FM Final Formulas

Future value

FV = PV x (1 + r)^t

Present value

PV = FV / (1 + r) ^t

NPV

= -Co + Cn / (1 + r)ⁿ +…

Perpetuity

PV = C / r

Perpetuity due

PV = C + (C / r)

Growing perpetuity

PVo = C1 / (r - g)

Annuity

PV = C x [ (1 / r) - (1 / (r x (1 + r)ⁿ) ]

Annuity due

PV = C x [ (1 / r) - (1 / (r x (1 + r)ⁿ) ] x (1 + r)

Growing annuity

PV = ( C / (r - g) ) - [ ( C (1 + g)ⁿ / ( (r - g) (1 + r )ⁿ)

Inflation

1 + real rate = (1 + nominal rate) / (1 + inflation rate)

Real amount

= Nominal amount / (1 + inflation rate)ⁿ

Effective Annual Rate (EAR)

= (1 + r)ⁿ - 1

Annual Percentage Rate (APR)

= r x n

IRR

0 = Co + Cn / (1 + IRR)ⁿ + …

Profitability index

PI = NPV / Investment

EAA

= NPV / Annuity factor

Calculating cash flow

1. Initial investment in fixed assets and WC

2. Cash flows come in and perhaps more money in WC

3. Sell plant and equipment or move them to different project and disinvestment in WC

Total cash flow

= Cash flow from capital investment + cash flow from investments in WC + cash flow from operations

Steps for capital investment

1. find annual depreciation

2. find cumulative depreciation

3. find BV

4. Find ATSV

BV

= Initial cost - Accumulated depreciation

ATSV

= SV - t x (SV - BV)

Steps of investing in working capital

1. Level of WC

2. Change in working capital

3. NWC - change

WC

= AR + Inventory - Accounts payable

Steps for cash flow from operations

1. Revenue - expenses - depreciation

2. Calculate and subtract out taxes

3. Add back depreciation

CF from operation = after tax profit + depreciation

Bond pricing PV

Po = cpn x [ (1 / r ) - (1 / r ( 1 + r )ⁿ) ] + par / ( 1 + r )ⁿ

Total return formula

[ (reinvested coupons + bond selling price) / price paid ] ^ 1/n -1

Dividend formula

Div1 = EPS (1 - b(reinvestment rate)) or Div 1 = Do * (1 + g)

Constant growth price of stock formula

Po = Div1(div next year) / r(discount rate or required rate of return) - g

Growth rate

Plowback ratio(earnings reinvested in firm) * ROE(return on equity)

PVGO=

PVG - PVNG

Dividend yield for year t

= Divt (Div paid for that year) / Pt-1 (price of stock at beginning of that year)

Expected return

E(R)= (Pi(probability of outcome i) * Ri(return outcome i) +…

Expected return of portfolio

E(Rportfolio)= (wA*(RA)) + (wB *(RB)) +…

Variance of returns

𝜎² = Pi(probability of outcome i) (Ri(return outcome i) - E(R)expected return))²

Standard deviation

𝜎 = square root variance

Covariance of A and B

= Pi* (RiA​−E(RA​))(RiB​−E(RB​)) +…

Correlation coefficient of A and B

Covar / 𝜎 A * 𝜎 B

Portfolio Beta

= (weight1 B1) + (weight2 * B2) + …

CAPM expected return

E(ri)= rf + B*(rm - rf)

Market risk premium

= rm - rf

Security risk premium

= B*(rm - rf)

WACC

= (D/V)*(1 - t)*(rD) + (E/V)*(rE)

V

= D + E, market value of firm, calculate by using perpetuity or NPV/DCF formula where r is WACC

D

= # of bonds * price, market value of debt

E

= # of shares * price, market value of equity

rE

Cost of common equity, comes from solving r of CAPM model

rD

Before tax cost of debt, comes from r of bond

Weighted avg before cost debt

= (Div1 / Div1 + Div2) r1 + (Div2 / Div1 + Div2) *r2

After tax cost of debt

= rD before * (1 - t)

Expected rate of return=

[Div1 + Capital gains (P1 - Po)] / Po

PV tax shield

tD = TC(corporate tax rate)*D

Value of levered firm

=Vu(value of all equity financed) + tD(PV tax shield)

Rasssets

= (D/V)*(rD) + (E/V)*(rE)

Calculate rate of return on equity as firm leverages and firm’s debt to equity ratio increases

rE = rassets + (D/E)*(rassets - rD)

Net Income

=(EBIT - Interest expense)(1 - t)

rassets to unlever debt by removing tax shield

rassets= rwacc / 1 - (t*(D/V))

rassets to relever adding leverage risk back in to get equity return

re = rassets + (D/E)(rassets - rD)

EPS

NI / # of shares