# Corporate Finance

**Topics:**Net present value, Corporate finance, Finance

**Pages:**11 (2588 words)

**Published:**October 24, 2013

(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(ๅฎๆฏๅบๅธ): 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(้ถๆฏๅบๅธ): 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 CFโs + 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 (donโt forget salvage value); NWC(donโt forget NWC return)

(10) Average Return=(R1+R2+โฆ.RT)/T; Standard deviation={[(R1-average R)^2+(R2-average R)^2+โฆ. (RT-average R)^2]/(T-1)}^(1/2) ๆณจๆๆๅผไธๅๆถ ็็ฎๆณ

(11) Rate of return on portfolio: rp=WbRb +WsRs; variance of the rate of return

on

two

risky

assets

portfolio:

ฯ2 = (WB ฯB )2 + (WS ฯS )2 + 2(WB ฯB )(WS ฯS )ฮฒBS ; ฮฒBS = Corr(R B , R S ) P

ฬ

ฬ

ฯAB = ๐ธ๐ฅ๐๐๐๐ก๐๐ ๐ฃ๐๐๐ข๐ ๐๐ [(R ๐ด โ R A ) โ (R ๐ต โ R B ) (12) Correlation and covariance: ๐ ๐ด๐ต = ๐ถ๐๐๐(๐ ๐ด , ๐ ๐ต ) =

๐ถ๐๐ฃ(๐ ๐ด ,๐ ๐ต )

;

๐ ๐ด ,๐ ๐ต

Beta(the

responsiveness of a security to movements in the market portfolio): ๐ฝ ๐ = ๐ถ๐๐ฃ(๐ ๐ ,๐ ๐ )

๐2 (๐ ๐ )

ฬ

ฬ

ฬ

(13) Capital Asset Pricing Model: R = R F + ฮฒ โ (R M โ R F ) ; R M โ R F is market risk premium

(14) Financial Leverage and Beta: ๐ฝ ๐ด๐ ๐ ๐๐ก = ๐ฝ ๐ธ๐๐ข๐๐ก๐ฆ ;

๐ฝ ๐ธ๐๐ข๐๐ก๐ฆ = ๐ฝ ๐ด๐ ๐ ๐๐ก โ (1 +

๐ท๐๐๐ก

๐ธ๐๐ข๐๐ก๐ฆ

๐ท๐๐๐ก

๐ท๐๐๐ก+๐ธ๐๐ข๐๐ก๐ฆ

โ ๐ฝ ๐ท๐๐๐ก +

๐ธ๐๐ข๐๐ก๐ฆ

๐ท๐๐๐ก+๐ธ๐๐ข๐๐ก๐ฆ

โ

) ; (useful in adjustment for financial

leverage)

(15) Cost of Capital: ๐ ๐๐ด๐ถ๐ถ = (

๐

๐+๐ต

) โ ๐๐ + (

๐ต

๐+๐ต

) โ ๐ ๐ต โ (1 โ ๐ ๐ถ )

(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

2ใKey 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 โค 1 , the smaller the correlation, the greater the risk reduction potential. If ๐ = 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 ๐ฟ = ๐ ๐ + ๐ก ๐ถ ๐ต, ๐ก ๐ถ ๐ต is the present value of the tax shield. ๐ ๐ 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 firmโs 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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