How big must your savings account be today if you want to receive a payment of $500 each year
for the next three years? Assume an interest/discount rate of 4%.
-ordinary annuity as payments didn’t start today
PV=500((1/.04)-(1/(.04(1+.04)^3))=$1387.55
• How big must your savings account be today if you want to receive a payment of $500 each year
for the next three years starting today? Assume an interest/discount rate of 4%. Sample problem
• You borrowed $20,000 to fund your education. How big will your educational loan payments be
if you want to have the loan paid off in four years, you make the first payment at the end of this
year, and the discount rate is 3%?
Perpetuity
• Annuity that goes on forever, e.g. dividend on a preferred share
• What is the value of an investment in a 5% preferred with a par value of $12 if interest rates are
3%?
Payment & compounding periods
• Payment and interest periods must be the same
• Always multiply “n” by number of payments per year
• Adjust compounding rate to match payment frequency (this is your new “r”)
Interest and payment periods same but mo

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