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:

FVA

n

=

PMT

n-1 t=0

(1 +

r )t

=

PMT

(1 +

r)n r

-

1

FVA(DUE

)n

=

PMT

n-1 t=0

(1 +

r

)t

(1+

r

)

=

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 t=1

1

(1+

r

)t

(1+ r

) = 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:

n-1

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

m

Effective annual rate

=

EAR

=rEAR

=

1

+

r

SIMPLE

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

( ) ( ) ( ) nY-iyeeldarobnoannd=

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 (1+r)1

+

+

CFn (1+r)n

=

n t=1

CFt

(1+r)t

Bond Valuation:

Bond Value

= Vd

=

INT (1+ r d)1

+

... +

INT+M (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

V

d

=

INT (1+ YT

C)1

+

...

+

(1

INT + 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^

=

D^ t

(1+rs ) t=1 (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 (1+ rs

)1

+

D^ 2 (1+rs )2

+

+

D^ n +P^n (1+rs )n

;

where

P^n

=

D^ n(1+ gnorm 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

( ) ( ) vEalcuoenaodmdiecd=EVA

=EBIT(1-

T)

-

Average cost of funds

Invested capital

Risk and Rates of Return

n

Expected rate of return

=

r ^

=

Pr1r1

+

Pr2r2

+

...

+

Prnrn

=

Priri

i=1

n

Variance = 2 = (ri - r^)2Pri i=1

n

Standard deviation = = 2 =

(ri - r^)2Pri

i=1

Estimated = s =

n

(rt - r )2Pr t

t=1

n -1

r = r1 +r2 + n

n

+ rn

=

rt

t=1

n

Coefficient

of

variation

=

CV

= Risk Return

=

r^

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

(1+r)n t=0 (1+r)t

CF0

+

CF1 (1+IRR)1

+

+

CFn

(1+IRR)n

=

n t=0

CFt

(1+IRR)t

=0

IRR = internal rate of return

MIRR: PV of cash outflows = FV of cash inflows = TV

;

(1+MIRR)n

(1+ MIRR)n

n

n t=0

COFt (1+r)t

=

CIFt (1+r)t

t=0

(1+MIRR)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 (1-T)+ Deprt

=(NOIt + Deprt )(1-T)+ T(Deprt )

Cost of Capital

( ) ( ) After-tax cost

component of debt

=

Bondholders' required rate of return

-

Tax savings associated with debt

=rd -rdT=rd(1-T) =

YTM(1

?

T)

Component cost of preferred stock

= rps

=

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 dTrdT

+

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

Managing Short-Term Financing

Cash Inventory Receivables Pyables

Conversion = conversion + collection - deferral

Cycle

period

period

period

= (ICP + DSO) - DPO

Cost of short-term credit

$ cost of

Percentage cost per period

=

rPER

=

borrowing

$ amount of

usable

funds

EAR = rEAR = (1+ rPER )m -1.0

APR = rPER ? m = rSIMPLE

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