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Stockholm Business School

Formula sheet Corporate Finance (COF)

2

Present Value calculation Discount factor

𝐷𝐹 =

Present value of single cash flow

1 (1 + 𝑟)𝑘

PV =

𝐶 (1 + 𝑟)𝑛

Present value of an annuity

PV(𝐴𝑛𝑛𝑢𝑖𝑡𝑦) = 𝐶 ∙

1 1 ∙ [1 − ] 𝑟 (1 + 𝑟)𝑁

Present value of a growing annuity with growth rate g

1 1+𝑔 𝑁 PV = 𝐶 ∙ ∙ [1 − ( ) ] 𝑟−𝑔 1+𝑟 Present value of a growing perpetuity with growth rate g

PV = 𝐶 ∙

1 𝑟−𝑔

Constant dividend growth model

PV (share)0 =

𝐷𝑖𝑣1 𝑟𝐸 − 𝑔

Future Value calculations Future value

Future value of Annuity

FV𝑛 = 𝑃𝑉 ∙ (1 + 𝑟)𝑛

1 FV (𝐴𝑛𝑛𝑢𝑖𝑡𝑦) = 𝐶 ∙ ∙ [(1 + 𝑟)𝑁 − 1] 𝑟

3

Conversion of interest rates Nominal and real rates 𝒓𝒓 =

𝒓−𝒊 𝟏+𝒊

𝒓 ∙ (𝟏 − 𝝉)

Effective annual rate to effective period rate

𝟏 + 𝒓 = (𝟏 + 𝒓𝒑𝒆𝒓𝒊𝒐𝒅 )

Nominal rate after taxes

𝒏

Effective annual rate to annual percentage rate

𝑨𝑷𝑹 𝒌 ) 𝟏 + 𝑬𝑨𝑹 = (𝟏 + 𝒌

Bonds, MV of debt Coupon bonds, debt with interest payments

𝐹𝑉 1 1 ]+ P = 𝐶𝑃𝑁 [1 − 𝑁 (1 + 𝑦) 𝑦 (1 + 𝑦)𝑁

CAPM (Capital Asset Pricing Model) Security Market Line

𝐸[𝑅𝑖 ] = 𝑅𝑓 + 𝛽𝑖 (𝐸[𝑅𝑀 ] − 𝑅𝑓 )

Beta

𝛽𝑖 =

𝜎𝑖,𝑀 𝜎𝑀2

Levered beta vs Unlevered beta Levered beta

D BetaL  BetaU1  1 - t m  E

Unlevered beta

BetaU 

BetaL 1  1 - t m 

D E

4

WACC (Weighted Average Cost of Capital) 𝑊𝐴𝐶𝐶 =

𝐸

𝐸+𝐷

𝐷 𝑟𝑒 + 𝐸 + 𝐷 𝑟𝑑 (1 − 𝑡𝑎𝑥)

Valuation Value of Equity t=n

Value of Equity= t=1

Value of Firm

CF to Equity t (1+k e )t

t =n

Value of Firm =  t =1

CF to Firm t (1 + WACC) t

Free Cash Flows FCFF

FCFE

FCFF = EBIT (1- tax rate) - Net Capital Expenditures - Change in Net Working Capital

FCFE = Net Income - Net Capital Expenditure Change in Net Working Capital + New Debt - Debt Repayment.

FCFF from FCFE

Net Capital Expenditures

FCFF = Net Income + Interest (1 tax rate) – Net Capital Expenditures Net Capital Expenditures = Changes in Capital Expenditures - Depreciation - Change in Net Working Capital

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Expected Growth Expected Growth in EPS

Expected Growth Rate in EBIT

Expected Growth in EPS = ROE * Retention Rate

Expected Growth Rate in EBIT =ROC * Reinvestment Rate

Interest Coverage Ratio Interest Coverage Ratio 

EBIT Interest Expense

Value Created in Change of WACC Value Created  FV Bef o reth e Chan g e

WACC OLD  WACC NEW WACC NE W - Growth In NE W W ACC

Dividend Dividends Yields Annual Dividends per share Dividend Yield  Price per share

Dividend Payout Ratio Dividend Payout Ratio 

Dividends Earnings

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NPV, IRR, MIRR, Payback Period and Profitability Index Net Present Value (NPV) n

NPV  - CF0   t 0

CF t t  (1 r )

Internal Rate of Return (IRR) n

0  - CF0   t0

Modified Internal Rate of Return (MIRR)

MIRR  (

Ter min al Value 1 / n ) 1 Initial Investment

CFt (1  IRR ) t

Payback Period

PB 

Initial Cash Outlay Annual Net Cash Flow

Profitability Index n

CFt

 (1  r )

t

PI 

t 1

CF0

Return on Capital (ROC) Return on Capital (After - tax) 

EBIT (1  t ) Average BV of Total Investment in

Return on Equity (ROE) Return on Equity 

Net Income Average BV of Equity Investment in Pr oject...