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Review Item
An firm has a project with NPV>0 that costs a lot of money.
It pays off after the owner dies. Should she invest? In the project? In
financial assets? How?
0c
1c
),( 10 cc
Time zero cash flow
Timeonecashflow
An investment opportunity that increases value.
NPV
Invest to here
Finance to here
Do write:
The interest rate is the premium for current delivery of money.
P0 is the price of current money in current money, namely 1.
P1 is the price of time-one money in terms of current money, something <1.
P 11
0 P
Pr
Office hours Anderson
Monday 10:30 – 12:30 Tuesday 10-11
Seo Monday 2-4 Tuesday 9-10
Marshall Monday 4-6 Tuesday 11-12
Answer
Old equity means the shareholders at the time the decision is made.
Old equity gets the gains. Why? Old equity has no competitors.
Everyone else is competitive and must accept a market return.
Review item
Two assets have the same expected return.
Each has a standard deviation of 2%. The correlation coefficient is .5. What is the standard deviation of an
equally weighted portfolio?
Review item
A firm has a project with positive NPV. The project costs 100M to start. The firm has only 50M. What should it do?
EPS and ROE under Proposed Capital Structure
Shares Outstanding = 240
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 5% 10% 15%
ROE 3% 11% 20%
Proposition II of M-M
rB is the interest rate
rs is the return on (levered) equity r0 is the return on unlevered equity
B is value of debt SL is value of levered equity
rs = r0 + (B / SL) (r0 - rB)
MM Proposition II no tax
Debt-to-equityratio (B/S)
Cost of capital: r(%)
.r0
rS
rWACC
rB
LBS S
Brrrr )( 00
MM II (with taxes)
Corporate taxes, not personal rB = interest rate rS = return on equity r0 = return on unlevered equity B = value of debt SL = value of levered equity Previously, without taxes
rS = r0 + (B/SL)(r0 - rB)
Effect of tax shield
Increase of equity risk is partly offset by the tax shield
rS = r0 + (1-TC)(r0 - rB)(B/SL) Leverage raises the required return less
because of the tax shield.
MM II and WACC
Debt-to-equityratio (B/S)
Cost of capital: r(%)
.r0
rS
rB.0.200=
0.100
. rWACC
.0.2351
200370
Optimal Debt and Value
Debt (B)
Value of firm (V)
0
Present value of taxshield on debt
Present value offinancial distress costs
Value of firm underMM with corporatetaxes and debt
VL=VU+TCB=
V=Actual value of firm
VU=Value of firm with no debt
B*
Maximumfirm value
Optimal amount of debt
Value asequity
Value asdebt
Operating C.F.’s ofthe whole economy
D of Institutions D of rich investors
V* = 1/RB V* = 1/RS
asdebt
as equity
Miller: Tax-class clienteles
Separation theorem interpreted for dividends (Figure 18.4)
C1
C0
s lo p e = - (1 + r)
L o w -d iv id e n d firm
H ig h -d iv id e n dfirm
w
F u tu rere tu rno r
d iv id e n d n o
Dividend equilibrium
$ of operatingcash flows
HiDivvalueper $1
LoDivvalueper $1
mq ili riuo iv
EL
mEquilibriuHiD iv
u bD
V*=1/Rh V*=1/RL
...
Answer
Give the definitions and the formula. rB = bond rate
rS = expected return on shares
B = market value of bonds S = market value of shares TC = corporate tax rate
Pay-off pitch
rWACC =(S/(S+B))rS + (B/(S+B))(1-TC)rB
Now say that it applies when (1) the physical project has the same
risk as the firm (2) it is financed like the firm.
Answer
IRR is the discount rate that makes NPV(IRR) = 0.
The hurdle rate is the market rate for the risk-class.
Investing means cash flows are first negative, then positive.
Financing (in this context) means cash flows are first positive, then negative.
More answer
Other sign patterns, IRR is not useful. Investing, a good project has IRR >
hurdle rate. Financing, a good project has hurdle
rate > IRR.