Corporate Finance

Topics: Net present value, Corporate finance, Finance Pages: 11 (2588 words) Published: October 24, 2013
1ใ€Formulas๏ผš
(1) Sustainable growth rate=retention ratio*ROE=PRAT (P: Profit margin, R: retention ratio=retained E/E; A: Asset turnover ratio=sales/asset; T: Asset/beginning of the period equity)
(2) Compounding an investment m times a year for T years provides for future value of wealth: FV=C0*(1+r/m)^(m*T)
(3) Future value of an investment compounded continuously over many periods: FV=C0*e^(r*T) e=2.718
(4) Perpetuity: PV=C/r; Growing Perpetuity: PV=C/(r-g) g=growth rate; Annuity: PV=C/r*[1-1/(1+r)^T];
Growing Annuity: PV=C/(r-g) *
{1-[(1+g)/(1+r)]^T}
(5) Bonds: Level-coupon bonds(ๅฎšๆฏๅ€บๅˆธ): PV= C/r*[1-1/(1+r)^T]+F/(1+r)^T C=Coupon payment per period, F=Face value, T=Time to maturity. Pure Discount Bonds(้›ถๆฏๅ€บๅˆธ): PV=F/(1+r)^T
(6) Stocks: Zero growth: P0=Div/r
Constant growth: : P0=Div/(r-g);
R=Dividend yield +capital gain yield = Div/P0 + g
(7) Price Earnings Ratio(P/E ratio)=Price per share/earnings per share (8) NPV=Total PV of future CFโ€™s + Initial investment, initial investment should be negative number
(9)CFs=OCF+Net capital spending+change in NWC:
Operating cash flow=EBIT-Taxes+Depreciation; Net capital spending (donโ€™t forget salvage value); NWC(donโ€™t forget NWC return)
(10) Average Return=(R1+R2+โ€ฆ.RT)/T; Standard deviation={[(R1-average R)^2+(R2-average R)^2+โ€ฆ. (RT-average R)^2]/(T-1)}^(1/2) ๆณจๆ„ๆƒๅ€ผไธๅŒๆ—ถ ็š„็ฎ—ๆณ•
(11) Rate of return on portfolio: rp=WbRb +WsRs; variance of the rate of return
on
two
risky
assets
portfolio:
ฯƒ2 = (WB ฯƒB )2 + (WS ฯƒS )2 + 2(WB ฯƒB )(WS ฯƒS )ฮฒBS ; ฮฒBS = Corr(R B , R S ) P
ฬ…
ฬ…
ฯƒAB = ๐ธ๐‘ฅ๐‘๐‘’๐‘๐‘ก๐‘’๐‘‘ ๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’ ๐‘œ๐‘“ [(R ๐ด โˆ’ R A ) โˆ— (R ๐ต โˆ’ R B ) (12) Correlation and covariance: ๐œŒ ๐ด๐ต = ๐ถ๐‘œ๐‘Ÿ๐‘Ÿ(๐‘… ๐ด , ๐‘… ๐ต ) =

๐ถ๐‘œ๐‘ฃ(๐‘… ๐ด ,๐‘… ๐ต )
;
๐œŽ ๐ด ,๐œŽ ๐ต

Beta(the

responsiveness of a security to movements in the market portfolio): ๐›ฝ ๐‘– = ๐ถ๐‘œ๐‘ฃ(๐‘… ๐‘– ,๐‘… ๐‘€ )
๐œŽ2 (๐‘… ๐‘€ )

ฬ…
ฬ…
ฬ…
(13) Capital Asset Pricing Model: R = R F + ฮฒ โˆ— (R M โˆ’ R F ) ; R M โˆ’ R F is market risk premium
(14) Financial Leverage and Beta: ๐›ฝ ๐ด๐‘ ๐‘ ๐‘’๐‘ก = ๐›ฝ ๐ธ๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ ;

๐›ฝ ๐ธ๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ = ๐›ฝ ๐ด๐‘ ๐‘ ๐‘’๐‘ก โˆ— (1 +

๐ท๐‘’๐‘๐‘ก
๐ธ๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ

๐ท๐‘’๐‘๐‘ก
๐ท๐‘’๐‘๐‘ก+๐ธ๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ

โˆ— ๐›ฝ ๐ท๐‘’๐‘๐‘ก +

๐ธ๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ
๐ท๐‘’๐‘๐‘ก+๐ธ๐‘ž๐‘ข๐‘–๐‘ก๐‘ฆ

โˆ—

) ; (useful in adjustment for financial

leverage)
(15) Cost of Capital: ๐‘Ÿ ๐‘Š๐ด๐ถ๐ถ = (

๐‘†
๐‘†+๐ต

) โˆ— ๐‘Ÿ๐‘† + (

๐ต
๐‘†+๐ต

) โˆ— ๐‘Ÿ ๐ต โˆ— (1 โˆ’ ๐‘‡ ๐ถ )

(16) Capital structure decision: Firm value=PV of the firm if it were all equity financed + PV of tax shield โ€“ PV of financial distress
2ใ€Key Concepts
(1) When calculating NPV, consider opportunity cost, ignore sunk cost. (2) For bonds, the longer the time to maturity, the greater the interest rate risk; the lower the coupon rate, the greater the interest rate risk. (3) -1< ๐œŒ โ‰ค 1 , the smaller the correlation, the greater the risk reduction potential. If ๐œŒ = 1, no risk reduction is possible.

(4)The value of firm is always the same under different capital structures. (MM Proposition I (no taxes)).
(5) The expected return on equity is positively related to leverage because the risk to equity holders increase with leverage.(MM Proposition II (no taxes) ๐‘‰ ๐ฟ = ๐‘‰ ๐‘ˆ + ๐‘ก ๐ถ ๐ต, ๐‘ก ๐ถ ๐ต is the present value of the tax shield. ๐‘‰ ๐‘ˆ is unleveraged firm value.

(6) Goals of Corporate Finance management: maximize the shareholder wealth/ maximize share price/ maximize firm value.
(7) Stock holders may maximize their wealth at the expense of bondholders: increasing leverage, increasing dividends, taking risky projects. (8) Bond concepts: a. Bond prices and market interest rates move in opposite directions. b. When coupon rate = YTM, price = par value, when coupon rate > YTM, price > par value(premium bond)

(9) IRR disadvantage: IRR may not exist or there may be multiple IRR; Problems with mutually exclusive investments(scale problem and timing problem).
(10) Portfolio risk=nonsystematic risk (diversifiable) + systematic risk (non-diversifiable).
(11) From the firmโ€™s perspective, the expected return is the Cost of Equity Capital. An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall...
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