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Corporate Finance Formulas

In: Business and Management

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FORMULAS

Expected return of a stock portfolio - E[rp]: (3 stocks)
E[rp] = X1 ( E(r1) + X2 ( E(r2) + X3 ( E(r3)

Portfolio variance ((P)2 : (3 stocks) ((P)2 = X12 ( (12 + X1( X2((12 + X1( X3((13 + + X2( X1((21 + X22 ( (22 + X2( X3((23 + + X3( X1((31 + X3( X2((32 + X32 ( (32

where: X1 , X2 och X3 is respective stocks amount of the total value of the portfolio. (12 , (22 and (32 is respective stocks variance (12 = (21 is the covariance between stock 1 and stock 2 (13 = (31 is the covariance协方差 between stock 1 and stock 3 (23 = (32 is the covariance between stock 2 and stock 3

CAPM:
E(rj) = rf + (j ( [E(rm) -rf]

where: E(rj) is the expected return of stock j E(rm) is the expected return of the market portfolio rf is the risk-free interest rate (j is the beta-value of stock j

(j = Cov (rj,rm)/var(rm) = (jm ( [pic]

Stock j:s contribution to the risk of the portfolio (j = [pic]

MODIGLIANI & MILLER

M&M Prop I. Without corporate taxes:
VL = VU

M&M Prop II. Without corporate taxes: rS = rU + (rU - rB) ( [pic]

M&M Prop I. With corporate taxes:
VL = VU + TC (B

M&M Prop II. With corporate taxes: rS = rU + (rU - rB) ( [pic] ((1-TC)

rWACC = [pic]rB ((1-TC) + [pic]( rS

VL = [pic] where: VU = Value of the all equity financed firm (Unlevered firm)
VL = Value of the Levered firm
B = Value of the debt (bond value)
S = Value of the equity (Stock value)
TC = Corporate tax rate) rU = Required rate of return of an unlevered firm rS = Required rate of return of the Stocks rB = The cost of Bonds rWACC = Weighted Average Cost of Capital
EBIT = Earnings before interest and tax
Beta and Leverage

Without corporate tax
(asset = (equity ( Equity/(Equity+Debt) + (debt ( Debt/(Equity+Debt)

if (debt = 0 ( (equity = (Equity+Debt)/Equity ( (asset

With corporate tax if (debt = 0 (
(equity = [1 + (1-TC)(Debt/Equity] ( (Unlevered firm

ADJUSTED PRESENT VALUE (=APV)
APV = NPV + NPVF

where:
NPV = The value of the project to an unlevered firm
NPVF = Net present value of the financing side effects

FLOW TO_EQUITY APPROACH

[pic]

The Black-Scholes option pricing model

[pic]

where: [pic]

[pic]

1. S = Current stock price
1. E = Exercise price of call
1. r = Continuous risk-free rate of return (annualized)
1. (2 = Variance (per year) of the continuous return on stock
1. t = Time (in years) to expiration date

In addition, there is the statistical concept:

N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d

Put Call Parity
|Value of put = Value of call +Present value of exercise price-Value of stock) |
|P(E) = C(E) + E/(1+r)t – S |

Annuityfactor (n years, r %) = Nusummefaktorn (n år, r %):
[1 – (1+r)-n]/r

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