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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