TOPIC 2 Time value of money

Present Value
Present Value
Value today of a future cash flow.
Discount Factor
Present value of a $1 future payment.
Discount Rate
Interest rate used to compute
present values of future cash flows.
Calculation Recommendations
Four primary approaches to solving the problems.
Using the formulas and a standard calculator. You will need basic algebra skills and a calculator that will raise numbers to a power and take roots.
Using tables from the text. Before the ready accessibility of computing power, this method was used for all TVM problems.
Definitions and Abbreviations
CF0, CF1 , etc: cash flows, a series of payments or receipts or both.
EAR: effective annual [interest] rate, the annual interest rate that reflects the effects of compounding.
PV: present value, the value on a given date of a future payment or series of future payments.
Time Value of Money Formulas
Future value of a lump-sum: FV PV (1 r)n
r or i: interest rate.
lump sum: a single payment or receipt, in contrast with annuity or perpetuity.
n or t: number of time periods, months, half-years, years, etc.
FV: future value, the accumulated value of an investment once all payments are made, including interest or return received.
g: growth rate, we assume this is constant over time.
Present value of a lump-sum:
PV FV (1 r) n
Present value of a perpetuity: Present value of an annuity:
PV C r
PV

C
1 r

1 r(1
r
)n

Future value of an annuity:
Using a financial calculator. A wide variety of financial calculators are available, in a wide range of prices.
Using Excel on a personal computer. Excel contains built-in functions that will perform most Time Value of Money calculations.
Compare with FV of an annuity
PMT or C: payment, the constant payment or receipt of an annuity or perpetuity.
perpetuity: a series of payments that never ends, where each payment is the same amount and the payments occur at the end of evenly spaced time periods.
ASSET EVALUATION
Time Value of Money
TOPIC 2
Topics Covered
Present Value & Future Value Annuity & Perpetuity Effective Annual Interest Rate Inflation Currencies
annuity: a series of payments or receipts having three specific characteristics, also called ordinary annuity or annuity in arrears（迟付年金）.
annuity due（即付年金）: an annuity where the payments occur at the beginning of evenly spaced time periods.
FV

C
(1
r)n r
1
Time Value of Money Formulas
Present value of an annuity due:
PV

C

r

r
(1
1
r)n
(1

r)
Compare with PV of an annuity
Future value of an annuity due: