Micro Ch 15
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Transcript of Micro Ch 15
© 2015 Pearson Education, Inc.
15 Trade-offs Involving Time and Risk
Chapter Outline
15.1 Modeling Time and Risk15.2 The Time Value of Money15.3 Time Preferences15.4 Probability and Risk15.5 Risk Preferences
© 2015 Pearson Education, Inc.
15 Trade-offs Involving Time and Risk
Key Ideas
1. Interest is the payment received for temporarily giving up the use of money.
2. Economists have developed tools to calculate the present value of payments received at different points in the future.
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15 Trade-offs Involving Time and Risk
Key Ideas
3. Economists have developed tools to calculate the value of risky payments.
© 2015 Pearson Education, Inc.
15 Trade-offs Involving Time and Risk
Evidenced-Based Economics Example:
Do people exhibit a preference for immediate gratification?
© 2015 Pearson Education, Inc.
15 Trade-offs Involving Time and Risk
One-third of long- term smokers die prematurely.
So what?
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15.1 Modeling Time and Risk
To compare costs/benefits of current events with costs/benefits of future events, use factors to weight time and risk.
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
PrincipalThe amount of an original investment
InterestThe payment received for temporarily giving
up the use of money (or payment for the opportunity to temporarily use someone else’s money)
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Starting Principal: $100 After One Year: $100 + $100 x (0.08) = $100 x (1 + 0.08) = $108.00
After Two Years: $108 + $108 x (0.08) = $108 x (1 + 0.08) = $116.64 = [$100 x (1 + 0.08)](1 + 0.08) = $100 x (1 + 0.08)2
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
After Three Years: $116.64 + $116.64 x (0.08) = $116.64x (1 + 0.08) = $125.97 = [$100x(1 + 0.08)2] (1 + 0.08) = $100 x (1 + 0.08)3
After T Years: = $100 x (1 + 0.08)T
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Future value
The sum of principal and interest In general,
Compound interest formula
Future value = principal x (1 + r)T
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
“Compound interest is the greatest invention of all time.”
A. Einstein
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Cousin It:• Starts saving $2,000 per year beginning at
age 18• Saves at this rate up to and including age
25, then stops saving and lets the account sit• Earns 10% per year
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Cousin Id:• Picks up where It left off and starts saving
$2,000 per year beginning at age 26• Saves at this rate up to and including age 62,
then stops saving• Earns 10% per year
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Exhibit 15.1 Value of a $1 Investment over the Next 50 Years
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Exhibit 15.2 The Mechanics of Lending and Borrowing
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Assume:
• Credit card has a balance of $897.30• Pay monthly minimum of $15 per month• 18% APR = 1.5% per month
• How long will it take to pay off the balance if you do not add new purchases?
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15.2 The Time Value of MoneyFuture Value and the Compounding of Interest
Payment Balance PaymentAmt. Applied
to InterestAmt. Applied to Principle New Balance
1 $897.30 $15 $13.46 $1.54 $895.762 895.76 15 13.44 1.56 894.203 894.20 15 13.41 1.59 892.614 892.61 15 13.39 1.61 891.005 891.00 15 13.37 1.63 889.376 889.37 15 13.34 1.66 887.717 887.71 15 13.32 1.68 886.038 886.03 15 13.29 1.71 884.329 884.32 15 13.26 1.74 882.58
10 882.58 15 13.24 1.76 880.8211 880.82 15 13.21 1.79 879.0312 879.03 15 13.19 1.81 877.22
Total $180
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15.2 The Time Value of MoneyPresent Value and Discounting
When is $1 not worth $1?
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15.2 The Time Value of MoneyPresent Value and Discounting
Future value = principal x (1 + r)T
$3,000 = principal x (1.08)3
$3,000/(1.08)3 = principal
Or $2,381.50 = principal
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15.2 The Time Value of MoneyPresent Value and Discounting
Present value
The present value of a future payment is the amount of money that would need to be invested today to produce that future payment.
Also called the discounted value of a future payment
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15.2 The Time Value of MoneyPresent Value and Discounting
General present value formula:
Present value = Payment T periods from now (1 + interest rate)T
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15.2 The Time Value of MoneyPresent Value and Discounting
Invest $10,000 today to get $20,000 in 20 years.
Good deal?
Present value = $20,000/(1.05)20 = $7,538
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15.2 The Time Value of MoneyPresent Value and Discounting
$20,000 in 20 years is worth $7,538 today.
Why would you pay $10,000 for something worth $7,538? That’s $2,462 too much!
Net present valuePresent value of benefits minus present
value of costs
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15.2 The Time Value of MoneyPresent Value and Discounting
Does it matter how you get the $20,000? What if you got $10,000 of it in ten years and $10,000 five years later?
Good deal?
