Topic 2 Time Value of Money

# Topic 2 Time Value of Money - Topic Two part 1 First...

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Topic Two – part 1 First Principles of Valuation: The Time Value of Money

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Overview Distinguish between simple and compound interest. Calculate the present value and future value of a single amount for both one period and multiple periods. Calculate the present value and future value of multiple cash flows. Calculate the present value and future value of annuities.
Compound versus Simple Interest Assume you make a deposit into a bank account If the Bank pays you simple interest the interest payment each year will be the same and will be the interest rate times the initial amount. If the bank pays you compound interest you will receive interest payments not just on the initial amount but also on previous interest payments

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Receiving \$1 today is worth more than \$1 in the future The opportunity cost of \$1 in the future is the interest we could have earned on \$1 if received earlier Today Future Time value of money
Compounding Translating \$1 today into its equivalent future value Discounting Translating a future \$1 into its equivalent present value today Compounding & discounting

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Future value (FV) is the amount an investment is worth after one or more periods. (the amount it has grown to) Present value (PV) is the current value of future cash flows of an investment. (the amount in today’s dollars) 0 1 2 3 4 PV FV End End End End
Time value terminology The number of “interest paying” time periods between the present value and the future value is represented by ‘n’. The rate of interest for discounting or compounding is called ‘r’. n and r need to be consistent. if interest is paid monthly the number of periods n has to be worked out in terms of months All time value questions involve four values: PV, FV, r and n. Given three of them, it is always possible to calculate the fourth.

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Future value of a single amount Example 1 You invest \$100 in a savings account that earns 10% interest per annum (compounded) for three years. After one year: \$100 × (1+0.1) = \$110 After two years: \$100 × (1+0.1)(1+0.1) = \$121 After three years: \$100 × (1+0.1)(1+0.1)(1+ 0.1) = \$133.10
More Generally For one period: ( 29 n r 1 V FV + = P

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Comparing Simple and Compound Interest Simple interest refers to interest earned only on the original capital investment amount. FV = PV(1 + r n) (Eg \$100 for 3 years at 10% Simple Interest will accumulate to \$130) Compound interest refers to interest earned on both the initial capital investment and on the interest reinvested from prior periods. FV = PV(1 + r ) n In finance it is almost always compound interest that is used
Making use of Example 1: \$100 invested at 10% for 3 years The accumulated value of this investment at the end of three years can be split into two components: original principal \$100 interest earned \$33.10 Using simple interest, the total interest earned would only have been \$30. The other \$3.10 is from compounding that is, interest on interest. Comparing Simple and Compound Interest

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## This note was uploaded on 04/24/2011 for the course BAFI 1012 taught by Professor Michaelgangemi during the Three '10 term at Royal Melbourne Institute of Technology.

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Topic 2 Time Value of Money - Topic Two part 1 First...

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