# Ch4 - Dr Yi Ch 4 Introduction to Time Value of Money Outlines of Ch 4 and 5 Time Value of Money(TVM Time is money Piazzas \$91 million contract Time

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Ch 4: Introduction to Time Value of Money Dr. Yi

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2 Outlines of Ch 4 and 5: Time Value of Money (TVM) Time is money ??? Piazza’s \$91 million contract Time value of money = opportunity cost Solve TVM problems Basics Simple present / future value problem Simple vs. Compound Interest (Power of Compound) Compounding Frequency Annuity / Annuity Due / Perpetuity Uneven cash flow Amortization Table Effective annual rate
3 Mike Piazza’s \$91 million Contract Mike Piazza's Contract (million) Today Contract Sum 1998 1999 2000 2001 2002 2003 2004 2005 Signing Bon 7.5 \$ 4.0 \$ 3.5 \$ Salary 83.5 \$ 6.0 \$ 11.0 \$ 12.5 \$ 9.5 \$ 14.5 \$ 15.0 \$ 15.0 \$ Total 91.0 \$ 10.0 \$ 11.0 \$ 12.5 \$ 13.0 \$ 14.5 \$ 15.0 \$ 15.0 \$ 0 1 2 3 4 5 6 7 Discount Rate Value in 1998 Dollars 9.7 \$ 10.4 \$ 11.4 \$ 11.6 \$ 12.5 \$ 12.6 \$ 12.2 \$ 3% 80.3 \$

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4 Basics: Time lines show timing of cash flows. CF 0 CF 1 CF 3 CF 2 0 1 2 3 i% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2. Today End of second year Start of third year
5 Basics: Four variables PV FV Interest rate, i Period, time length, or investment horizon, n FV 0 1 2 Year, n i% PV ( 29 1 n n FV PV i = +

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6 FV and PV Future Value Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate. Present Value Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.
7 Basics: What’s the FV of an initial \$100 after 3 years if i = 10%? FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding . 100

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8 10% Basics: What’s the PV of \$100 due in 3 years if i = 10%? Finding PVs is discounting , and it’s the reverse of compounding. 100 0 1 2 3 PV = ?
9 Compounding vs. Discounting

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10 Find the time-weighted value of three \$100s at year 2. 100 100 100 0 1 2 3 10% Compound the first 100 = 100 *1.1 = 110 Discount the last 100 = 100 / 1.1 = 90.9 PV at year 2 = 110 + 100 + 90.9 = 300.9 Alternatively, 248.69 * 1.1 2 = 300.9 Second alternatively, 331 / 1.1 = 300.9
11 Financial calculators solve this equation: There are 4 variables. If 3 are known, the calculator will solve for the 4th.

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## This note was uploaded on 02/28/2012 for the course FIN 3313 taught by Professor Yi during the Spring '12 term at Texas State.

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Ch4 - Dr Yi Ch 4 Introduction to Time Value of Money Outlines of Ch 4 and 5 Time Value of Money(TVM Time is money Piazzas \$91 million contract Time

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