Corporate Finance

FORMULAS TIME VALUE OF MONEY
PV (simple without compounding) = FV/1+r
FV (simple without compounding) = PV (1+r)

PV (compounding) = FV / (1+r)n
FV (compounding) = PV (1+r)n

PV (for monthly, daily or bi-annually basis) = FV / (1+r/m)n*m
FV (for monthly, daily or bi-annually basis) = PV(1+r/m)n*m To find interest rate: FV = PV (1+r(?))n (FV and PV are given)
APR (Annual Present Rate) = r * Total days in a year/given days
In Excel: =RATE(n,pmt,PV)

EAR (Effective Annual Rate) OR EAY (Effective Annual Yield):
EAR/EAY = [1+r/m]m – 1 (m = no. of periods)
In Excel: =EFFECT(r,n)

Continuous Compounding (to find FV) = Co * er*t Co = initial investment e = 2.718 (constant) r = APR (rate of interest) t = No. of years (periods)
Continuous Compounding (to find PV) = Co * 1/er*t

PERPETUITY
PV = C/r (C = Cash inflow)
PV of Growing Perpetuity = PV = C/r-g (r = initial rate, g = growth rate) * Initial rate is always greater than growth rate.

Perpetuity Interest Rate
Perpetuity Interest Rate

Annuity
PVA (Present value of annuity) = C[1/r – 1/r(1+r)t ] PV Of Growing Annuity = C[(1+r)t -1/r] FVA (Future value of annuity) = PMT/r-g[1- (1+g)n/(1+r)n]

NET PRESENT VALUE
NPV = - Cost (PV) + Benefit (PV) * ‘-‘sign shows outflow of cash while ‘+’ sign shows inflow of cash.

Investment is profitable, if-----------------------Cost (PV) Benefit (PV)
Investment is not profitable, if-------------------Cost (PV) Benefit