Chapter 10
Rd (YTM): interest rate on the firm’s new debt
WACC=
Rs: cost of common equity raised by
=R
d
(1-T)(D/A) + R
s
(E/A)
retained earnings, or internal equity(RoR)
=W
d
R
d
(1-T) + WeRe
Re: cost of common equity raised by issuing
=W
d
R
d
(1-T)+WcRs
new stock, or external equity
Three approaches to cost of equity:
Cost of debt = YTM
•
CAPM
: R
s
=R
rf
+ RP
M
*b OR Rrf + (r
m
-r
rf
)*b
Wd:
weight of debt
•
Dividend growth model
: D
1
/P
o
+ g
We:
weight of equity
•
Rs = Bond Yield+ Risk Premium
To estimate g
: ROE (NI/Equity) x Retention Ratio (1- dividend payout ratio)
Cost of preferred stock:
D
p
/P
p
Cost of common stock
: D
1
/P
o
+ growth rate (if given)
After tax cost of debt
: interest rate- tax savings= r
d
(1-T)
Required rate of return = Expected rate of return:
•
Rs = Rrf +RP = D1/(Po+g) = Rs
P
n
=P
0
*(1+g)
n
Cost of equity from new stock issues:
r
e
= (D
1
/P
o
(1-F))+g ,
D
1
=D
o
(1+g) ; D
0
= E
0
*dividend payout ratio
•
F is the % flotation cost
R.E Breakpoint
=(Addition to RE)/Equity Fraction
•
When choosing an optimal capital budget, choose those are
above the WACC
•
Each component of WACC represents the opportunity cost of
that component and WACC represents the opportunity cost of capital for the
company as a whole. WACC is weighted average of the marginal cost of
each relevant capital component
Chapter 11
NPV(WACC,Cfo, {Cf1, Cf2…})
IRR(Cfo, {Cf1, Cf2…})
An
NPV profile
has the discount rate on the X axis and the NPV on the Y axis.
As the discount rate increases, NPV declines. Intersects x axis at IRR. If
mutually exclusive the crossover point represents the point that NPVs of both
are equal.
To find crossover, find difference in cash flows and then take IRR.
To find
Y axis, add and subtract all cash flows. To find x axis, do IRR.
NPV WILL ALWAYS GIVE YOU THE CORRECT ANSWER
Examples of unconventional cash flows are borrowing projects & strip mines
MIRR: use Cf0 as PV in calculator; for FV do Cf1 x (1+WACC)^(n-
1)+Cf2*(1+WACC)^(n-2)... Plug
N and PMT of 0 and solve for I to get MIRR
•
IRR must be greater than the cost of capital to be accepted, whereas NPV
must just be greater than zero. Projects can be independent and mutually
exclusive
•
If the IRR of two projects is higher than the cost of capital, than
they both have a positive NPV
•
MIRR uses a more reasonable assumption about reinvestment rates than the
IRR. IRR and NPV can conflict on mutually exclusive projects if different in
size
Year
0
1
2
3
Revenues
$80,000,000
$83,200,000
$86,528,000
Expenses
$40,000,000
$41,600,000
$43,264,000
Depreciation
$6,000,000
$6,000,000
$6,000,000
Leasing cost
$1,000,000
$1,000,000
$1,000,000
Pretax
income
$33,000,000
$34,600,000
$36,264,000
Taxes
$13,200,000
$13,840,000
$14,505,600
Net income
$19,800,000
$20,760,000
$21,758,400
Opportunity
cost
$0
$0
$0
$19,800,000
$20,760,000
$21,758,400
Plus
depreciation
$25,800,000
$26,760,000
$27,758,400
Capex
-$20,000,000
$1,200,000
Working
capital
-$900,000
$900,000
Tax impact
of sale
$320,000
Cash flow
-$20,900,000
$25,800,000
$26,760,000
$30,178,400
Depreciation = (20000000-2000000)/3 =
6000000
Tax impact
of sale
Market value
1,200,000
Book value
2,000,000
Hamada Problems
:
1. Find unlevered beta using {
Β
L
= Β
U
[1 + (1-T)*(D/E)]}
2. Relever beta using new ratio {
Β
L
= Β
U
[1 + (1-T)*(D/E)]}
3. Use new B
L ,
CAPM to find new
K
E
[K
RF
+ β*(K
M
- K
RF
)]
4. Use new K
E
and plug into WACC ***K
E
=K
S
WACC=(W
d
)(r
d
)(1-T) + (W
s
)(r
s
)
WACC
Expansion will produce a rate of return on 11%. Debt to Equity
Ratio is 0.8. Bond issue outstanding that will mature in 25 years
and has a 7% annual coupon rate. The bond is currently selling

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