Chapter 11 - Time and uncertainty. After studying this chapter you will be able to understand: Why money is worth more now than in the future? How compounding works over time? How to calculate the present value of a future sum? What the costs and benefits are of a choice using expected value? How risk aversion makes a market for insurance possible?...
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Chapter 11
Time and Uncertainty
What will you learn in this chapter?
expected value
possible
for managing risk
pose for insurance
Value over time
• When a decision requires weighing uncertain
future costs and benefits, two complications
are faced:
inaccurate direct comparison of current costs and
benefits to future costs and benefits
costs to be only approximate estimates
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Timing matters
• When costs and benefits of a choice occur at
different times , this profoundly affects the
choice.
• Consider the following scenario: You have won
a competition and can choose one of the
following prizes:
Option A: $100,000 now.
Option B: $105,000 ten years from now.
• Which would you choose and why?
Interest rates
of waiting until the future to receive the money
–The interest rate tells how much today’s money is
worth in the future
rate is worth in one year:
$100,000 + ($100,000*5%) = $105,000
the above example, $105,000 in one year is worth
$100,000 today
Compounding
period longer than one year, compoundingthe
interest payments is necessary
at a 5% annual interest rate for two years earns:
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Active Learning: Computing future value
What is the future value of depositing $100,000 in a bank
at a 5% annual interest rate for ten years?
Present value
value and future value of a sum
money in the future versus receiving it today
interest rate of 8% annually
$100,000
Present value
individual’s preferred interest rate, his or her
present value of any sum can be determined
=
• Present value translates future costs or benefits
into the equivalent amount of value today
future amounts with the present sums
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Active Learning: Comparing present and
future values
Suppose you have a preferred interest rate of 9%
annually You just won the lottery and have two
options:
option will you prefer?
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Present value
• Sometimes benefits and costs accrue over
several years.
• To calculate the present value of a flow of
money in the future, add up the present value
of each amount in the future.
Present value
income every year after earning a college degree
$20,000 each year after starting their first job in 5 years
and working for 30 years Their preferred annual
interest rate is 5%
( ) ( )$ ⋯ $. $ ,
college is less than $252,939, the individual will attend
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Present value
useful in making other decisions when the
benefits and opportunity cost occur at different
times
how much should you save into your retirement fund
now?
be needed to make it worthwhile to invest in a new
piece of machinery?
leads to informed decision making
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Risk and uncertainty
• The previous examples assumed certain future
costs and benefits.
• Many decisions are based on weighing
uncertain future costs and benefits against
today’s costs and benefits.
–Riskis a special class of uncertainty in which the
costs or benefits of an event or choice are
uncertain, but calculable
• Evaluating risk requires analysis of different
possible outcomes.
Expected value
set of outcomes are known
that the outcome will be realized
cost or benefit estimate can be calculated
• The expected value of a choice, EV, is equal to the
sum of each possible event, S, weighted by its
probability of occurring, P.
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Expected value
Our previous analysis of the decision to attend
higher education can be extended by assuming
that additional future earnings is uncertain.
• Using the probabilities and outcomes, the
expected value of attending college and not
attending college can be calculated.
Lifetime earnings by
education level
College degree 25% 25% 50%
No college degree 50% 50% 0%
$0.9 million $1.5 million $2.4 million
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Expected value
= $1.2
expected future income
the difference in the expected values
Propensity for risk
financial decisions (Someone who does have a high
risk
–Option A: Heads, receive $100,001 Tails, receive $99,999
–Option B: Heads, receive $200,000 Tails, receive $0
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Propensity for risk
about worst-case outcome
expected value, the one with lower risk will
typically be chosen
for taking on risk
accept the risk of winning nothing
personal taste for risk
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Insurance and managing risk
ways
averse individuals (or companies) pay to reduce
some uncertainty
specific event occurring
Insurance and managing risk
• The cost of insurance is typically greater than
its expected value.
insurance worth the extra expense
• Individuals are generally willing to pay for
insurance because the costs of the worst-case
events are typically quite large.
• If the cost of insurance was equal to its
expected value , then insurance companies
would not make any profits.
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Pooling and diversifying risk
• Insurance does not reduce risk.
• Insurance reallocates costs from individuals to
insurance companies.
• Why are insurance companies better able to
handle the same risk?
which risks are shared across many different assets
or people
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Problems with insurance
companies having different information
(asymmetric information sets)
individuals are drawn towards insurance
riskier once they become insured
hazard would be eliminated
Summary
comparing current costs and benefits to future
costs and benefits
and other times they are uncertain, but
calculable
outcome can be determined
tend to avoid these activities or buy insurance to
reduce risk