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Formula sheet of the gods - APCB
Asset Pricing and Capital Budgeting (Rijksuniversiteit Groningen)
Studeersnel wordt niet gesponsord of ondersteund door een hogeschool of universiteit
Gedownload door Paul Bulten (paul.bulten@hotmail.nl)
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Chapter 2: Introduction to Financial Statement
Net Working Capital=Current Assets-Current Liabilities
Book Value of Equity=the difference between assets and liabilities
Market Capitalisation (also the total market value of equity)=market price per
share*the number of shares outstanding
Market-to-Book Ratio=
π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ π‘‰π‘Žπ‘™π‘’π‘’ π‘œπ‘“ π‘’π‘žπ‘’π‘–π‘‘π‘¦
π΅π‘œπ‘œπ‘˜ π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ π‘’π‘žπ‘’π‘–π‘‘π‘¦
Enterprise Value=Market Value of Equity+Debt-Cash
𝑁𝑒𝑑 πΌπ‘›π‘π‘œπ‘šπ‘’
Earnings Per Share= π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  π‘‚π‘’π‘‘π‘ π‘‘π‘Žπ‘›π‘‘π‘–π‘›π‘”
Retained Earnings=Net Income-Dividends
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠
Payout Ratio= 𝑁𝑒𝑑 πΌπ‘›π‘π‘œπ‘šπ‘’
Change in StockholderΕ› Equity= Retained Earnings+Net Sales of Stock=Net
Income-Dividends+Sales of Stock-Repurchases of Stock
Gross Margin=Gross Profit/Sales
Operating Margin=Operating Income/Sales
Net Profit Margin=Net Income/Salese
Current Ratio=Current Assets/Current Liabilities
Quick Ratio= (Current Assets-Inventory)/Current Liabilities
Cash Ratio=Cash/Current Liabilities
Asset Turnover=Sales/Total Assets
Fixed Asset Turnover=Sales/Fixed Assets
Gedownload door Paul Bulten (paul.bulten@hotmail.nl)
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Accounts Receivable Days=Accounts Receivable/Average Daily Sales
πΆπ‘œπ‘ π‘‘ π‘œπ‘“ πΊπ‘œπ‘œπ‘‘π‘ 
πΌπ‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦
Inventory Turnover=
Leverage ratios:
(debt as source of financing)
