BA 440 Final Formula Sheet

CAPM / Cost of Equity: re  rf   rm  rf
Market risk premium: rm - rf
Unlevered/Levered Beta:
u 

L
1  1  t D / E 
After tax cost of debt (rd) = Before-tax cost of debt * (1-t)
After tax cost of debt (rd) = BTrd * (1-t)
After tax cost of debt (rd) = YTM * (1-t)
After Tax Cost of debt = (Treasury yield + spread) * (1-t)
Cost of Preferred Stock:
rps 
D ps
Pps
E
D
PS






Costofcapital  WACC  re 
  rd 
  rps 

 E  D  PS 
 E  D  PS 
 E  D  PS 
Straight line depreciation: (Original asset value – salvage value) / number of years to be depreciated
Leases:
Operating lease cash flows:
lease payments * (1 – t)
Buy/borrow cash flows: Interest expense (after tax), Principal payment, Maintenance expenses (after tax),
Depreciation tax benefit (depreciation * tax rate), Salvage value (after tax)
The net advantage to leasing : NPV of lease option – NPV of buy option
Convertible Bonds:
Conversion option = Convertible bond price – value of straight bond component
Value of a bond
1

1 - (1 + r) n
=C
r



 Pr incipal

(1  r ) n


Conversion ratio = # of shares for which each bond may be exchanged
Conversion value = current value of shares for which the bonds can be exchanged
Conversion premium = bond price – conversion value
Venture Capital Method:
Exit or terminal value = P/E multiple * forecasted earnings
Discounted terminal value =
Exit value
1  target return n
VC ownership proportion = Capital provided / discounted terminal value
IPO Underpricing:
Underpricing (return) = (first day closing price – offer price) / offer price
Rights offerings:
Rights required to purchase one share =
Value of the right =
# of original shares
# of shares issued in RO
rights-on price – subscription price
n+1
OR rights-on price – ex-rights price
Ex-rights price =
New value of equity
New number of shares
Benefits/Costs of debt:
Yearly tax benefit from debt = Tax Rate * Interest Payment
Cost of Capital Approach to Optimal Capital Structure:
Interest Coverage Ratio = EBIT / Interest Expenses
Implied growth rate assuming constant growth model:
g
V *WACC  CF
CF  V
Firm Value (Stable growth) = CF to Firm (1 + g) / (WACC -g)
Firm Value opt WACC- Firm Value orig WACC
Dividend policy:
Free cash flow to equity = Net Income + Depr&Amort – Chg in WC – Cap Exp
+ (New Debt Issue – Debt Repay) – Pref. Dividends
Estimated FCFE = Net Income - (1- ) (Capital Expenditures - Depreciation)
- (1- ) (Chg in WC) – Preferred Dividends
where  is the debt ratio (D / (D+E) and
Chg in WC = WCt – WCt-1
where WC = Non-cash current assets – non-debt current liabilities
CF to stockholders to FCFE Ratio = (Dividends + Buybacks) / FCFE
Valuation:
Relative valuation (P/E, P/BV, P/S, EV/EBITDA):
Firm value = Comparable multiple * Firm-specific denominator value
PEG = (P/E)/ Growth in earnings
BV (of equity) = total shareholders equity – preferred stock
Profit margin = Net income/Sales
Retention ratio = 1 – Dividends/Earnings
Enterprise value = market cap + Debt – Cash
EBITDA = earnings before interest taxes depreciation and amortization
DCF valuation:
t=N
FCFE t TerminalVa lue

t
(1  re ) N
t =1 (1 + re )
Value of Equity = 
FCFEN * (1  g s )
re  g s
Terminal value:
Equity Reinvestme nt Rate 
(Cap Exp. - Depr   in WC)(1 -  )
Net Income - Interest Income
where  is the debt ratio (D / (D+E)) and
Chg in WC = WCt – WCt-1
where WC = Non-cash current assets – non-debt current liabilities
Growth in earnings = ERR * non-cash ROE
where
Non  cashROE 
NetIncome  InterestIncome
BVofequity  (cash  marketablesec urities )
PV equations:
Present value of a perpetuity: PV 
Present value of multiple cash flows:
CF
r
n
PV  
t 1
FV
Present value of single future cash flow: PV 
(1  r )t
1

1 - (1 + r) n
PV of an Annuity = PV(A, r, n) = A 
r







CFt
1  r t