Business Finance – Time Value of Money
Future Value and Compounding終值與複利
Future Value: the amount an investment is worth after one or more periods.
FV = PV(1+r)^t
Present Value and Discounting 現值與折現
Present Value: the current value of future cash flows discounted at the appropriate discount rate.
PV = FV/(1+r)^t
Future Value Interest Factor 終值利率因子(1+r)^t
Present Value Interest Factor 現值利率因子1/(1+r)^t
Business Finance – Discounted Cash Flow Valuation
Future and Present Values of Multiple Cash Flows
FVIFA = Future Value Interest Factor Annuity年金終值利率因子
PVIFA = Present Value Interest Factor Annuity 年金現值利率因子
年金PV = PMT[(1-1/((1+r)^t)/r) = PMT[(1-PVIF)/r] = PMT*PVIFA
年金FV = PMT[((1+r)^t-1)/r] = PMT[(FVIF-1)/r] = PMT*FVIFA
Annuity Due 期初年金= 普通年金*(1+r)
Perpetuity PV永續年金= C/r (A annuity that the cash flows continue forever)
Effective Annual Rate(EAR), Annual Percentage Rate(APR)
To compare different investments or interest rates, we need to convert to effective rates.
EAR = (1+Quoted Rate/m)^m-1
Loan Types and Loan Amortization 分期償還
Pure Discount Loan
A borrower receive money today and repays a simple lump sum at some time in the future.
先把要借出去的錢折現回來，來決定共要收多少錢。
PV = (1+r)^t
Interest-Only Loan
The loan that requires borrower to pay interest each period and to repay the entire principal at some point in the future.
Amortized Loan
