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