Debt-Equity Ratio=Total Debt/Total Equity
Debt-To-Capital Ratio=Total Debt/ (Total Equity+Total Debt)
Net Debt=Total Debt-(Excess Cash and Short-Term Investments)
Debt-to-enterprise Value Ratio=Net Debt/(Market Value of Equity+Net Debt)
=(Net Debt/Enterprise Value)
Valuation ratios:
P/E Ratio=Market Capitalisation/Net Income=Share Price/Earnings Per Share
Return on Equity=Net Income/Book Value of Equity
𝐸𝐡𝐼𝑇(1−π‘‡π‘Žπ‘₯ π‘…π‘Žπ‘‘π‘’
Return on Invested Capital= π΅π‘œπ‘œπ‘˜ π‘‰π‘Žπ‘™π‘’π‘’ π‘œπ‘“ πΈπ‘žπ‘’π‘–π‘‘π‘¦+𝑁𝑒𝑑 𝐷𝑒𝑏𝑑
DuPont Identity
𝑅𝑂𝐸 =
𝑁𝑒𝑑 πΌπ‘›π‘π‘œπ‘šπ‘’
π‘†π‘Žπ‘™π‘’π‘ 
π‘†π‘Žπ‘™π‘’π‘ 
π‘‡π‘œπ‘‘π‘Žπ‘™ πΈπ‘žπ‘’π‘–π‘‘π‘¦
*
*
π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐴𝑠𝑠𝑒𝑑𝑠
π‘‡π‘œπ‘‘π‘Žπ‘™ πΈπ‘žπ‘’π‘–π‘‘π‘¦
Chapter 3 and 4: Time Value of Money
𝑛
𝑃𝑉 = 𝐢 ÷ (1 + π‘Ÿ)
𝑛
𝐹𝑉 = 𝐢 * (1 + π‘Ÿ)
π‘ƒπ‘’π‘Ÿπ‘π‘’π‘‘π‘’π‘–π‘‘π‘¦ 𝑃𝑉 =
𝐢
π‘Ÿ
Gedownload door Paul Bulten (paul.bulten@hotmail.nl)
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1
π‘Ÿ
𝐴𝑛𝑛𝑒𝑖𝑑𝑦 𝑃𝑉 = 𝐢 *
(1 −
1
)
𝑛
(1+π‘Ÿ)
𝑃𝑉 (πΊπ‘Ÿπ‘œπ‘€π‘–π‘›π‘” π‘ƒπ‘’π‘Ÿπ‘π‘’π‘‘π‘’π‘–π‘‘π‘¦) =
𝐢
π‘Ÿ−𝑔
𝑃𝑣(π‘”π‘Ÿπ‘œπ‘€π‘–π‘›π‘” π‘Žπ‘›π‘›π‘’π‘–π‘‘π‘¦) = 𝐢 *
1
π‘Ÿ−𝑔
Cash Flow in an Annuity (Loan Payment)
𝐢=
1
π‘Ÿ
𝑃
(1−
P = principal
1
(1+π‘Ÿ)
𝑁
1+𝑔 𝑛
(1 − ( 1+π‘Ÿ ) )
)
Chapter 5 and Chapter 6
1 + 𝐸𝐴𝑅 = (1 +
π‘…π‘’π‘Žπ‘™ π‘…π‘Žπ‘‘π‘’ =
𝐴𝑃𝑅
π‘š
)
π‘š
(m=number of compounding periods per year)
π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘…π‘Žπ‘‘π‘’−πΌπ‘›π‘“π‘™π‘Žπ‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’
1+πΌπ‘›π‘“π‘™π‘Žπ‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’
≈ π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘…π‘Žπ‘‘π‘’ − πΌπ‘›π‘“π‘™π‘Žπ‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’
1+π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘…π‘Žπ‘‘π‘’
Growth in Purchasing Power=1+Real= 1+πΌπ‘›π‘“π‘™π‘Žπ‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’
𝑃𝑉 =
𝑃𝑉 =
𝐢𝑛
𝑛
(1+π‘Ÿπ‘›)
𝐢1
1+π‘Ÿ1
+
𝐢2
(1+π‘Ÿ2)
+... +
𝐢𝑛
(1+π‘Ÿ
𝑛
)
𝑛
