TIME VALUE OF MONEY
PV = Present Value FV = Future Value
i = Interest Rate
Future value of $100 earning 10% interest in one year
FV = 100 + (100* .10) = $110
FV = PV + Interest
FV = PV + (PV * i)
Future value of 100 in two years earning 10% per year is
FV=[100+(100 * .10)] +[100 + (100 *.1)]*.10 = $121
FV =[ PV +( PV * i)] + [PV +(PV * i)]* i
FV = PV(1+i)(1+i)
FV = PV(1+i)(1+i)
FV = PV(1+i)N N=number of periods (years)
TIME VALUE OF MONEY
Financial Calculator - BA II PLUS
Calculate the future value of $100 in 2 years earning 10% interest per year
2nd FV (clears calculator of any numbers)
2ND I/Y 1 Enter CE/C (computes interest
on yearly basis)
2nd . 6 Enter CE/C (6 decimal places)
2 N (2 year period)
10 I/Y (10% interest rate)
- 100 PV (100 is the present value amount)
CPT FV (computes future value = 121)
Calculate FV of 10,000 in 10 years at 15%
TIME VALUE OF MONEY
Present value amount - find the amount of money to invest today to have $1000 in 5
years if the investment earns 10%.
PV = FV(1/1+i)N
PV = 1000(1/1+.1)5
PV = 1000(.62092) = $620.92
Financial Calculator
2nd FV (Clears calculator)
5 N ( 5 years)
10 I/Y (10% interest)
1000 FV (1000 in 5 years)
CPT PV (Finds present value amt=$620.92)
Find PV of $1,000,000 in 30 yrs at 15%
1
RULE OF 72
72 / % = number of years to double
investment
If you earn 10% on your money per year, how long will it take to double your
investment?
72 / 10 = 7.2 years
If your investment doubles in 10 years, what return per year did
you make.
ANNUITIES
Find the future value of four $100 payments made at the end of each year for four years if
you earn 10%per year.
FV = $100(1+.10)3 + $100(1+.10)2 +$100(1+.10)1 +$100
FV = $100[(1+.10)3 + (1+.10)2
+ (1+.10)1 + 1]
FV = $100(4.6410) = $464.10
Financial Calculator
2nd FV (clear calculator)
4 N (4 payments)
10 I/Y (10% interest)
- 100 PMT (100 payments)
CPT FV (Calculates future value = $464.10)
Find PV
4N
10 I/Y
100 PMT
CPT PV (PV=-316.99)
Find PMT
10000 Loan 10% 5 year monthly payments
5*12 = 60 N
10/12 I/Y
-10,000 PV
CPT PMT (212.47)
TIME VALUE OF MOMEY
2
ANNUITIES
Find the present value of four $100 payments made at the end of each of the next four
years earning a return of 10% per year.
PV = 100(1/1+.1)1 + 100(1/1+.1)2 + 100(1/1+.1)3 + 100(1/1+.1)4 =
PV = 100[(1/1+.1)1 + (1/1+.1)2 +(1/1+.1)3 + (1/1+.1)4] = 100(3.1698) = $316.98
Financial Calculator
2nd FV (clears calculator)
4 N (4 payments)
10 I/Y (10% interest)
100 PMT ($100 payments)
CPT PV (calculates present value = 316.98)
TIME VALUE OF MONEY
PERPETUITIES
Find the present value of $100 payment made at the end of each and every year forever if
it earns 10% interest per year.
PV = 100 / .10 = 1000
PV (Perpetuity) = Payment / Interest Rate
CAPITAL BUDGETING TECHNIQIUES
WITH THE BA II PLUS
Required Return = 10% I = 10%
Year
0
1
2
3
4
Cash Flows
- $110,000
43,332
45,976
35,928
54,964
Find the NPV & IRR
2nd CE/C
CFo
-110000 Enter
↓
43332 Enter
↓
↓
[Clears Calculator]
[CFo=0.0000]
[CFo=-110000]
[C01 0.0000]
[C01 = 43332]
[F01= 1.000]
[C02 0.0000]
3
45976 Enter
↓
↓
35928 Enter
↓
↓
54964 Enter
NPV
10
Enter
↓
CPT
IRR
CPT
[C02= 45976]
[F02= 1.000]
[C03 0.0000]
[C03= 35928]
[F03= 1.000]
[C04 0.0000]
[C04= 54964]
[I = 0.00000]
[I = 10.0000]
[NPV= 0.0000]
[NPV= 31,923.8112]
[IRR= 0.0000]
[IRR= 22.4824]
4