EQUATION SHEET Principles of Finance Final Exam
[Pages:6]EQUATION SHEET Principles of Finance
Final Exam
FINANCIAL STATEMENT ANALYSIS
Net cash flow = Net income + Depreciation and amortization
DuPont equation: ROA=Net profit margin ? Total assets turnover
= Net income ?
Sales
Sales
Total assets
DuPont equation: ROE=
ROA
? Equity multiplier
=
Net income
Total assets
? Total assets Common equity
=
Pr ofit m arg in
Totutarnl aosvseer ts
Equity multiplier
=
Net income Sales ?
Sales Total assets
?
Total assets Common equity
THE FINANCIAL ENVIRONMENT
Net proceeds from issue = Amount of issue ? Flotation costs = (Amount of issue) x (1 ? Flotation costs)
Amount of issue Amount needed (Net proceeds) (Other cos ts)
(1 Flotation costs)
(1 Flotation costs)
TIME VALUE OF MONEY
Lump-sum (single) payments: FV n = PV(1+ r)n
PV
=
FV n (1+ r)n
=
FV n
1
(1 +
r
)n
Annuity payments:
FVAn
=
PMT
n1 t=0
(1 +
r)t
=
PMT
(1 +
r )n r
-
1
FVA(DUE
)n
=
PMT
n1 t=0
(1 +
r
)t
(1r
)
=
PMT
(1 +
r )n r
-
1
(1 +
r
)
PVAn = PMT
n t=1
1
(1 +
r
)t
= PMT
1
1 (1+ r )n
r
PVA(DUE
)n
= PMT
n t1
1
(1
r
)t
(1r
) PMT
1
1 (1+ r )n
r
(1 +
r)
Perpetuities: Present value of a perpetuity = PVP = Payment = PMT
Interest rate r
Uneven cash flow streams:
n1
FV CFn = CF1(1+ r)n-1 + ... + CFn(1+ r)0 = CFt(1+ r)t t=0
PV CFn
=
CF1
(1
1 + r
)1
+
...
+
CFn
1 (1+ r
)n
=
n t=1
CFt
1
(1
+
r
)t
Interest rates (yields):
Periodic
rate
=
rPER
Stated annual interest rate Number of interest payments per
year
rSIMPLE m
Number of
int erest periods
=
nPER
Number of years
Number of int erest payments per year
nYRS m
Effective annual rate
=
EAR
=rEAR
1 +
r
SIMPLE
m
m
-
1.0
=
(1 +
rPER
)m
-
1.0
Annual percentage rate = APR = rPER x m
COST OF MONEY
Dollar return = (Dollar income) +
(Capital gains)
= (Dollar income) + (Ending value ? Beginning value)
Yield Dollar return Dollar income Capital gains
Beginning value
Beginning value
Dollar income (Ending value - Beginning value) Beginning value
Rate of return = r = Risk-free rate + Risk premium = r = rRF + RP
Rate of return = r = rRF + RP = rRF + [DRP + LP + MRP] = [r* + IP] + [DRP + LP + MRP]
rTreasury = rRF + MRP = [r* + IP] + MRP
Yield on an
n-year bond
Interest rate in Year 1
Interest rate in Year 2
n
Interest rate in Year n
R1 R2
n
Rn
Valuation Concepts
General valuation model:
Value of an asset
V0
PV
of
CF
CF1 (1r)1
CFn
(1r)n
n t1
CFt
(1r)t
Bond Valuation:
Bond Value
= Vd
INT (1+ r d)1
+
...
+
INTM (1+ r d)N
=
INT
1
1 (1+rd )N
rd
+
M
1 (1+ r d)N
V
d
=
INT (1+ YTM
)1
+
...
+
INT (1+ YTM
)N
+
(1 +
M YTM
) N
Adjust rd, N, and INT if interest is paid more than once per year.
YTM = Yield to maturity
Vd
=
INT (1+ YT
C)1
+
...
