1 chapter 04 time value of money 1: analyzing single cash flows mcgraw-hill/irwin copyright © 2012...
TRANSCRIPT
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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.
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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)
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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
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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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