1 Chapter 04 Time Value of Money 1: Analyzing Single Cash Flows McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Saving and TVM! Very Important! saving-facts/ saving-facts/ statistics/ statistics/ database/economic-data/12065-household- saving-rates.html#axzz2sMoMbhkkhttp:// database/economic-data/12065-household- saving-rates.html#axzz2sMoMbhkk –Data from OECD (Org. for Economic Co- operation and Development)

Introduction Time Value of Money (TVM) –Powerful financial decision-making tool –Used by financial and nonfinancial business managers –Key to making sound personal financial decisions 4-3

TVM Basic Concept: –$1 today is worth more than $1 next year TVM Decision Based on: –Size of cash flows –Time between cash flows –Rate of return Introduction (cont.) $Today $ Next Year > 4-4

Organizing Cash Flows Cash flow timing key to successful business operations Cash flow analysis –Time line shows magnitude of cash flows at different points in time Monthly Quarterly Semi-annually Annually 4-5

Organizing Cash Flows Cash flow analysis *Inflow = Cash received a positive number *Outflow = Cash going out a negative number Inflow Positive # Inflow Positive # Outflow Negative # Outflow Negative # Organization 4-6

Time Line Example OutflowInflow 4-7

Future Value Value of an investment after one or more periods For example: the $105 payment your bank credits to your account one year from the original $100 investment at 5% annual interest 4-8

Single-period Future Value –Concept: Interest is earned on principal Today’s cash flow + Interest = Value in 1 year Formula: 4-9

Single-period Future Value Example –Assumptions: Invest $100 today Earn 5% interest annually (one period) 4-10

Compounding & Future Value –Concept: Compounding Interest is earned on both principal and interest Today’s cash flow + Interest on Principal and Interest on Interest = Value in 2 years Formula: 4-11

Compounding & Future Value Example –Assumptions: Invest $100 today Earn 5% interest for more than one period 4-12

The Power of Compounding Compound interest is powerful wealth- building tool  exponential growth 4-13

Present Value Opposite of Future Value –Future Value = Compounding –Present Value = Discounting 4-14

Present Value –Concept: Discounting Value today of sum expected to be received in future Next period’s valuation ÷ One period of discounting Formula: 4-15

Present Value Example –Assumptions: Banks pays $105 in 1 year Interest rate = 5% interest 4-16

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Present Value Over Multiple Periods –Concept: Discounting Reverse of compounding over multiple periods Formula: 4-18

Present Value Over Multiple Periods Example –Assumptions: $100 payment five years in the future Interest rate = 5% interest 4-19

Present Value with Multiple Rates –Concept: Discounting Value today of sum expected to be received in future -- variable rates of interest over time Formula: 4-20

Present Value with Multiple Rates Example –Assumptions: Banks pays $2,500 at end of 3rd year –Interest rate year 1 = 7% –Interest rate year 2 = 8% –Interest rate year 3 = 8.5% 4-21

Present Value & Future Value –Concepts: Discounting & Compounding Move cash flows around in time –Use PV Calculation to discount the Cash Flow –Use FV Calculation to compound the Cash Flow 4-22

PV & FV Example –Assumptions PV: Expected cash flow of $200 in 3 years Decision: change receipt of CF to 2 years (one year earlier) Discount rate = 6% –PV Calculation to Discount the Cash Flow for 1 year: 4-23

PV & FV Example –Assumptions FV: Expected cash flow of $200 in 3 years Decision: change receipt of CF to 5 years later Compound rate = 6% –FV Calculation to Compound the Cash Flow for 5 years: 4-24

Rule of 72 –Concept: Compound Interest How much time for an amount to double? Formula: 72 / i = Time for amount to double 4-25

Rule of 72 Example –Assumptions: Interest rate = 6% interest –Rule of 72 calculation: 72 = Amount of time for amount to double 6 72 / 6 = 12 years 4-26

Interest Rate to Double an Investment 4-27

Computing Interest Rates –Concept: Solving for Interest Rate –Complex Calculation – Use financial calculator Formula: 4-28

Computing Interest Rates Example –Assumptions: Bought asset for $350 Sold asset for $475 Timeframe: 3 years –Interest Rate Computation – Use financial calculator 4-29

Solving for Time –Concept: Solving for Time –Assumptions/Known Data: Starting Cash Flow Interest Rate Future Cash Flow –Complex calculation – use financial calculator 4-30

Solving for Time Example –Question: When interest rates are 9%, how long will it take $5,000 to double? –Assumptions: Interest = 9% PV = -5,000 PMT = 0 FV =10,000 –Solution: 8.04 years 4-31