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BONDS
𝐢𝑃𝑁 =
πΆπ‘œπ‘’π‘π‘œπ‘› π‘…π‘Žπ‘‘π‘’*πΉπ‘Žπ‘π‘’ π‘‰π‘Žπ‘™π‘’π‘’
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ πΆπ‘œπ‘’π‘π‘œπ‘› π‘ƒπ‘Žπ‘¦π‘šπ‘’π‘›π‘‘π‘  π‘ƒπ‘’π‘Ÿ π‘Œπ‘’π‘Žπ‘Ÿ
Yield to Maturity of an n-Year Zero-Coupon Bond
1 + π‘Œπ‘‡π‘€π‘› = (
πΉπ‘Žπ‘π‘’ π‘‰π‘Žπ‘™π‘’π‘’
π‘ƒπ‘Ÿπ‘–π‘π‘’
)
1
𝑛
Yield to Maturity of a Coupon Bond
(PV of coupon payments + repayment) & (x = coupon rate * face value)
𝑃 = 𝐢𝑃𝑁 *
1
𝑦
(1 −
1
𝑛
(1+𝑦)
)+
𝐹𝑉
𝑁
(1+𝑦)
πΆπ‘™π‘’π‘Žπ‘› π‘ƒπ‘Ÿπ‘–π‘π‘’ = πΆπ‘Žπ‘ β„Ž (π·π‘–π‘Ÿπ‘‘π‘¦ π‘π‘Ÿπ‘–π‘π‘’) − π΄π‘π‘π‘Ÿπ‘’π‘’π‘‘ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘
π΄π‘π‘π‘Ÿπ‘’π‘’π‘‘ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = πΆπ‘œπ‘’π‘π‘œπ‘› π΄π‘šπ‘œπ‘’π‘›π‘‘ *
π·π‘Žπ‘¦π‘  𝑠𝑖𝑛𝑐𝑒 πΏπ‘Žπ‘ π‘‘ πΆπ‘œπ‘’π‘π‘œπ‘› π‘ƒπ‘Žπ‘¦π‘šπ‘’π‘›π‘‘
π·π‘Žπ‘¦π‘  𝑖𝑛 πΆπ‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ πΆπ‘œπ‘’π‘π‘œπ‘› π‘ƒπ‘’π‘Ÿπ‘–π‘œπ‘‘
Chapter 8 and 9
𝑁𝑒𝑑 π‘ƒπ‘Ÿπ‘’π‘ π‘’π‘›π‘‘ π‘‰π‘Žπ‘™π‘’π‘’
𝑁𝑃𝑉 = 𝑃𝑉(𝐡𝑒𝑛𝑒𝑓𝑖𝑑𝑠) − 𝑃𝑉(πΆπ‘œπ‘ π‘‘π‘ )
IRR=the interest rates that sets the net present value of the cash flows equal to zero
𝑁𝑃𝑉
Profitability Index= π‘…π‘’π‘ π‘œπ‘’π‘Ÿπ‘π‘’ πΆπ‘œπ‘›π‘ π‘’π‘šπ‘’π‘‘
(𝐸𝐡𝐼𝑇) = πΌπ‘›π‘π‘Ÿπ‘’π‘šπ‘’π‘›π‘‘π‘Žπ‘™ 𝑅𝑒𝑣𝑒𝑛𝑒𝑒 − πΌπ‘›π‘π‘Ÿπ‘’π‘šπ‘’π‘›π‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘π‘  − π·π‘’π‘π‘Ÿπ‘’π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›
Net working capital=Current Assets-Current Liabilities
=Cash+Inventory+Receivables-Payables
πΉπ‘Ÿπ‘’π‘’ πΆπ‘Žπ‘ β„Ž πΉπ‘™π‘œπ‘€ = (𝑅𝑒𝑣𝑒𝑛𝑒𝑒𝑠 − πΆπ‘œπ‘ π‘‘π‘  − π·π‘’π‘π‘Ÿπ‘’π‘π‘–π‘Žπ‘‘π‘–π‘œ) * (1 − π‘‡π‘Žπ‘₯ π‘…π‘Žπ‘‘π‘’) + π·π‘’π‘π‘Ÿπ‘’π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘› − πΆπ‘Žπ‘ 𝐸𝑋
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Capital Expenditure (Gain)=Sale Price-Book Value
Book Value=Purchase Price-Accumulated Depreciation
After-Tax Cash Flow from Asset Sale=Sale Price-(Tax Rate*Capital Gain)
Chapter 7 and Chapter 10
