Lecture 1 + FTW 1 Hirshleifer
Model
You can create wealth when you sell a
project for more than you initially
spent on it. This will also increase your
wealth per share. We create value if
we invest in projects that are worth
more than they cost. We destroy
value if we invest in projects that are
worth less than they cost.
Fundamental topics in finance
The capital budgeting decision
The financing decision/ the capital structure decision
The relation between the capital budgeting and the financing decision
The financial investment decision
Asset pricing
Hirshleifer model, four types:
1. Without financial market and without real market ;
a. A1. A certain world is assumed: the individual knows all the decision
alternatives and the corresponding outcomes.
b. A2. There is a one-period model where only two moments are important:
the start of the period (now, t=0) and the end of the period (later, t=1).
c. A3. The individual has a current income of CF0 and a future income of
CF1.
2. With financial market and without real market;
a. A14. Each participant can borrow/ lend unlimitedly against the risk-free
market interest rate.
b. Consumption max at t=0 = CF0 + CF1/(1+r)
c. Consumption max.at t=1 = CF0 x (1+r) + CF1
d. If we assume that the individual is able to rank his preferences
consistently for the different consumption combinations (C0, C1) and
value these combinations by means of his utility function, then we can
derive indifference curves, which contains the collection of consumption
combinations to which the individual assigns an equal utility value. The
slope of an indifference curve is called the marginal rate of substitution
between the present and future consumption.
e. With financial markets it is possible to reallocate cash flows in time; the
consumption possibility line. The optimal consumption combination
(C0, C1) of the individual can be determined as the point where the
indifference curve is tangent to the consumption possibilities line.
3. With financial market and with real market;
a. We rank our real projects based on the return of these projects. We stop
when the marginal return is equal to the interest rate.
b. Invest until the marginal revenue = 1 + rf. Invest until the marginal return
= rf.
c. The existence of financial and real markets makes people happier; it gives
them higher utility.
d. Without financial markets, people have to consume in the same period as
they have income. Without real markets, profitable projects will be
unused. The existence of both markets makes it possible for people t
achieve at higher indifference curves.
4. Separation theorem;
, a. Theorem: the real investment decision is taken independently from the
consumption decision.
b. Step 1, optimal investments: marginal return = interest rate (opportunity
cost of capital).
c. Step 2, optimal consumption: marginal utility of consumption now and
later = interest rate.
d. Implications are:
i. Everybody wants the same level of capital investments (until marginal
return = interest rate).
ii. Managers should focus on real investment projects that add value.
iii. The financial market takes care of the individual choice with respect to
consumption now and later.
The maximum present consumption is
indicated by A. In this case, the
consumption later is equal to zero, because
the cash flow CF1 must be completely used
for redemption. Formula:
C 0=CF 0+CF 1/ (1+ rf )
The maximum future consumption is
indicated by B. In this case, all the present
income is passed on to the future. Formula:
C 1=CF1+CF 0 ( 1+rf ) .
These are the two extremes. In between
both extremes there are an infinite number
of possible combinations. The line AB forms
the consumption possibilities line. The slope of this line is: −(1+ rf ), with rf
being the risk-free interest rate.
Real investment possibilities generate more income later and, correspondingly,
to reach consumption combinations with a higher utility. The collection of
combinations of present investments and future returns is called the real
investment possibilities curve or production possibilities curve. Diminishing
marginal returns feature the real investment possibilities: each extra unit of real
investment yields a lower return compared to the previous unit of real
investment.
The curve AD shows the real investment possibilities with the slope equal to
−(1+ ri), where ri is the marginal return on the real investments. The line GH is
the consumption possibilities line if EA is invested in real projects. The present
value of total wealth increases from OA to OG, with the future value of this total
wealth equal to OH. OG = C0 + C1/(1+rf) or OG = OA + AG. OH = OG x rf.
EG is equal to the present value of the executed investment projects. To realise
this present value, an amount of EA has to be invested in real projects now, so
the net present value of the real investment is equal to AG. This NPV reflects
the net contribution of the executed investment projects to the present value of
Ix, 1
wealth. For the return on a real investment X we obtain: Ix , 0= . The future
1+rx
cash flow discounted against the internal rate of return, by definition gives the
present price of the project. The present value of project X however follows if we
Ix , 1
discount the future certain cash flow against the opportunity cost: PV ( X )= .
