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Law Outlines Corporate Finance Outlines

Corporate Finance Formulas Sheet Outline

Updated Corporate Finance Formulas Sheet Notes

Corporate Finance Outlines

Corporate Finance

Approximately 3 pages

This formula sheet includes formulas used in a law school corporate finance course. Formulas relate to present/future value; present/future values of perpetuities including those that are delayed or at constant growth; annuities; bonds including present value, yield to maturity, duration, and modified duration; calculating stock prices and dividends with and without growth; business metrics such as ROE, present value of growth opportunities, dividend yield, etc.; calculating risk; portfolio analy...

The following is a more accessible plain text extract of the PDF sample above, taken from our Corporate Finance Outlines. Due to the challenges of extracting text from PDFs, it will have odd formatting:

FORMULAS – CORPORATE FINANCE

Future Value = FV = P • (1 + r)t . . . (P = principle; r = risk free market rate; t = # of periods)

Present Value Formulas

PV = C1/(1+r)t = DF • C1 . . . (C1 = future cash flow; DF = discount factor)

Discount Factor = DF = 1/(1+r)t . . . (r = risk free market rate; t = # of periods)

Net PV = NPV = PV – required investment = C0 + [i=1 to T] Ci/(1+r)i

Present value of what an investment gives you over the market (+ = good investment)

C0 = initial investment (normally negative!); required investment = same thing

Perpetuity: set cash payment in every year (perpetuity that starts in year zero, begins payments in year 1)

PV of Perpetuity = Cash Flow / Market Rate = C / r . . . (see proof on p. 27) (first cash flow at t1)

PV of Delayed Perpetuity = C/(r • (1 + r)t) . . . (i.e. PV of CF discounted for delay) (perpetuity starts in year t, but the first payment comes in year t+1: delayed t years after normal perpetuity)

PV of constant growth perpetuity = PV0 = C1 / (r – g) . . . (g = growth rate of the cash flow)

PV of constant growth perpetuity at any time = PVt = Ct+1 / (r – g)

Annuity: annuity received in year zero, starts payments of C at year 1, and ceases at year t (i.e. t payments)

PV of Annuity year 1 to t = (C/r) – (C/r)•(1/(1+r)t) = (C/r)• (1 – (1/(1+r)t)) = perpetuity – delayed perpetuity

FV of Annuity year 1 to t = (C/r) • [(1+r)t-1]

Annuity Factor: (1/r) – (1/r)•(1/(1+r)t)

Equivalent annual annuity = present value of cash flows / annuity factor

Use this to find the cash flow per period (annuity) that has the same present value as the actual cash flow of the project

Bonds: purchase in year zero, first payment either at 6 months or 1 year

PV of Bond = annuity + deferred maturity value = C/(1+r)1 + C/(1+r)2 + . . . + (maturity value + C)/(1+r)N

Normally all Coupons (C) are equal, at C = coupon rate • maturity value

If paid semi-annually, half the market rate r for similar bonds, half of coupons C (assuming stated annually), and take periods as 6 months

Yield to Maturity = YTM = the market rate for similar bonds (note: this is essentially the return you will get after discount or premium)

Duration = [t=1 to T] t •PV(Ct)/PV = see back of book for easier formula using yield

(t = period; T is maturity time; PV(Ct) = present value of the payment in year t, PV is the current PV)

Duration measures how long before the bond price is paid via cash flows

Modified Duration = volatility(%) = duration / (1 + YTM)

Sensitivity of the bond to the market: percentage change in bond price for a 1 percentage-point change in the yield

Stock:

With Fixed Rate of Growth:

P0 = Div1 / (r – g) (for constant growth of dividends, value at t=0 with div1 paying out at t=1 NOT t=0)

In sum, you accumulate in year zero, use dividend in year 1 to calculate

Get “r” by CAPM; get “Div1” by ROE•payout ratio (“POR”); get “g” by ROE•PBR

Dividend growth rate = g = ROE • plowback ratio (conservative estimate)

Payout Ratio: fraction of earnings paid as dividends

Plowback Ratio: fraction of earnings retained by firm (POR + PBR = 1)

Without Growth (Fixed Dividends)

PV(stock) = P0 = PV(expected future dividends) = [t = 1 to inf.] Div1 / (1 + r)t . . . (r = expected return)

If Only Next Year’s Dividends are Known:

P0 = (Div1 + P1)/(1+r)

P1 = P0 • (1 + r) – Div1

In General

Expected Return= (Dividend + appreciation)/price = r = (Div1 + P1 - P0)/P0 = g + (Div1/P0) = g + dividend yield

(P0=current price; P1=price in one year; Div1=dividend to be paid in one year); (g=firm growth rate)

AKA Cost of Equity Capital, Market Capitalization Rate, Opportunity Cost of Capital

Dividend Yield = Div1/P0

Note: the dividend yield = r (expected return) when there is no growth

ROE = return on equity = Earnings per share / book value(equity) per share = earnings / book value(equity)

PVGO = present value of growth opportunities = P0 with new plowback – P0 without new plowback

P0 = (EPS/r) + PVGO

Valuing Business or Project

PV = PVH / (1+r)H + [t = 1 to H] FCFt / (1+r)t = FCF1 / (1+r)1 + FCF2 / (1+r)2 + . . . + PVH / (1+r)H

(H = valuation horizon, FCF = future cash flow, r = opportunity cost of capital)

First term is PV of free cash flows, whereas the second is PV of horizon value

Risk: a range of possible outcomes

r = rf + rp . . . (rf = risk free rate; rp = risk premium)

Standard Deviation and Variance

Variance= σ2 = (ř – r)2 . . . (ř = actual return, r = expected return)

= sum of all probabilities,...

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