𝑃0 =
𝐷𝑖𝑣1+𝑝1
1+π‘Ÿπ‘’
π‘Ÿπ‘’ =
𝐷𝑖𝑣1+𝑃1
𝑃0
π‘ƒπ‘œ =
𝐷𝑖𝑣1
1+π‘Ÿπ‘’
− 1=
Dividend Discount Model
+
𝐷𝑖𝑣2
2
(1+π‘Ÿπ‘’ )
𝐷𝑖𝑣1
𝑃0
+... +
+
𝑃1−𝑃𝑂
𝑃0
𝐷𝑖𝑣𝑁
𝑁
(1+π‘Ÿπ‘’)
+
𝑃𝑁
𝑁
(1+π‘Ÿπ‘’)
Constant Dividend Growth Model
𝑃0 =
𝐷𝑖𝑣1
π‘Ÿπ‘’−𝑔
𝐷𝑖𝑣𝑑 =
πΈπ‘Žπ‘Ÿπ‘›π‘–π‘›π‘”π‘ π‘‘
π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  π‘‚π‘’π‘‘π‘ π‘‘π‘Žπ‘›π‘‘π‘–π‘›π‘”
π‘Ÿπ‘’ =
𝐷𝑖𝑣1
𝑃0
+𝑔
* 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘ƒπ‘Žπ‘¦π‘œπ‘’π‘‘ π‘…π‘Žπ‘‘π‘’
Change in Earnings=New Investment*Return on New Investment
New Investment=Earnings*Retention Rate
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Earnings Growth Rate=
πΆβ„Žπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 πΈπ‘Žπ‘Ÿπ‘›π‘–π‘›π‘”π‘ 
πΈπ‘Žπ‘Ÿπ‘›π‘–π‘›π‘”π‘ 
= π‘…π‘’π‘‘π‘’π‘›π‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’ * π‘…π‘’π‘‘π‘’π‘Ÿπ‘› π‘œπ‘› 𝑁𝑒𝑀 πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘
𝑔 = π‘…π‘’π‘‘π‘’π‘›π‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’ * π‘…π‘’π‘‘π‘’π‘Ÿπ‘› π‘œπ‘› 𝑁𝑒𝑀 πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘
Retention Rate=1-Payout
If early growth is variable followed by constant growth
π‘ƒπ‘œ =
π‘ƒπ‘œ =
𝑃𝑉(πΉπ‘’π‘‘π‘’π‘Ÿπ‘’ π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 π‘Žπ‘›π‘‘ 𝑁𝑒𝑑 π‘…π‘’π‘π‘’π‘Ÿπ‘β„Žπ‘Žπ‘ π‘’π‘ )
π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  π‘‚π‘’π‘ π‘‘π‘Žπ‘›π‘‘π‘–π‘›π‘”
+
𝐷𝑖𝑣2
𝐷𝑖𝑣𝑁
𝐷𝑖𝑣1
1+π‘Ÿπ‘’
+... +
2
(1+π‘Ÿπ‘’ )
(
𝑁
(1+π‘Ÿπ‘’)
1
𝑁
(1+π‘Ÿπ‘’)
)(
𝐷𝑖𝑣𝑁+1
π‘Ÿπ‘’−𝑔
)
Enterprise Value=Market value of Equity+Debt-Cash
π‘‰π‘œ(enterprise value)=PV(Future Cash Flow of Firm)
π‘ƒπ‘œ =
𝑉0+πΆπ‘Žπ‘ β„Ž0−𝐷𝑒𝑏𝑑0
π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  π‘‚π‘’π‘ π‘‘π‘Žπ‘›π‘‘π‘–π‘›π‘”0
πΈπ‘›π‘‘π‘’π‘Ÿπ‘π‘Ÿπ‘–π‘ π‘’ π‘£π‘Žπ‘™π‘’π‘’, π‘‰π‘œ =
𝑉𝑁 =
𝐹𝐢𝐹𝑁+1
π‘Ÿπ‘€π‘Žπ‘π‘−𝑔𝐹𝐢𝐹
= (π‘Ÿ
πΉπ‘œπ‘Ÿπ‘€π‘Žπ‘Ÿπ‘‘ 𝑃/𝐸 =
(1+π‘Ÿπ‘Šπ‘Žπ‘π‘)
1+𝑔𝐹𝐢𝐹
−𝑔𝐹𝐢𝐹
π‘€π‘Žπ‘π‘
π‘ƒπ‘œ
𝐹𝐢𝐹1
𝐸𝑃𝑆1
=
+
𝐹𝐢𝐹2
) * 𝐹𝐢𝐹𝑁
𝐷𝑖𝑣1/𝐸𝑃𝑆1
π‘Ÿπ‘’−𝑔
2
(1+π‘Ÿπ‘€π‘Žπ‘π‘)
=
.....