1+ rf
Model
You can create wealth when you sell a
project for more than you initially
spent on it. This will also increase your
wealth per share. We create value if
we invest in projects that are worth
more than they cost. We destroy
value if we invest in projects that are
worth less than they cost.
Fundamental topics in finance
The capital budgeting decision
The financing decision/ the capital structure decision
The relation between the capital budgeting and the financing decision
The financial investment decision
Asset pricing
Hirshleifer model, four types:
1. Without financial market and without real market ;
a. A1. A certain world is assumed: the individual knows all the decision
alternatives and the corresponding outcomes.
b. A2. There is a one-period model where only two moments are important:
the start of the period (now, t=0) and the end of the period (later, t=1).
c. A3. The individual has a current income of CF0 and a future income of
CF1.
2. With financial market and without real market;
a. A14. Each participant can borrow/ lend unlimitedly against the risk-free
market interest rate.
b. Consumption max at t=0 = CF0 + CF1/(1+r)
c. Consumption max.at t=1 = CF0 x (1+r) + CF1
d. If we assume that the individual is able to rank his preferences
consistently for the different consumption combinations (C0, C1) and
value these combinations by means of his utility function, then we can
derive indifference curves, which contains the collection of consumption
combinations to which the individual assigns an equal utility value. The
slope of an indifference curve is called the marginal rate of substitution
between the present and future consumption.
e. With financial markets it is possible to reallocate cash flows in time; the
consumption possibility line. The optimal consumption combination
(C0, C1) of the individual can be determined as the point where the
indifference curve is tangent to the consumption possibilities line.
3. With financial market and with real market;
a. We rank our real projects based on the return of these projects. We stop
when the marginal return is equal to the interest rate.
b. Invest until the marginal revenue = 1 + rf. Invest until the marginal return
= rf.
c. The existence of financial and real markets makes people happier; it gives
them higher utility.
d. Without financial markets, people have to consume in the same period as
they have income. Without real markets, profitable projects will be
unused. The existence of both markets makes it possible for people t
achieve at higher indifference curves.
4. Separation theorem;
, a. Theorem: the real investment decision is taken independently from the
consumption decision.
b. Step 1, optimal investments: marginal return = interest rate (opportunity
cost of capital).
c. Step 2, optimal consumption: marginal utility of consumption now and
later = interest rate.
d. Implications are:
i. Everybody wants the same level of capital investments (until marginal
return = interest rate).
ii. Managers should focus on real investment projects that add value.
iii. The financial market takes care of the individual choice with respect to
consumption now and later.
The maximum present consumption is
indicated by A. In this case, the
consumption later is equal to zero, because
the cash flow CF1 must be completely used
for redemption. Formula:
C 0=CF 0+CF 1/ (1+ rf )
The maximum future consumption is
indicated by B. In this case, all the present
income is passed on to the future. Formula:
C 1=CF1+CF 0 ( 1+rf ) .
These are the two extremes. In between
both extremes there are an infinite number
of possible combinations. The line AB forms
the consumption possibilities line. The slope of this line is: −(1+ rf ), with rf
being the risk-free interest rate.
Real investment possibilities generate more income later and, correspondingly,
to reach consumption combinations with a higher utility. The collection of
combinations of present investments and future returns is called the real
investment possibilities curve or production possibilities curve. Diminishing
marginal returns feature the real investment possibilities: each extra unit of real
investment yields a lower return compared to the previous unit of real
investment.
The curve AD shows the real investment possibilities with the slope equal to
−(1+ ri), where ri is the marginal return on the real investments. The line GH is
the consumption possibilities line if EA is invested in real projects. The present
value of total wealth increases from OA to OG, with the future value of this total
wealth equal to OH. OG = C0 + C1/(1+rf) or OG = OA + AG. OH = OG x rf.
EG is equal to the present value of the executed investment projects. To realise
this present value, an amount of EA has to be invested in real projects now, so
the net present value of the real investment is equal to AG. This NPV reflects
the net contribution of the executed investment projects to the present value of
Ix, 1
wealth. For the return on a real investment X we obtain: Ix , 0= . The future
1+rx
cash flow discounted against the internal rate of return, by definition gives the
present price of the project. The present value of project X however follows if we
Ix , 1
discount the future certain cash flow against the opportunity cost: PV ( X )= .
1+ rf
