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Financial Markets and Net Present ValueLecture Outline
I. IntroductionII. Perfect markets and arbitrageIII. Two-period modelIV. Real investment opportunitiesV. Corporate investment decision
makingVI. The separation TheoremVII. Summary and conclusions
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I. Introduction – Financial Markets
Individuals may desire to consume amounts different from their incomes.
Financial markets facilitate this.
The interest rate is the price of money in borrowing or lending transactions.
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Introduction – Financial Markets
The job of balancing the supply of and demand for loanable funds is taken by the money market.
When the quantity supplied equals the quantity demanded, the market is in equilibrium at the equilibrium price.
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II. Perfect Markets and Arbitrage
For simplicity, consider a perfect market where
Trading is costless. Information about borrowing and lending is
freely available to all participants. Everyone is a price taker: many competitive
traders; no one can move market prices.The result is that only one equilibrium interest rate will exist otherwise arbitrage opportunities would arise.
Under such assumptions, the one interest rate would apply to both borrowing and lending transactions.
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Arbitrage Defined Arbitrage – the ability to earn a risk-free
profit from a zero net investment.
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III. Two-period model
Consider a simple model where an individual lives for 2 periods, has an income endowment, and has preferences about when to consume.
Endowment (or given income) is $40,000 now and $60,000 next year
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
Two-period model: no market
Without the ability to borrow or lend using
financial markets, the individual is restricted to
just consuming his/her endowment as it is earned:
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
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mp
tio
n t
+1
Intertemporal Consumption Opportunity Set
Assume a market for borrowing or lending exists and the interest
rate is 10%. This opens up a large set of consumption patterns
across the two periods.
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Intertemporal Consumption Opportunity Set
1. What is the maximum possible consumption in t+1 and how is this achieved?
2. What is the maximum possible consumption today and how is this achieved?
3. What is the slope of the consumption opportunity set?
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
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mp
tio
n t
+1
Intertemporal Consumption Opportunity Set
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Notes on calculations Present value of a
cash flow received in one time period
Future value in one time period of a cash flow received today
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
Intertemporal Consumption Opportunity Set
A person’s preferences will impact where on the consumption opportunity set they will choose to be.
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An increase in interest rates
$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
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IV. Real Investment Opportunities
The basic financial principle of investment decision making is this: An investment must be at least
as desirable as the opportunities available in the financial markets.
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Real Investment Opportunities – Example 1
Consider an investment opportunity that costs $35,000 this year and provides a certain cash flow of $36,000 next year.
Is this a good opportunity?
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
Real Investment Opportunities – Example 1
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
Real Investment Opportunities – Example 1
Should the individual take the real investment opportunity?
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Real Investment Opportunities – Example 1 – Methods to Analyze
What rate of return does the investment earn?
Time 0 1
Cashflows -$35,000 +$36,000
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Real Investment Opportunities – Example 1 – Methods to Analyze
What is the most that can be consumed today if the real investment is taken?
Time 0 1
Investment Cf.s: -$35,000 +$36,000
Endowment Cf.s +$40,000 +$60,000
Net Cfs: + $5,000 +$96,000
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Real Investment Opportunities – Example 1 – Methods to Analyze
What is the most that can be consumed today if the real investment is taken?
What is the most that can be consumed today if the real investment is NOT taken?
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Real Investment Opportunities – Example 1 – Methods to Analyze
Net Present Value (NPV)
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Real Investment Opportunities – Example 2
Consider an investment opportunity that costs $25,000 this year and provides a certain cash flow of $47,500 next year.
Is this a good opportunity?
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
Real Investment Opportunities – Example 2
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$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Th
ou
san
ds
Thousands
Consumption Today
Co
nsu
mp
tio
n t
+1
Real Investment Opportunities – Example 2
Should the individual take the real investment opportunity?
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Real Investment Opportunities – Example 2
Verify with NPV
Verify with IRR
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V. Corporate Investment Decision‑Making Real investments may be done
through corporations where investors buy shares of the firm.
Shareholders will be united in their preference for the firm to undertake positive net present value projects, regardless of their personal intertemporal consumption preferences.
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Corporate Investment Decision‑Making
Positive NPV projects shift the shareholder’s opportunity set out,
which is unambiguously good.
All shareholders agree on their preference for positive NPV
projects, whether they are borrowers or lenders.
Consumption Today
Co
nsu
mp
tio
n t
+1
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Corporate Investment Decision‑Making
In reality, shareholders do not vote on every investment decision faced by a firm and the managers of firms need decision rules to follow.
All shareholders of a firm will be made better off if managers follow the NPV rule — undertake projects with NPV ≥ 0 and reject negative NPV projects.
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VI. The Separation Theorem The separation theorem in financial markets says that
all investors will want to accept or reject the same investment projects by using the NPV rule, regardless of their personal preferences. Separation between consumption preferences and
real investment decisions Logistically, separating investment decision making
from the shareholders is a basic requirement for the efficient operation of the modern corporation. Managers don’t need to worry about individual
investor consumption preferences – just be concerned about maximizing their wealth.
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VII. Summary and Conclusions Financial markets exist because people want to
adjust their consumption over time. They do this by borrowing or lending.
An investment should be rejected if a superior alternative exists in the financial markets.
If no superior alternative exists in the financial markets, an investment has a positive net present value and should be accepted.
NPV, IRR, PV and FV concepts are useful for working with cash flows through time and analyzing consumption and investment opportunities.
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