Economics and Finance, 2014-15
Lecture 4: Implications of the model of investment under perfect capital
markets
Luca Deidda
UNISS, CRENoS, DiSEA
October 2014
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
1/9
Plan
I
Separation between investment decisions and individual preferences
I
Efficient investment decision
I
Value of the firm
I
Financial structure
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
2/9
Fisher separation theorem
Separation between investment decisions and
individual preferences
C2
€
€
y 2p
y2
€
I
y1p
y1
C1
€ A and B have different preferences. Yet, they choose the
Individuals
EF
October 2014
€
same level €
of investment
Luca Deidda (UNISS, CRENoS, DiSEA)
3/9
Fisher separation theorem
Investment decisions and the value of wealth
I
In our model, the present value of individual wealth as a function of I has
the following expression:
W1 =
I
R(I) + y2
−I
1+r
(1)
Question: What is the optimal level of investment?
max
{I}
R(I) + y2
−I
1+r
(2)
The first order condition yields:
R 0 (I) = 1 + r
I
I
(3)
That is, the optimal level of investment, I ∗ , is such that the marginal return
to investment (Internal rate of return), R 0 (I ∗ ) equals marginal cost of
capital, 1 + r
Why should individual choose such level of investment?
Because, given the presence of perfect capital markets, it maximizes the
consumption possibilities set
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
4/9
Value of the firm
Corporate finance interpretation
I
Mr A is the owner of a firm. Firm’s existing assets are bound to generate
a cash flow y1 in the current period and a stream of future cash flows
whose present value at time 2 is y2 .
I
The firm faces an investment opportunity that yields a cash flow R(I) in
period 2.
I
Which is the efficient investment decision?
I
It is the one that maximizes the current value of the firm, which is
V1 = W1 =
R(I) + y2
−I
1+r
(4)
I
Suppose there are two possible levels of investment, I1 and I2 . Which
criterion should the firm adopt to choose between the two?
I
The Net Present Value criterion: choose the one that yields the highest
NPV
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
5/9
Value of the firm
The value of the firm
Definition
The intrinsic value of a firm is the present value of all present and future cash
flows generated by the firm’s assets.
In a world with perfect capital markets
I
The value of a firm is always maximum
I
The market value of the firm equals the intrinsic value
I
The capital market has a powerful governance role
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
6/9
Financial structure
Financial structure
Firm’s sources of external financed can be classified into two broad
categories:
I
Debt
(Outside) Equity
Both debt and equity give rise to claims over firms’ cash flow
I
I
The creditor has the right to get back the principal plus interest
I
The shareholder has the right to claim firms’ earnings
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
7/9
Financial structure
Firm’s financial structure: Example
Let us consider a firm that lives for two periods
I
The firm is financed during the first period with a mix of debt, D, and
equity, E
I
In the second period, the firm generates a return R(I) (overall value of the
firm at time 2)
I
Such return is appropriated part by shareholders and part by creditors
I
The return to shareholders is VE = max(0, R − D2 )
I
The return to creditors is VD = min(R, D), where D measure the value of
debt in the second period
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
8/9
Financial structure
Irrelevance of financial structure
I
I
We can see that, so long as the choice of debt and equity does not affect
the investment decision I, firms’ value is independent of the financial
structure
In fact, the value of the firm in period 2 is
VE + VD = R(I)
I
(5)
The question is: can it be that creditors and equity holders might have
conflicting interests?
Luca Deidda (UNISS, CRENoS, DiSEA)
EF
October 2014
9/9