Micro Ch 15

© 2015 Pearson Education, Inc.

Chapter 15 Trade-offs

Involving Time and Risk


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



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.



Key Ideas

3. Economists have developed tools to calculate the value of risky payments.



Evidenced-Based Economics Example:

Do people exhibit a preference for immediate gratification?



One-third of long- term smokers die prematurely.

So what?


15.1 Modeling Time and Risk

When is $1 not worth $1?



In the future = less value



Future outcomes have risk.



To compare costs/benefits of current events with costs/benefits of future events, use factors to weight time and risk.


15.2 The Time Value of Money



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)



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



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



Future value

The sum of principal and interest In general,

Compound interest formula

Future value = principal x (1 + r)T



“Compound interest is the greatest invention of all time.”

A. Einstein



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



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



Exhibit 15.1 Value of a $1 Investment over the Next 50 Years



Exhibit 15.2 The Mechanics of Lending and Borrowing



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?



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


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



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



General present value formula:

Present value = Payment T periods from now (1 + interest rate)T



Invest $10,000 today to get $20,000 in 20 years.

Good deal?

Present value = $20,000/(1.05)20 = $7,538



$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



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?



$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


15.3 Time PreferencesTime Discounting

What does time preference have to do with marshmallows?

http://www.youtube.com/watch?v=QX_oy9614HQ



Utils

Individual measures of utility or happiness

Discount weight

Multiplies future utils to translate them into

current utils



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



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



What about starting a diet? Should you start a diet today or wait until tomorrow?



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



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”



One-third of long- term smokers die prematurely.

So what?



Evidenced-Based Economics Example:

Do people exhibit a preference for immediate gratification?


15.4 Probability and Risk

Risk

When an outcome is not known with certainty in advance


15.4 Probability and RiskRoulette Wheels and Probabilities

Probability

Frequency with which something occurs


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?


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.



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



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



If number is 50 or below, win $200

If number is 51 or higher, lose $100



PayoffProbability of Occurring

Expected Value (payoff x probability)

$200 50/100 = .5 $100

-$100 50/100 = .5 -$50

Sum 100/100 $50


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?



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



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


15.5. Risk Preferences

Given that, in general, extended warranties are not a good deal, why do people buy them?



Loss aversion

Psychologically weighting a loss more heavily thanweighting a gain



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



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



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%



Risk aversePrefer less risk (Option 1)

Risk seekingPrefer more risk (Option 3)

Risk neutralDon’t care about risk (any option)

Micro Ch 15

Economy & Finance

Transcript of Micro Ch 15