𝐹𝐢𝐹𝑁
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘ƒπ‘Žπ‘¦π‘œπ‘’π‘‘ π‘…π‘Žπ‘‘π‘’
π‘Ÿπ‘’−𝑔
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𝑁
(1+π‘Ÿπ‘€π‘Žπ‘π‘)
+
𝑉𝑁
𝑁
(1+π‘Ÿπ‘€π‘Žπ‘π‘)
lOMoARcPSD|16790850
𝑉0
𝐸𝐡𝐼𝑇𝐷𝐴1
=
𝐹𝐢𝐹1
π‘…π‘€π‘Žπ‘π‘−𝐺𝑓𝑐𝑓
𝐸𝐡𝐼𝑇𝐷𝐴1
=
𝐹𝐢𝐹1/𝐸𝐡𝐼𝑇𝐷𝐴1
π‘…π‘€π‘Žπ‘π‘−𝐺𝑓𝑐𝑓
Chapter 11 and Chapter 12
Realized return = Dividend yield + Capital gain yield
Realized return:
Annual realized return =
Average annual returns (Arithmetic): =
Geometric Average = ((1+R1) (1+R2) (1+R3) … (1+Rn))
Standard deviation =
Prediction interval:
1/𝑛
(𝑅)
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Portfolio weights (w):
Return of Portfolio:
*Return is a %
(Expected) return of Portfolio:
6
Variance of two-stock portfolio:
Market capitalization = (No. of shares outstanding) x (Price per share)
Expected Return = Risk-Free Rate + Risk Premium for Systematic Risk
Expected return of a stock/investment : Capital asset Pricing model:
CAPM(Security market line):
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= expected Rate of return = Rf + β(Rmarketportflio - Rf)
= Risk-Free Rate + BETA * Risk Premium per Unit of Systematic Risk
Beta of a portfolio with securities weight w:
β𝑝 = 𝑀1β1 + 𝑀2β2 + ... + 𝑀𝑛β𝑛
Constant dividend growth model: P= (
Chapter 13
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑
π‘Ÿ−𝑔
)
CAPM model = cost of equity = expected return
Market value of equity + Market value of debt = Market value of assets
Rwacc = (Fraction of firm value financed by equity) (Equity cost of capital) + (Fraction of
firm value financed by debt) (Debt cost of capital) = Asset cost of capital
Effective after-tax borrowing rate: rd (1- Tc)
Cost of Preferred stock Capital = (Preferred dividend / Preferred stock price)
=𝐷𝑖𝑣 𝑝𝑓𝑑 / 𝑃 𝑝𝑓𝑑
Cost of Equity = (Dividend (in one year) / Current Price) + Dividend Growth rate =
𝐷𝑖𝑣1
𝑃𝑒
+ 𝑔
Rwacc = ReE% + RpfdP% + Rd (1-Tc) D%
Rwacc = ReE% + Rd (1-Tc)D%
Net Debt = Debt - Cash and Risk-Free Securities
𝐿
V 0= FCF 0+
𝐹𝐢𝐹1
(1+π‘…π‘€π‘Žπ‘π‘)
+
𝐹𝐢𝐹2
(1+π‘…π‘€π‘Žπ‘π‘)
2
+...
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STOCKS
Tradeoff between dividends and growth
-
Increasing growth requires investment yet money spent on investments cannot
be paid out as dividends. This means that to increase growth a firm must retain
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more of its earnings at the expense of dividend payouts. Nevertheless, retaining
more earnings is not necessarily a guarantee of increased growth. The reason
for this is that for a cut in dividends to increase the firm’s value by raising the
stock price, the investments in which the retained earnings will be used for MUST
generate a return that exceeds the firm’s cost of capital.
Drawbacks of the CDGM
-
-
Certain firms pay no dividends. Specifically younger firms in their early growth
stages must retain their earnings and reinvest them. Once they mature and their
growth rate lessens, their earnings will usually exceed their investment needs
and then start paying dividends.
Certain firms do not have a steady growth rate until they mature.
Drawbacks of the DDM
- Reliance on uncertain dividend forecasts
= the DDM values a stock based on a forecast of the future dividends. However, such cash
flows are uncertain. The slightest change in the assumed dividend growth rate will lead to large
changes in the stock price estimation, especially at higher growth rates. Moreover, it is hard to
confidently estimate the appropriate dividend growth rate. Essentially forecasting dividends
implies that we must also forecast the firm’s earnings which heavily depend on the firm’s
financing practices and therefore its interest expenses. Furthermore, we must also forecast the
dividend payout rate and the future number of shares outstanding which both depend on
whether the firm decides to embark on a share repurchase program. Given how this decision is
at the management’s discretion, it is hard to reach a reliable forecast of the future dividends.
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Not all stocks pay dividends
Share repurchases and the Total Payout Method
Gedownload door Paul Bulten (paul.bulten@hotmail.nl)
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