Lecture02_Canvas.pdf - Lecture 2 Valuing Investment Prof Zhang University of Texas at Austin McCombs School of Business Outline 1 Compounding 2

Lecture02_Canvas.pdf - Lecture 2 Valuing Investment Prof...

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Lecture 2 Valuing Investment Prof. Zhang University of Texas at Austin McCombs School of Business Outline 1 Compounding 2 Discounting 3 Perpetuities 4 Annuities FIN 367, Lecture 2 Valuing Investment 2 / 42
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Outline 1 Compounding 2 Discounting 3 Perpetuities 4 Annuities FIN 367, Lecture 2 Valuing Investment 2 / 42 Motivation At the most general level, an investment is a claim to a stream of cash flows. Both real and financial investments. In order to choose between different investments, we must therefore find a way to compare cash flows differing in Size Timing Risk We will first focus on the size and timing of the cash flows and ignore risk for now. Compounding and discounting allow us to compare cash flows differing in size and timing. FIN 367, Lecture 2 Valuing Investment 3 / 42
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Time Value of Money In general, a dollar today is worth more than a dollar in one year. The difference in value between money today and money in the future is called the time value of money . Suppose you deposit $100 in a bank account which pays 10% interest, you will have $110 at the end of next year. When we compare cash flows at different periods of time, we should take the time value of money into consideration. FIN 367, Lecture 2 Valuing Investment 4 / 42 Compounding and Future Value: Illustrative Example Suppose you deposit $100 in a bank account which pays 10% interest: Money in the account after one year: Investment: $100 Interest: $10 = $100 × 10% Total: $110 = $100(1+10%) Suppose that the interest is credited to your account once a year. Money in the account after two years: Investment: $110 Interest: $11 =$110 × 10% Total: $121 = $100(1 + 10%) 2 Money in the account after three years: Investment: $121 Interest: $12.1 = $121 × 10% Total: $133.1 = $100(1 + 10%) 3 Continuing this reasoning, you will have $100(1 + 10%) T at the end of T years. FIN 367, Lecture 2 Valuing Investment 5 / 42
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Compounding and Future Value: General Case More generally, suppose you deposit $ C in a bank account which pays an interest rate of r % per year: Money in the account after one year: Investment: $C Interest: $C × r% Total: $C(1+r%) Suppose that the interest is credited to your account once a year. Money in the account after two years: Investment: $C(1+r%) Interest: $C(1+r%) × r% Total: $ C (1 + r %) 2 Continuing this reasoning, you will have $ C (1 + r %) T at the end of T years. FIN 367, Lecture 2 Valuing Investment 6 / 42 Future Value and Compounding Factor $ C (1 + r %) T is the future value in T years of an initial investment of $C that earns r% compounded annually. (1 + r %) T is called the T-period compounding factor. FIN 367, Lecture 2 Valuing Investment 7 / 42
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More Frequent Compounding Suppose you deposit $ C in a bank account which pays r % interest, and that interest is credited to your account twice a year: You can then show that you will have $ C (1 + r % 2 ) after 6 months, $ C (1 + r % 2 ) 2 after a year, ..., $ C (1 + r % 2 ) 2 T after T years.
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