EQUATION SHEET
Principles of Finance
Exam 3
Capital Budgeting
Evaluation techniques:
Amount of the initial investment that is 

 Number of years just   unrecovered at the start of therecovery year 
Payback =  before full recovery of  + 

 original investment 
Total cash flow generated


 
during
t
he
recovery
year


Traditional payback—unadjusted cash flows are used
Discounted payback—discounted cash flows, or present values, are used
NPV= CF0 +
∧
∧
CF1
CFn
(1+ r)1
+L +
∧
(1+ r)n
n
=
∧
CF1
CFn
CF0 +
+L + =
(1+ IRR)1
(1+ IRR)n
∧
∑ (1+ r)
CFt
t=0
n
∑
t=0
t
∧
CFt
= 0
(1+ IRR)t
IRR = internal rate of return
n
MIRR: PV of cash outflows =
FV of cash inflows
(1+ MIRR)
n
=
n
TV
(1+ MIRR)
n
∑ (1+ r) =
;
t=0
COFt
t
∑ CIF (1+ r)
t
t=0
(1+ MIRR)n
Cash Flow Estimation
Net cash flow = Net income + Depreciation = Return on capital + Return of capital
Supplemental
∆Cash revenuest -∆Cash expensest -∆Taxest
operating cash flow t =
=∆NOIt ×(1− T) + ∆Deprt
= ( ∆NOIt + ∆Deprt )×(1− T) + T( ∆Deprt )
Cost of Capital
)(
(
)
Tax savings
After-tax component = Bondholders' required =
cost of debt
rate of return
associated with debt
Component cost
of preferred stock
= r ps =
Dps
Dps
=
P 0(1 - F)
NP 0
ˆ
Component cost
= r s = rRF + (rM -rRF )β s = D1 + g = rˆs
of retained earnings
P0
rd -rd ×T
= rd (1-T)
t
Component cost
of new equity
= re =
ˆ1
ˆ
D
+ g = D1 + g
NP
P 0(1 - F)
 Proportion   After-tax  
 Proportion   Cost of  
 Proportion   Cost of  



 

 

 

WACC = 
of
 x  cost of   +  of preferred  x  preferred   +  of common  x  common  
 

  stock  


 equity   equity  
 

 

 debt   debt  
 stock

=
WACC
Break Point
w dTrdT
=
+
w psrps
+
w s (rs or re )
Total dollar amount of lower cost of capital of a given type
Proportion of this type of capital in the capital structure
Planning and Control
Full capacity sales =
Sales level
Percent
of capacity used 



 to generate sales level 
Operating Breakeven Analysis
Sales
Total operating
Total
Total
=
=
+
revenues
costs
variable costs fixed costs
(P×Q) =
QOpBE =
TOC
=
(V×Q)
+
F
F
F
=
P-V Contribution margin
SOpBE =
Degree of
Percentage change in NOI
= DOL =
=
operating leverage
Percentage change in sales
DOL =
F
F
=
 V  Gross profit margin
1-  
P
( ΔNOI
NOI )
( ΔSales
Sales )
=
( ΔEBIT
EBIT )
( ΔSales
Sales )
=
( ΔEBIT
EBIT )
 ΔQ 


 Q 
(Q ×P) - (Q × V)
S - VC
Gross profit
=
=
(Q × P) - (Q × V) - F
S - VC - F
EBIT
Financial Breakeven Analysis
EPS=
Earnings available to common stockholders (EBIT-I)(1-T)-Dps
=
=0
Number of common shares outstanding
ShrsC
EBIT FinBE = I +
Dps
(1 - T)
Degree of
Percent change in EPS
= DFL =
=
financial leverage
Percent change in EBIT
DFL =
EBIT
EBIT
=
EBIT - I
EBIT - [Financial BEP]
( ΔEPS
EPS )
ΔEBIT
( EBIT )
Financial BEP = I +
Dps
(1 - T)
DFL =
EBIT
EBIT - I
Degree of
= DTL =
total leverage
DTL =
=
When there is no preferred stock.
( ΔEPS
EPS )
ΔSales
( Sales )
=
( ΔEBIT
( ΔEPS )
EBIT )
x EPS
ΔEBIT
( ΔSales
Sales ) ( EBIT )
= DOL x DFL
Gross Profit
EBIT
Gross Profit
x
=
EBIT
EBIT - [Financial BEP]
EBIT - [Financial BEP]
S - VC
Q(P - V)
=
EBIT - I
[Q(P - V) - F ]- I
When there is no preferred stock.