Law Outlines Corporate Finance Outlines
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,...
Buy the full version of these notes or essay plans and more in our Corporate Finance Outlines.
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...
Ask questions 🙋 Get answers 📔 It's simple 👁️👄👁️
Our AI is educated by the highest scoring students across all subjects and schools. Join hundreds of your peers today.
Get Started