+
INT (1+ YT C)N
+
(1 +
M YT C)N
rd
YTM = Bond
yield =
Current yield
+
Capital gains yield
=
INT V d0
+
V d1 - V d0 V d0
YTC = Yield to call
Stock Valuation:
Stock value
Vs
P^0
D^ 1 (1 rs
)1
D^ (1rs )
t1
D^ t (1 rs
) t
Constant growth stock:
P 0
=
D0 r
(1+ g) s-g
=
r
D^ 1 s-g
Nonconstant growth stock:
P 0
D^ 1 (1rs
)1
D^ 2 (1rs
)2
D^ n P^n (1rs )n
;
where
P^n
D^ n(1gnorm rs gnorm
)
gnorm = normal, or constant growth
r^s = Stock yield =
Dividend yield
+
Capital gains yield
D^ 1 g = P0
D^ 1 P0
+
P^1 P0 P0
vEalcuoenaodmdiecdEVA
EBIT(1
T)
Average cost of funds
Invested capital
Risk and Rates of Return
n
Expected rate of return
=
r ^
=
Pr1r1
+
Pr2r2
+
...
+
Prnrn
=
Pri ri
i=1
n
Standard deviation = = 2 =
(ri r^)2Pri
i=1
n
Variance = 2 = (ri - r^)2Pri i=1
Estimated = s =
n
(rt r )2Pr t
t=1
n1
Coefficient of variation = CV = Risk = Return r^
r r1 r2 n
n
rn
rt
t1
n
N
r^P = w1r^1 + w2r^2 + ... + wNr^N = w jr^j j=1
N
P = w11 + w22 + ... + wNN = w jj j=1
Return = Risk-free return + Risk Premium = rRF + RP
RP = Return - rRF RPInvestment = RPM x Investment
rInvestment = = =
rRF + RPInvestment rRF + (RPM)Investment rRF + (rM - rRF)Investment
Capital Budgeting
Evaluation techniques:
Payback
=
Number of years just before full recovery of original investment
+
Amount of the initial investment that
unrecovered at the start of therecovery
Total cash flow generated during the recovery year
is year
Traditional payback--unadjusted cash flows are used Discounted payback--discounted cash flows, or present values, are used
NPV
CF0
CF1 (1 r )1
CFn
n
CFt
(1r)n t0 (1r)t
CF0
CF1 (1IRR)1
CFn (1IRR)n
n t0
CFt
(1IRR)t
0
IRR = internal rate of return
MIRR:
PV of cash outflows =
FV
of cash inflows
TV
(1MIRR)n (1MIRR)n
;
n
n t0
COFt (1 r )t
CIFt (1r)t
t0
(1MIRR)n
Cash Flow Estimation
Net cash flow = Net income + Depreciation = Return on capital + Return of capital
Supplemental operating cash flowt
Cash
revenuest
-Cash
expensest
-Taxest
NOIt (1T) Deprt
(NOIt Deprt )(1T) T(Deprt )
Cost of Capital
After-tax cost
component of debt
=
Bondholders' required rate of return
-
Tax savings associated with debt
rd -rdTrd(1-T) = YTM(1 ? T)
Component cost of preferred stock
=
r ps
=
Dps P0(1 - F)
=
D ps NP 0
Component cost =
of retained earnings
rs
= rRF
+ (rM -rRF )s
=
D^ 1 P 0
+ g = r^s
Component cost of new equity
= re =
D^ 1 P0 (1 - F)
+ g =
D^ 1 NP
+ g
Proportion After-tax Proportion Cost of Proportion Cost of
WACC
=
of
x
cost of
+
of
preferred
x
preferred
+
of
common
x
common
debt debt stock stock equity equity
=
w dT rdT
+
wpsrps
+
ws (rs or re )
WACC = Total dollar amount of lower cost of capital of a given type Break Point 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) =
TOC = (V?Q) + F
QOpBE
=
F P-V
=
F Contribution
margin
SOpBE
=
1-
F V P
=
Gross
F profit
margin
Degree of
= DOL = Percentage change in NOI =
NOI NOI
EBIT
EBIT
= EBIT = EBIT
operating leverage
Percentage change in sales
Sales Sales
Sales Sales
Q Q
DOL
= (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
EBITFinBE
= I
+
D ps (1 - T)
Degree of
= DFL = Percent change in EPS =
EPS EPS
financial leverage
Percent change in EBIT EBIT
EBIT
DFL = EBIT =
EBIT
EBIT - I EBIT - [Financial BEP]
Financial BEP = I + Dps (1 - T)
EBIT DFL =
EBIT - I
When there is no preferred stock.
Degree of
= DTL =
EPS EPS
=
EBIT
EPS
EBIT x EPS
= DOL x DFL
total leverage
Sales
Sales
EBIT
Sales
Sales
EBIT
DTL = Gross Profit x
EBIT
=
Gross Profit
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.
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