Corporate Finance Formulas

Overview of Relevant Formulas Corporate Finance (B40.2302) _________________________________________________________________________________________ 1. Present value of $1 to be received after t years at discount rate r: 2. Present value of annuity of $1 per year for t years at discount rate r:
$1 (1 + r )t

⎡1 − (1 + r ) − t ⎤ ⎢ ⎥ × $1 r ⎣ ⎦ 1 ⎡ (1 + g )t ⎤ 3. Present value of growing annuity of $1 at rate g per year at discount rate r: ⎢1 − ⎥ × $1 r − g ⎣ (1 + r )t ⎦
$1 r

4. Present value of perpetuity of $1 per year at discount rate r:

5. Present value of perpetuity of $1 with constant growth rate g at discount rate r:

$1 r−g

6. Measures of risk for individual financial asset i:

Variance of returns:
Standard deviation of returns: Covariance of returns assets i and j:

Var (ri ) = σ i2 = Expected value of [ri − E (ri )]2

σ i = σ i2
Cov(ri , rj ) = σ ij = Exp. value of [ri − E (ri )][rj − E (rj )]

Correlation between returns i and j: Expected portfolio return (N assets):

ρij =

σ ij σ iσ j
N i =1 N

E (rp ) = ∑ wi ri (weights wi)

Portfolio variance (N assets): 7. Beta of financial asset i:

σ = ∑∑ wi w jσ ij (weights wi, wj)
2 p i =1 j =1

N

βi =

Cov(ri , rm ) σ im = 2 Var (rm ) σm

8. Capital Asset Pricing Model → Expected return financial asset i: r = rD ×

E ( ri ) = rf + [ E (rm ) − rf ] × β i

9. Weighted Average Cost of Capital (WACC):

D E × (1 − T ) + rE × V V

D⎤ D ⎡ 10. Cost of capital levered firm: r = rA ⎢1 − T × ⎥ (scenario 1) or r = rA − T × rD × (scenario 2) V V⎦ ⎣ D D 11. Cost of equity levered firm: rE = rA + [rA − rD ] × × (1 − T ) (scenario 1) or rE = rA + [rA − rD ] × (scenario 2) E E D D 12. Equity beta levered firm: β E = β A + [ β A − β D ] × × (1 − T ) (scenario 1) or β E = β A + [ β A − β D ] × (scenario 2) E E 13. Asset beta levered firm: β A = (1 − T ) D E D E × βD + × β E (scenario 1) or β A = × β D + × β E (scenario 2) V V E + (1 − T ) D E + (1 − T ) D

14. Value of the