M.Sc. Finance
M.Sc. Investment & Finance
M.Sc. International Banking & Finance
and
M.Sc. International Accounting & Finance
Time Value of Money – The Role of Interest
Rates in Decision Taking
30th September 2009
J R Davies
Finance I
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Understanding Interest Rates: Determination and Future Value Factors, Lecture notes of Finance
The concept of interest rates, their relationship with productivity and preference, and how to calculate the future value of a sum using future value factors. It also covers the time dimension in investment/financing decisions and provides examples of using future value factors to determine the future value of a sum.
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2010/2011
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M.Sc. Finance
M.Sc. Investment & Finance
M.Sc. International Banking & Finance
and
M.Sc. International Accounting & Finance
Time Value of Money – The Role of Interest
Rates in Decision Taking
30
th
September 2009
J R Davies
Finance I
Time Value of Money
A pound today is worth more than a pound to-morrow………even in the absence of
Risk and uncertainty
Inflation
The time value of money stems from the interest rate– effectively the price that balances the supply anddemand for loans.
The rate of interest in turn reflects
The productivity (at the margin) of realinvestments
The preference (at the margin) for consumptiontoday rather than some time later
As a result of the time value of money it is notpossible to sum costs and benefits anticipated atdifferent points in time
Interest Rates
The riskless real rate of interest (r
0
): the rate of
interest that can be expected in the absence of
Risk and uncertainty
Inflation
A premium is added to the real rate of interest for
Risk and uncertainty.
Inflation.
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Time Dimension – Investment/Financing Decisions
Capital Budgeting (RealInvestments)
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Adjusting Values to Allow for Interest (1)
Assume the interest rate is 10 % ie 0.10 What are the equivalent values at the end of one year, year two,
etc to a sum of £100 available today?
100
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Adjusting Values to Allow for Interest (2)
Given an interest rate of 10 % what is the equivalent value at the
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1
2
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The original sum (£100) plus interest that can be earnedover one year (£10).
time
Adjusting Values to Allow for Interest (4)
Given an interest rate of 10 %
£100 today £110 next year^ £121 two years from now
all have the same value, and are equally acceptable (assume no risk and no inflation for simplicity).
Future Value Factors
To obtain the equivalent value at a point in time in thefuture of a sum available today we must multiply this sumby a future value factor – also referred to as a compoundinterest factor, or more simply as the interest factor – toallow for interest that can be earned on the sum availableto-day:
FVF
n/r
= (1 + r)
n
where
r
is the rate of interest
n
is the number of time periods in thefuture
Developing Future Value Factors
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