Final Exam Formula Sheets FINE 5200, Dr. Y.S. Tian

1

1. Cash Flow Analysis

1.1. Cash flow from assets

Operating Cash Flow (OCF) – Net Capital

Spending (NCS) – ∆NWC

where

OCF = EBIT + Depreciation – Taxes

= NI + Interest Paid + Depreciation

NCS = End. F/A + Depreciation – Begin. F/A

∆NWC = End. NWC – Begin. NWC

1.2. Cash flow to creditors Interest Paid – Net New Debt

where

Net New Debt = End. L-T Debt – Begin. L-T Debt

1.3. Cash flow to shareholders

Dividends Paid – Net New Equity

where

Net New Equity = End. Common Share – Begin.

Common Share

2. Ratios

2.1. Liquidity ratios

sliabilitieCurrent

assetsCurrent ratioCurrent =

sliabilitieCurrent

Inventory assetsCurrent ratioQuick

−=

sliabilitieCurrent

CashratioCash =

assets Total

NWCratio NWC =

costs operatingdaily Avg.

assetsCurrent measure Interval =

2.2. Financial leverage ratios

assets Total

equity Total assets Totalratiodebt Total

−=

equity Total

debt Totalratioy Debt/equit =

equity Total

assets TotalmultiplierEquity =

equity Totaldebt LT

debt LTratiodebt LT

+=

Interest

EBITearnedinterest Times =

Interest

onDepreciatiEBITratio coverageCash

+=

2.3. Asset utilization turnover ratios

Inventory

sold goods ofCost turnoverInventory =

turnoverInventory

365inventoryin sales Days' =

receivable Accounts

Sales turnoversReceivable =

turnoversReceivable

365sreceivablein sales Days' =

NWC

Sales turnoverNWC =

assets fixedNet

Sales turnoverassets Fixed =

assets Total

Sales turnoverassets Total =

2.4. Profitability ratios

Sales

incomeNet marginProfit =

assets Total

incomeNet ROA =

equity Total

incomeNet ROE =

2.5. Market value ratios

shareper Earnings

shareper priceStock ratio P/E =

shareper Book value

shareper ueMarket valratiobook -to-Market =

s)]/EBITDAequivalentcash (andCash -interest Minority

shares dPref'debt MVequity [MVEV/EBITDA

+

++=

2.6. Du Pont analysis

multiplierEquity rTA turnovemarginProfit

equity Total

assets Total

assets Total

Sales

Sales

incomeNet ROE

××=

××=

3. Financial Planning and Growth

3.1. Internal growth rate

RROA

RROAg

×−−

×+=

ρ

ρ

1

3.2. Sustainable growth rate

RROE

RROEg

×−−

×+=

ρ

ρ

1

*

4. Time Value of Money

4.1. Future value

),()1( trFVIFCrCFVt

t ×=+=

where t

rtrFVIF )1(),( +=

4.2. Present value

),()1(

trPVIFCr

CPV

t×=

+=

where

Final Exam Formula Sheets FINE 5200, Dr. Y.S. Tian

2

tr

trPVIF)1(

1),(

+=

4.3. Multiple cash flows

∑=

−+=n

t

tn

tn rCFV1

)1( , ∑= +

=n

tt

t

r

CPV

1 )1(

4.4. Annuities

),( trPVIFACPVA ×= , ),( trFVIFACFVA ×=

where

r

rtrPVIFA

t)1(

11

),(+

−

= , r

rtrFVIFA

t 1)1(),(

−+=

4.5. Annuities due

)1(),( rtrPVIFACPVAD +××=

)1(),( rtrFVIFACFVAD +××=

4.6. Perpetuities

r

CPVP =

4.7. Growing annuities

+

+−×

−=

t

r

g

gr

CPVGA

1

11

[ ]tt grgr

CFVGA )1()1( +−+×

−=

4.8. Growing perpetuities

gr

CPVGP

−=

4.9. Annual Percentage Rate (APR) and Effective

Annual Rate (EAR)

Discrete: 11 −

+=

m

m

APREAR

Continuous: 1−= APReEAR

4.10. Mortgage loans: Effective Monthly Rate

12

1

6/1

−

+=

APREMR

5. Bond Valuation

),(),(Value Bond trPVIFFtrPVIFAC ×+×=

6. Stock Valuation

6.1. Constant growth model

gr

D

gr

gDP

−=

−

+= 10

0

)1(

6.2. Non-constant/supernormal growth model

t

t

t

t

r

P

r

D

r

D

r

DP

)1()1(...

