chapter 10 choices involving time copyright © 2014 mcgraw-hill education. all rights reserved. no...
TRANSCRIPT
chapter 10
Choices Involving Time
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
10-2
Learning Objectives
• Explain how consumers and firms move cash from one point in time to another by borrowing and lending.
• Calculate the present discounted value of a claim on future resources.
• Understand consumers’ decisions regarding saving and borrowing.
• Analyze the profitability of investment projects with future cash flows.
• Explain how saving, borrowing, and investment depend on the interest rate.
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
10-3
Overview
• Transactions involving time • Saving and borrowing by consumers • Investment
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10-4
Interest Rates and Compound Interest
• Principal: amount borrowed when one person lends money to another
• Interest: amount of money a borrower is obliged to pay a lender, over the principal
• Interest Rate: amount of interest paid on a loan during a particular period, stated as a percentage of the principal
• Compounding: payment of interest on loan balances that include interest earned in the past
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10-5
Principal and Interest
Today One Year Two Years
$121$110$100
+$10 +$11
10% 10%
Interest Compound Interest
Principal
Annual Interest Rate
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10-6
Effects of Compound Interest
– Account balance – Dollars – Rate of interest – Time, years
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10-7
Present Value and the Price of a Future Dollar
• Present Discounted Value (PDV): monetary value of a claim on future resources
–
• At a positive interest, $1 received in the future is valued at less than $1 today
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10-8
Present Value and the Price of a Future Dollar
TT
R
F
R
F
R
FF StreamOf PDV
)1(...
)1(1 221
0
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10-9
Price of a Bond vs. the Prime Interest Rate
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10-10
Why Do Interest Rates Differ
• Risk: Risk exists whenever the consequences of a decision are uncertain. The higher the risk the higher the interest payment demanded by lenders
• Default: the failure to pay back borrowed money• Detail of agreements• Timing of repayment
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10-11
Real versus Nominal Interest
• Nominal interest: compensation received by the lender over and above the principal, without adjusting for inflation
• Real interest: compensation measured in real dollars, adjusted for inflation
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10-12
Real versus Nominal Interest
DepositedDollarsReal
DepositedDollarsRealYearNextDollarsRealR real
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10-13
Preferences for the Timing of Consumption
Higher marginal rate of substitution than Brian
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10-14
Saving and Borrowing(a) Saving
0
638
580
418
Savings plus interest
220
Earnings next year
200
Savings this year
Food this year (kg)
Food
nex
t yea
r (kg
)
A
380
Earnings this year
Interest rate = 10 %Slope = - 1.1
B
A
C110Debt plus interest
380
Earnings this year
480
Borrowing this year
220
Earnings next year
0
(b) Borrowing
Food
nex
t yea
r (kg
)
Food this year (kg)
580
638 Slope = - 1.1
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10-15
Affordable Consumption Bundles
• A consumption bundle is affordable if, through borrowing and lending, the consumer can make all the required payments as they come due.
• Given the more-is-better principle, the best choice leaves no income unspent.
• PDV of consumption stream = PDV of income stream• The slope of the budget is equal to the (negative) ratio of the
goods’ prices. P0 is the price of the good this year and P1 /(1+R) the price of the good next year (from today’s perspective).
))(1()1(
1
0
1
0
P
PR
RP
PLineBudgetOfSlope
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10-16
Best Choices with Saving and Borrowing
Best choice
Best choice
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10-17
Effect of a Change in the Interest Rate on Savings
(a) Effect of a change in the interest rate
Food this year (kg)
Food
nex
t yea
r (kg
)
(b) The substitution and income effects
Food this year (kg)
Food
nex
t yea
r (kg
)
Effect of increasing interest rate Substitution effect
Income effectL2
l2
l1
L1
B
D
AL3
L2
L1
A
l2
l1
B
E
D
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10-18
Saving, Borrowing, and the Interest Rate
• Interest rate increases: saving becomes more rewarding and borrowing becomes more costly (substitution effect)
• However, if interest rates rise you may decide to save less because you’ll earn more interest on each dollar saved, reaching your future income target with less put in savings (income effect)
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10-19
Effect of a Change in the Interest Rate on Borrowing
(a) Effect of a change in the interest rate
Food this year (kg)
Food
nex
t yea
r (kg
)
(b) The substitution and income effects
Food this year (kg)
Food
nex
t yea
r (kg
)
Effect of increasing interest rate Substitution effect
Income effect
L1
L2
l3l4
L4
AC
F F
L1
L2l4
l3
AC
G
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10-20
Life Cycle Hypothesis
• Life cycle hypothesis: theory of consumption and saving; describes the choices of consumers with realistic life spans
• Assumptions:1. Typical person’s adult life has 2 main stages:
- First stage: employed- Second stage: retired, earning nothing
2. People prefer stability in consumption
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10-21
Life Cycle Hypothesis
Not feasible
Best feasible alternative
Does not exhaust consumer’s lifetime resources
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10-22
Investment
• Investment: up-front costs incurred with the expectation of generating future profits
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10-23
Measuring the Profitability of Investments
• Net present value (NPV): difference between the PDV of the revenue stream and the PDV of the cost stream
–
• NPV criterion: states that an investment project is profitable when its NPV is positive, and unprofitable when its NPV is negative
• Net cash flow (NCF): difference between revenue and cost during a single year of a project’s life
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10-24
Profitability of Investments
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10-25
Profitability of Investments
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10-26
NPV and the Opportunity Cost of Funds
• Time value of money (opportunity cost of funds): opportunity cost associated with the economic benefit an investor could receive by lending money at the prevailing interest rate
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10-27
Internal Rate of Return
• Internal rate of return (IRR): rate of interest at which a project’s NPV is exactly zero
• Importance:– if IRR > rate of interest, project is profitable– if IRR < rate of interest, project is unprofitable
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10-28
Internal Rate of Return
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10-29
Investment and the Interest Rate
• An increase in the interest rate usually makes investment projects less attractive – At a higher interest rate, future dollars are worth less
compared to current dollars– At a higher interest rate, putting money in the bank
becomes more attractive (and borrowing becomes less attractive)
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10-30
Choosing Between Mutually Exclusive Projects
• Best choice among mutually exclusive alternatives is the one that yields the greatest profit. For investment projects, that means the one with the highest NPV.
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10-31
Other Criteria for Choosing between Mutually Exclusive Projects
• Comparing mutually exclusive projects using criteria other than NPV can lead to poor decision making– Choosing based on higher IRR– Payback period: amount of time required before a project’s
total inflows match its total outflows
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10-32
Investing in Human Capital
• Human capital consists of marketable skills acquired through investments in education and training
• Education is an investment and is not always worthwhile
• Financial returns of education often summarized by calculating the IRR
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10-33
Review• Interest rates differ because of variations in default risk,
flexibility, and the timing of payments.• Saving reflects decisions about the optimal timing of
consumption• NPV is a measure of profitability—it is the difference
between the value of a project’s outputs and the value of its inputs, from today’s perspective. An investment project is profitable when its NPV is positive and unprofitable when its NPV is negative.
• When interest rates rise, most potential projects become less profitable, and the general level of investment falls. Falling interest rates have the opposite effects.
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10-34
Looking Forward
• Next we will study risk and how people make decisions under uncertainty
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