0

20

20

30

30

5%

5%

Periods

Periods

10

10

4.1 Time Lines PV=$100 PV=$100

PV=$100

Cash

Cash

FV=?

FV=?

FV= 3 years I= 5% 4.2 Future Values -A dollar today is worth more than a dollar to be received in the future -Compounding: Process of going forward from present values to future values -FVN: Future Value or ending amount in an account after N periods -CFt: Cash Flow. Can be + or – For a borrower the first cash flow is positive and the next are negative ex. CF0 = PV = the cash flow at Time 0 can be at the beginning or ends of periods -I: Interest rate earned per year. Interest is earned based on the balance at the beginning of each year. Interest is paid at the end of the year. I/YR Also can be r = rate of return. -INT: $ of interest earned during the year = beginning amount -N: Number of periods involved in the analysis -Step-by-Step Approach -Timeline can be used. Periods

Periods

0

0

2

2

30

30

40

40

5%

5%

$100

$100

$105

$105

$110.25

$110.25

$115.76

$115.76

Cash

Cash

(1+I) = (1.05)

(1+I) = (1.05)

Multiply initial amount & each succeeding beginning of year amount by this.

Multiply initial amount & each succeeding beginning of year amount by this.

PV=$100

PV=$100

-Amount at end of year 1 FV1 = PV + INT FV1 = PV + PV(I) FV1 = PV (1+I) FV1 = $100(1+.05) = $100(1.05) = $105 FV2 = -Earn more interest in 2nd year because earn $5(.05) = .25 on interest on the first year’s interest of $5 = Compounding & interest earned on interest = Compound Interest Formula:

FVN = PV(1+I)N

Formula:

FVN = PV(1+I)N

-Formula Approach FV2 = FV1(1+I) FV2 = PV(1+I)(1+I) FV2 = PV(1+I)2 FV2 = $100(1+.05) 2 = $110.25 -Financial Calculators -5 Keys N

N

I/YR

I/YR

PV

PV

PMT

PMT

FV

FV

Press value then key

Press value then key

-N = # of periods -I/YR = Interest Rate Per Year -PV = Present Value (Making a deposit so a negative outflow = negative number) -PMT = Payment – used if have a series of equal or constant payments -FV = Future Value Calculator Tips -Set to 1 payment per year -End Mode vs. Beginning Mode: KNOW -Negative sign for outflows: one transaction has to be negative: type value then +/- sign -Decimal places -Interest Rates: enter as percent (5.25) not (.025) -Spreadsheets -Create area called inputs as “references” for solving -Timelines: Each column designates a different period on it -Future Value Function (fx) symbol financial function FV Function =FV(I,N,O,PV) -“Sensitivity Analysis”: use cell reference so can swap out values -% based on how cell is formatted -Graphic View