Formulas Flashcards
Present value of an Annuity
Either:
PV = C x (1/r - 1/r x (1+r)^t )
Or PV= c x annuity factor
C = cash flow
R = interest rate
T= time
Future Value (FV)
FV = PV x (1+r)^t
Present value with annual compounding
PV = FV / (1+R)^t
Using discount factor
PV = FV x discount factor
Using annuity
PV= C x annuity factor
Annuity due
C x (1/r - 1/r x (1+r)^t ) x (1+r)^t
Present value today
PV = FV/ (1+r)^t
Future value of annuity
PV annuity x (1+r)^t
Effective interest rate
Effective interest rate = (1 + r/n) ^n -1
NPV of project
NPV of project = CF0 + CF x annuity factor
CF0 = initial investment
CF = cash flow
Profitability index
Profitability index = NPV / initial investment
NPV of year t today
NPV of year t today = NPVt / (1+r)^t
Pre tax profit
Pre tax profit = earnings - depreciation
Taxes
Taxes = tax rate x pre tax profit
Profit after tax
Profit after tax = pre tax profit - taxes
Operating cash flow
Operating cash flow = profit after tax + depreciation
Net cash flow
Net cash flow = ( rev- expenses) x (1- tax rate) + (tax rate x dep) + (additional investment in working capital, if pos minus it, if neg add it )
WACC(opportunity cost of capital)
WACC = ((equity / equity + debt) x Te) + (debt / debt + equity) x Td x (1 - Tr))
PV of growing perpuity or value of firm
PV of growing perpuity or value of firm = PV = c / r - g
Or annual free cash flow / WACC - constant rate
Underwriting spread
Underwriting spread = offered shares price - underwriter share
Subscription price
Subscription price = how much they need to raise / how many they’re offering
Value of merged firm
Value of merged firm = value of acquiring + value of target + economic gains
Value of acquiring / value of firm
Value of acquiring / value of firm = price per share x no. Of shares
Value of target
Value of target = shares outstanding x share price
Earnings of merged firms
Earnings of merged firms = earning of acquiring + earnings of target
Mm prop 1 - for when there are no taxes and you’re working out WACC
R assets = r debt x D/+E + r assets x E/D+E
For equation for mm proposition 2 for when restructuring
R equity = r assets (WACC) + D/E (r assets - r debt)
