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Chapter 04Chapter 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!• http://www.timothysykes.com/2013/08/scary-

saving-facts/• http://www.statisticbrain.com/retirement-stati

stics/• http://www.gfmag.com/tools/global-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

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• 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 $Today $ Next Year$ 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

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Organizing Cash Flows

• Cash flow analysis*Inflow = Cash received

• a positive number

*Outflow = Cash going out• a negative number

InflowPositive #

InflowPositive #

OutflowNegative #Outflow

Negative #OrganizationOrganization

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Time Line Example

Outflow Inflow

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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

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Single-period Future Value

– Concept: Interest is earned on principal• Today’s cash flow + Interest = Value in 1 year

Formula:

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Single-period Future Value Example

– Assumptions:• Invest $100 today• Earn 5% interest annually (one period)

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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:

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Compounding & Future ValueExample

– Assumptions:• Invest $100 today• Earn 5% interest for more than one period

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The Power of Compounding• Compound interest is powerful wealth-

building tool exponential growth

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Present Value

• Opposite of Future Value– Future Value = Compounding– Present Value = Discounting

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Present Value

– Concept: Discounting• Value today of sum expected to be received in

future• Next period’s valuation ÷ One period of

discounting

Formula:

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Present Value Example

– Assumptions:• Banks pays $105 in 1 year• Interest rate = 5% interest

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Present Value Over Multiple Periods

– Concept: Discounting• Reverse of compounding over multiple periods

Formula:

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Present Value Over Multiple Periods Example

– Assumptions:• $100 payment five years in the future• Interest rate = 5% interest

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Present Value with Multiple Rates

– Concept: Discounting• Value today of sum expected to be received in

future -- variable rates of interest over time

Formula:

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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%

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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

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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:

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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:

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Rule of 72

– Concept: Compound Interest• How much time for an amount to double?

Formula: 72 / i = Time for amount to double

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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

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Interest Rate to Double an Investment

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Computing Interest Rates

– Concept: Solving for Interest Rate– Complex Calculation – Use financial

calculator

Formula:

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Computing Interest Rates Example

– Assumptions:• Bought asset for $350• Sold asset for $475• Timeframe: 3 years

– Interest Rate Computation – Use financial calculator

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Solving for Time

– Concept: Solving for Time

– Assumptions/Known Data:• Starting Cash Flow

• Interest Rate

• Future Cash Flow

– Complex calculation – use financial calculator

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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

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