CF

473.32

5

Winter 2014

The Time Value of Money

ch 5

Time Value of Money

What is the Present Value

• of $ received in future?

Future Value• of $ given today?

Interest Rate• during the periods between?

Present Value

$1,000

-$900

Present Value

FP

$1,000

-$900

Present Value

-$800

P F

$1,000

-$900

Present Value

-$800

P

-$700

F

$1,000

-$900

Present Value

-$800

P

-$700

F

-$600

$1,000

-$900

Present Value

-$800

P

-$700

F

-$600-$500

$1,000

-$500 -$600 -$700 -$800 -$900

Present Value

FV5PV0

? ? ? ? ?

Present Value

tr

FVPV

1

$1,000-$500 -$600 -$700 -$800 -$900

FV

1=t

10%=r

$1,000=FV

= ?PV

t

“discounting”

110.1

000,1

PV

vfvp

PV

Present Value

tr

FVPV

1

$1,000-$909.09

FV

1=t

10%=r

$1,000=FV

= -$909.09PV

t

“discounting”

09.909

10.1

000,11

PV

? PV

Present Value

tr

FVPV

1

$1,000-$909.09

FV

2=t

10%=r

$1,000.00=FV

= ?PV

t

“discounting”

210.1

00.000,1

PV

-$826.45

t

45.826

Present Value

tr

FVPV

1

$1,000

FV

=t

10%=r

$1,000.00=FV

=PV

“discounting”

-$751.31-$683.01-$620.92 -$909.09-$826.45

1…5

PV FV

Future Value

trPVFV )1(

=t

10%=r

?=FV

= -$1,000PV

$1,100-$1,000

t

1

?

1)10.1(000,1 FV

100,1

PV FV

Future Value

trPVFV )1(

=t

10%=r

$1,210=FV

= -$1,000PV

$1,100-$1,000

t

2

?

2)10.1(000,1 FV

210,1

t

“compounding”

Why not $1,200?

$1,210

Future Value

trPVFV )1(

=t

10.00%=r

=FV

= -$1,000.00PV

$1,100.00-$1,000.00

1…5

“compounding”

$1,210.00

t=4 t=5t=3t=2t=1

$1,331.00 $1,464.10 $1,610.51

PV

FV

Future Value

also works as a general growth formula suppose we

• currently sell 1,000 widgets/year

• expect to increase sales at 10%/year for 5 years

how many will we be selling in five years?

useful for figuring out building projects & capital needs

trPVFV )1( 5

)10.1(00.000,1 51.610,1

tt

rPVFV )1(

=r

?=t

$1,100.00=FV

= -$1,000.00 PV

$1,100.00-$1,000.00

10%

“time periods”

PV

r

PVFVt

1log

loglog

FV

$2,000.00

$2,000.00

years 72.7t

rt

rPVFV )1(

=t

?=r

$1,100.00=FV

= -$1,000.00 PV

$1,100.00-$1,000.00

1

“discount rate”

FVPV

1

1

t

PV

FVr

100.000,1

00.100,1 1

1

r 10.

r

=t

?=r

$1,420.00=FV

= -$1,000.00 PV

$1,420.00-$1,000.00

1

“discount rate”

FVPV

1

1

t

PV

FVr

100.000,1

00.420,1 1

1

r 42. %00.42

r

=t

?=r

$1,420.00=FV

= -$1,000.00 PV

$1,420.00-$1,000.00

5

“discount rate”

FVPV

1

1

t

PV

FVr

100.000,1

00.420,1 5

1

r 0726. %26.7

r “discount rate” interest rate IRR

• internal rate of return

ERR• equivalent rate of return

CAGR• compound annual growth rate

Time Value of Money

useful for choosing between options suppose we can choose between

a. investing $500 in a company receiving $600 in 5 years

b. putting $500 in the bank at 4%

which is better?

r ?

FV ?$608.33

3.71%

trPVFV )1(

Remember

this is the most important chapter

read work on problems meet think

next Tue report due