How to calculate present values

How to calculate present values

Back to the future

Chapter 3

Discounted Cash Flow Analysis

(Time Value of Money)

? Discounted Cash Flow (DCF) analysis is the foundation of

valuation in corporate finance

? To use DCF we need to know three things

? The size of the expected cash flows

? The timing of the cash flows

? The proper discount (interest) rate

? DCF allows us to compare the values of alternative cash

flow streams in dollars today (Present Value)

1

FUTURE VALUE

(COMPOUNDING):

What will $100 grow to after 1 year at 10% ?

0

10%

1

|----------------------|

-100

interest

10

end of period value 110

FV1 = PV0 (1+r) = 100 (1.1) = 110

where FV1 is the future value in period 1

PV0 is the present value in period 0 (today)

NOTE: When r=10%, $100 received now (t=0) is

equivalent to $110 received in one year (t=1).

What will $100 grow to after 2 years at 10% ?

0

10%

1

10%

2

|---------------------|---------------------|

100

interest

10

11

end of period value 110

121

FV2 = PV0 (1+r) (1+r)= PV0 (1+r)2

= 100 (1.1)2 = 100 (1.21) = 121

NOTE: $100 received now (t=0) is equivalent to

$110 received in one year (t=1) which is also

equivalent to $121 in 2 years (t=2).

2

The general formula for future value in year N (FVN)

FVN = PV0 (1+r)N

What will $100 grow to after 8 years at 6% ?

What is the present value of $159.40 received

in 8 years at 6%?

Or

How much would you have to invest today at 6%

in order to have $159.40 in 8 years?

COMPOUND INTEREST

Future value of $1

18

16

Year

1

2

5

10

20

14

12

10

FUTURE VALUE

5%

10%

15%

1.050

1.100

1.150

1.103

1.210

1.323

1.276

1.331

2.011

1.629

2.594

4.046

2.653

6.727

16.37

8

6

4

2

0

0

2

4

6

8

10

12

14

Year

r = 5%

3

r = 10%

r = 15%

16

18

20

PRESENT VALUE IS THE RECIPROCAL

OF FUTURE VALUE:

PV0 = FVN /(1+r)N

Note: Brealey & Myers refer to 1/(1+r)N as a

¡°discount factor¡±.

The discount factor for 8 years at 6% is

1/(1+.06)8 = 0.627

Thus, the present value of $1.00 in 8 years

at 6% is $0.627.

What¡¯s the present value of $50 in 8 years?

PRESENT VALUES

Present value of $1

1

PRESENT VALUE

Year

1

2

5

10

20

0.8

0.6

5%

.952

.907

.784

.614

.377

10%

.909

.826

.621

.386

.149

15%

.870

.756

.497

.247

.061

0.4

r = 5%

0.2

r = 10%

r = 15%

0

0

2

4

6

8

10

Years

4

12

14

16

18

20

PRESENT VALUE PROBLEMS

Which would you prefer at r=10%?

$1000 today vs. $2000 in 10 years

There are 4 variables in the analysis

PV, FV, N, and r

Given three, you can always solve

for the other

5

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