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Ryerson University
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Finance
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FIN 502
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Joan Lobo
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Chapter 2

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CFIN502- Chapter 2- Time Value of Money
LEARNING OBJECTIVES
How to compare monetary amounts that you pay or receive at different times
Arithmetic of personal financial management
Time value of money—concept of rate of return
Understanding rate of return is an essential preparation for debt and credit management
and investment management
RATE OF RETURN—SINGLE PERIOD
Discount bond- investment that pays no interest during its life time
o Interest you receive on it is part of the final payment
k= CF -CF /CF
1 0 0
o Only holds for a single period with cash flows at the beginning and end of the period
Discount rate- interest rate or rate of return that we use to equate amounts of money paid or
received in different periods
Opportunity costs- what you can earn if you don’t spend the money today
o Discount rate simply tells you in monetary value the amount you are giving up
o You can look at it as the discount rate what makes us indifferent between present
and future amounts
Best alternative available
o In order to compare alternative investments—must keep everything equal (risk,
income tax, time of length)
RATE OF RETURN—MULTIPERIOD
∑
Arithmetic mean return=
o Used in analyzing investments when we want to estimate an average or expected
return across different investments in the same period
∏ [ ]
Geometric mean return=
o Rate of return compounded to the same final answer as the individual rates
multiplied together
o Lower than or equal to the arithmetic mean return
COMPOUNDING MORE FREQUENTLY THAN ANNUALLY
Annual percentage rate- conventional method of quoting interest rates that ignores the
compounding effect completely
o Used for quoting rates for consumers, residential mortgages, corporate/ commercial
mortgages and other loans, and bond yields
o APR=
Effective annual rate- compound the periodic rate the number of times there are periods in
the year
o EAR=
MECHANICS OF TIME VALUE
Discount rate- opportunity cost of spending your money now instead of investing it in the
best available investment
Future and present value—single period
o FV= PV (1+k)
o PV=FV/(1+k)
o Important mathematical fact most interest rate mathematics deals with
(1+discount rate)—preserve this relationship
Future and present value—multiperiod
o Compound interest- each year the interest earned increases—interest on interest
o FV= PV(1+k)t
o PV= FV/(1+k)t
o Future value interest factor- 1/(1+k)
Annuities (IFA) - any payment that is the same amount for many consecutive periods
o End of the period—ordinary or deferred annuity
o Beginning of the period—annuity due
o FVIFA=(1+k) -1/k
o PVIFA=[1-[1/(1+k) ]]/1
Constant growth annuity (CGA)- stream of payments that grows at a constant rate
1 CFIN502- Chapter 2- Time Value of Money
[ ]
o PVCGA= { }
[ ]
o FVCGA= { }
o If the first payment is paid at the beginning of the year—constant growth annuity
due (CGAD)
FVCGAD=(1+k)(FVCGA)
PVCGAD= (1+k)(PVCGA)
FACTORS AFFECTING DISCOUNT RATES
Pure time premium- the price that we demand for waiting before we consume
o Rate of return that would theoretically exist if there were no risk of any kind that
the rate will change or not be paid—no inflation and no income taxes
o Economist estimate that it is 2-4% per annum
Risk
o May take in a form of a probability that we wont be paid a

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