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15.2 The Time Value of MoneyPresent Value and Discounting
$10,000 in 10 years:
Present value = $10,000/(1.05)10 = $6,139
$10,000 in 15 years:
Present value = $10,000/(1.05)15 = $4,810
$6,139 + $4,810 = $10,949 - $10,000 = $949
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15.3 Time PreferencesTime Discounting
What does time preference have to do with marshmallows?
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15.3 Time PreferencesTime Discounting
Utils
Individual measures of utility or happiness
Discount weight
Multiplies future utils to translate them into
current utils
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15.3 Time PreferencesTime Discounting
Choose between one marshmallow now or 2 marshmallows in 10 minutes.
Suppose each marshmallow has a utility of 6 utils. But the discount rate for waiting 10 minutes is 1/3.
One marshmallow now = 6 utilsTwo marshmallows in 10 minutes = 4 utils
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15.3 Time PreferencesTime Discounting
Choose between one marshmallow now or 2 marshmallows in 10 minutes.
Suppose each marshmallow has a utility of 6 utils. If you are better at waiting, the discount rate could be 2/3.
One marshmallow now = 6 utilsTwo marshmallows in 10 minutes = 8 utils
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15.3 Time PreferencesTime Discounting
What about starting a diet? Should you start a diet today or wait until tomorrow?
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15.3 Time PreferencesTime Discounting
Starting today:Benefit is become healthier more quicklyCost is giving up food you enjoy earlier
Starting tomorrow:Benefit is you get to eat what you want for
another dayCost is delaying becoming healthier
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15.3 Time PreferencesTime Discounting
Problem:
The benefit of starting today is in the future, while its cost is immediate.
The benefit of starting tomorrow is immediate, while the cost is in the future.
Result: diets that always start “tomorrow”
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15.3 Time PreferencesTime Discounting
One-third of long- term smokers die prematurely.
So what?
© 2015 Pearson Education, Inc.
15.3 Time PreferencesTime Discounting
Evidenced-Based Economics Example:
Do people exhibit a preference for immediate gratification?
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15.4 Probability and Risk
Risk
When an outcome is not known with certainty in advance
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15.4 Probability and RiskRoulette Wheels and Probabilities
Probability
Frequency with which something occurs
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15.4 Probability and RiskIndependence and the Gambler’s Fallacy
Your lucky number is 27 and you’ve won 10 times in a row!
What number should you bet next?
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15.4 Probability and RiskExpected Value
Expected value
A probability-weighted value
Present and future values are weighted by time.
Expected values are weighted by probability of occurrence, or risk.
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15.4 Probability and RiskExpected Value
Bet on number 64.If win, get $100If ball goes on number 15, lose $200If ball goes on another number, nothing
Expected value = sum of payoffs x probability of occurring
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15.4 Probability and RiskExpected Value
PayoffProbability of Occurring
Expected Value (payoff x probability)
$100 1/100 = .01 $1
-$200 1/100 = .01 -$2
$0 98/100 = .98 $0
Sum 100/100 -$1
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15.4 Probability and RiskExpected Value
If number is 50 or below, win $200
If number is 51 or higher, lose $100
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15.4 Probability and RiskExpected Value
PayoffProbability of Occurring
Expected Value (payoff x probability)
$200 50/100 = .5 $100
-$100 50/100 = .5 -$50
Sum 100/100 $50
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15.4 Probability and RiskExtended Warranties
You buy a $300 TV with a 1-year warranty included.
You can buy an extended warranty for years 2 and 3 for another $75.
Should you do it?
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15.4 Probability and RiskExtended Warranties
Two components: risk and present value
Risk—assume the probability of breakdown is 10% per year.
Present value—if TV breaks in year 2, could replace it for $250 without a warranty;
in year 3, could replace for $200
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15.4 Probability and RiskExtended Warranties
First, present value (assume 10%):
Present value = - $75 + $250/(1.1)2 + $200/(1.1)3
= -$75 + $206.61 + $150.26
But these benefits do not occur with certainty, so to get expected value:
-$75 + $206.61(10/100) + $150.26(10/100)= -$39.31
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15.5. Risk Preferences
Given that, in general, extended warranties are not a good deal, why do people buy them?
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15.5. Risk Preferences
Loss aversion
Psychologically weighting a loss more heavily thanweighting a gain
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15.5. Risk Preferences
Choose between:
Option 1: getting $0, OROption 2: $200 gain if heads or $100 loss if
tails
Expected value of Option 1: $0Expected value of Option 2: $200(1/2) + (-$100)(1/2) = $50
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15.5. Risk Preferences
What if you’re this person?
Would you pick Option 2 if you have this amount of loss aversion?
Expected value = $200(1/2) + 2 x (-$100)(1/2) = $0
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15.5. Risk Preferences
Option 1: 1 Possible Outcome: 6% Expected Rate of Return = 6% Option 2: 3 Possible Outcomes: 5%, 6%, and 7% (all equally likely) Expected Rate of Return = 6% Option 3: 5 Possible Outcomes: -4%, 1%, 6%, 11%, and 16% (all equally likely) Expected Rate of Return = 6%