Formulas

Question 1

Present value of an Annuity

Answer 1

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

Question 2

Future Value (FV)

Answer 2

FV = PV x (1+r)^t

Question 3

Present value with annual compounding

Answer 3

PV = FV / (1+R)^t

Question 4

Using discount factor

Answer 4

PV = FV x discount factor

Question 5

Using annuity

Answer 5

PV= C x annuity factor

Question 6

Annuity due

Answer 6

C x (1/r - 1/r x (1+r)^t ) x (1+r)^t

Question 7

Present value today

Answer 7

PV = FV/ (1+r)^t

Question 8

Future value of annuity

Answer 8

PV annuity x (1+r)^t

Question 9

Effective interest rate

Answer 9

Effective interest rate = (1 + r/n) ^n -1

Question 10

NPV of project

Answer 10

NPV of project = CF0 + CF x annuity factor

CF0 = initial investment

CF = cash flow

Question 11

Profitability index

Answer 11

Profitability index = NPV / initial investment

Question 12

NPV of year t today

Answer 12

NPV of year t today = NPVt / (1+r)^t

Question 13

Pre tax profit

Answer 13

Pre tax profit = earnings - depreciation

Question 14

Taxes

Answer 14

Taxes = tax rate x pre tax profit

Question 15

Profit after tax

Answer 15

Profit after tax = pre tax profit - taxes

Question 16

Operating cash flow

Answer 16

Operating cash flow = profit after tax + depreciation

Question 17

Net cash flow

Answer 17

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 )

Question 18

WACC(opportunity cost of capital)

Answer 18

WACC = ((equity / equity + debt) x Te) + (debt / debt + equity) x Td x (1 - Tr))

Question 19

PV of growing perpuity or value of firm

Answer 19

PV of growing perpuity or value of firm = PV = c / r - g

Or annual free cash flow / WACC - constant rate

Question 20

Underwriting spread

Answer 20

Underwriting spread = offered shares price - underwriter share

Question 21

Subscription price

Answer 21

Subscription price = how much they need to raise / how many they’re offering

Question 22

Value of merged firm

Answer 22

Value of merged firm = value of acquiring + value of target + economic gains

Question 23

Value of acquiring / value of firm

Answer 23

Value of acquiring / value of firm = price per share x no. Of shares

Question 24

Value of target

Answer 24

Value of target = shares outstanding x share price

Question 25

Earnings of merged firms

Answer 25

Earnings of merged firms = earning of acquiring + earnings of target

Question 26

Mm prop 1 - for when there are no taxes and you’re working out WACC

Answer 26

R assets = r debt x D/+E + r assets x E/D+E

Question 27

For equation for mm proposition 2 for when restructuring

Answer 27

R equity = r assets (WACC) + D/E (r assets - r debt)