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Chapter 04 McGraw-Hill/Irwin Time Value of Money 1: Analyzing Single Cash Flows Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.1 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 4-2 Introduction (cont.) • 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 $Today > $ Next Year 4-3 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 4-4 Organizing Cash Flows • Cash flow analysis *Inflow = Cash received • a positive number *Outflow = Cash going out • a negative number Inflow Positive # Organization Outflow Negative # 4-5 Time Line Example Outflow Inflow 4-6 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 4-7 Single-period Future Value – Concept: Interest is earned on principal • Today’s cash flow + Interest = Value in 1 year Formula: 4-8 Single-period Future Value Example – Assumptions: • Invest $100 today • Earn 5% interest annually (one period) 4-9 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: 4-10 Compounding & Future Value Example – Assumptions: • Invest $100 today • Earn 5% interest for more than one period 4-11 The Power of Compounding • Compound interest is powerful wealthbuilding tool exponential growth 4-12 Present Value • Opposite of Future Value – Future Value = Compounding – Present Value = Discounting 4-13 Present Value – Concept: Discounting • Value today of sum expected to be received in future • Next period’s valuation ÷ One period of discounting Formula: 4-14 Present Value Example – Assumptions: • Banks pays $105 in 1 year • Interest rate = 5% interest 4-15 4-16 Present Value Over Multiple Periods – Concept: Discounting • Reverse of compounding over multiple periods Formula: 4-17 Present Value Over Multiple Periods Example – Assumptions: • $100 payment five years in the future • Interest rate = 5% interest 4-18 Present Value with Multiple Rates – Concept: Discounting • Value today of sum expected to be received in future -- variable rates of interest over time Formula: 4-19 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% 4-20 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 4-21 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: 4-22 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: 4-23 Rule of 72 – Concept: Compound Interest • How much time for an amount to double? Formula: 72 / i = Time for amount to double 4-24 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 4-25 Interest Rate to Double an Investment 4-26 Computing Interest Rates – Concept: Solving for Interest Rate – Complex Calculation – Use financial calculator Formula: 4-27 Computing Interest Rates Example – Assumptions: • Bought asset for $350 • Sold asset for $475 • Timeframe: 3 years – Interest Rate Computation – Use financial calculator 4-28 Solving for Time – Concept: Solving for Time – Assumptions/Known Data: • Starting Cash Flow • Interest Rate • Future Cash Flow – Complex calculation – use financial calculator 4-29 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 4-30