)1(1 2

210

++

+++

++

+=

where

gr

gDP t

t−

+=

)1(

6.3. Required rate of return a) Constant growth model

gP

Dr +=

0

1

b) Nonconstant/supernormal growth model

t

t

t

t

r

P

r

D

r

D

r

DP

)1()1(...

)1(1 2

210

++

+++

++

+=

where

gr

gDP t

t−

+=

)1(

6.4. P/E ratio

NPVGOEPS

Price +=r

7. NPV and Other Investment Criteria

7.1. The NPV rule NPV = PV of future CFs – Cost

7.2. The payback rule

• Number of years it takes to pay back the initial

investment.

7.3. The discounted payback rule

• Use discounted cash flows.

7.4. The IRR rule

• The discount rate such that NPV = 0.

7.5. The profitability index rule

• The ratio of PV of future cash flows to initial

cost.

8. Project Cash Flow Analysis

8.1. PV of CCA tax savings a) No half-year rule:

dk

TdI c

+

××

b) Half-year rule:

+

+

+

××

k

k

dk

TdI c

1

2/1

8.2. (After-tax) operating cash flows (OCF) a) Basic:

OCF = EBIT + Depn – Taxes

b) Bottom-up:

OCF = NI + Depn

c) Top-down:

OCF = Sales – Costs – Taxes

d) Tax shield:

OCF = (Sales–Costs)(1–Tc) + Depn × Tc

8.3. Equivalent annual cost (EAC)

Final Exam Formula Sheets FINE 5200, Dr. Y.S. Tian

3

• The annual payment of an annuity over the same

investment horizon that has the same PV as the

NPV of a project.

8.4. Accounting break-even quantity

vP

DFCQ

−

+=

8.5. Cash break-even quantity

vP

T

TDFC

Q−

−

×−

= 1

8.6. Financial break-even quantity

• Q such that NPV = 0.

8.7. Degree of operating leverage

QQQ /

OCF)/OCF(

)%(

OCF)%(DOL

∆

∆=

∆

∆=

OCF

)1(1DOL

TDTFC ×−−+=

9. Risk and Return

9.1. Returns (sample average) a) Simple (arithmetic) average return

T

RRRR T

A

+++=

...21

b) Compound (geometric) average return

[ ] 1)1)...(1)(1(/1

21 −+++=T

TG RRRR

9.2. Risk (sample estimate)

• Variance:

( ) ( ) ( )1

...)(

22

2

2

1

−

−++−+−=

T

RRRRRRRVar T

• Standard deviation: )()( RVarRSD =

9.3. Expected return and risk

(population/theoretical)

• Expected return: ∑=

=n

i

ii RpRE1

)(

• Variance: [ ]2

1

2 )(∑=

−=n

i

iii RERpσ

• Standard deviation:

[ ] 2

1

2)( σσ =−= ∑

=

n

i

ii RERp

where 1...21 =++ nppp

• Risk Premium = E(R) − Rf

9.4. Stock portfolios

• Portfolio expected return:

)()()( bbaaP RExRExRE +=

• Portfolio variance:

bababbaaP xxxx σρσσσσ 222222 ++=

• Portfolio standard deviation:

bababbaaP xxxx σρσσσσ 22222 ++=

9.5. Systematic risk and beta

M

iMii

σ

σβ ,CORR=

9.6. Portfolio beta

∑=

=n

i

iiP x1

ββ

9.7. Security market line (CAPM)

])([)( fMifi RRERRE −+= β

9.8. Risk-to-reward ratio

• Total risk (Sharpe ratio):

σfRRE −)(

• Alpha: excess return

)]([ fMifii RRRR −+−= βα

• Systematic risk (Treynor ratio):

βfRRE −)(

10. Cost of Capital

10.1. WACC

PPDDEE RwTRwRwWACC +−+= )1(

where

DEPDE wwVPwVDwVEw −−==== 1/,/,/

10.2. Cost of equity a) Dividend growth model

gP

DRE +=

0

1

b) Security market line/CAPM

])([)( fMEfE RRERRE −+= β

c) Bond yield plus risk premium

RE = LT bond yield + Risk Premium

10.3. Cost of debt (1-T) RD where RD is before-tax yield to maturity

10.4. Cost of preferred stock

0P

DRP =

10.5. Floatation cost

PPDDEEA fwfwfwf ++=

costsFlotation proceedsNet

costsFlotation

+=Af

Final Exam Formula Sheets FINE 5200, Dr. Y.S. Tian

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11. Derivatives

11.1. Forward/futures contracts

11.2. Options

• Call options

• Put options