Principles of cororate finance 6th brealey myers chapter 03

Principles of Corporate Finance
Brealey and Myers



Sixth Edition

How to Calculate Present Values

Slides by
Matthew Will
Irwin/McGraw Hill

Chapter 3

©The McGraw-Hill Companies, Inc., 200


3- 2

Topics Covered
 Valuing Long-Lived Assets
 PV Calculation Short Cuts
 Compound Interest
 Interest Rates and Inflation
 Example: Present Values and Bonds

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200

3- 3

Present Values
Discount Factor = DF = PV of $1

 Discount Factors can be used to compute
the present value of any cash flow.
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 4

Present Values
Discount Factor = DF = PV of $1

DF 

1
t
(1r )

 Discount Factors can be used to compute
the present value of any cash flow.
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200

3- 5

Present Values
C1
PV DF C1 
1  r1
DF  (11r ) t
 Discount Factors can be used to compute
the present value of any cash flow.

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 6

Present Values

Ct
PV DF Ct 
1  rt
 Replacing “1” with “t” allows the formula to be
used for cash flows that exist at any point in
time.
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200

3- 7

Present Values
Example
You just bought a new computer for $3,000. The payment
terms are 2 years same as cash. If you can earn 8% on
your money, how much money should you set aside today
in order to make the payment when due in two years?

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 8

Present Values
Example
You just bought a new computer for $3,000. The payment
terms are 2 years same as cash. If you can earn 8% on
your money, how much money should you set aside today
in order to make the payment when due in two years?

PV 

Irwin/McGraw Hill

3000
(1.08 ) 2

$2,572.02

©The McGraw-Hill Companies, Inc., 200


3- 9

Present Values
 PVs can be added together to evaluate
multiple cash flows.

C1

C2

PV  (1r )1  (1r ) 2 ....

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 10

Present Values
 Given two dollars, one received a year from
now and the other two years from now, the
value of each is commonly called the Discount
Factor. Assume r1 = 20% and r2 = 7%.

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 11

Present Values
 Given two dollars, one received a year from
now and the other two years from now, the
value of each is commonly called the Discount
Factor. Assume r1 = 20% and r2 = 7%.

DF1 

1.00
(1.20 )1

DF2 
Irwin/McGraw Hill

1.00
(1.07 ) 2

.83
.87

©The McGraw-Hill Companies, Inc., 200

3- 12

Present Values
Example
Assume that the cash flows
from the construction and sale
of an office building is as
follows. Given a 7% required
rate of return, create a present
value worksheet and show the
net present value.

Year 0
Year 1
Year 2
 150,000  100,000  300,000
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 13

Present Values
Example - continued
Assume that the cash flows from the construction and sale of an office
building is as follows. Given a 7% required rate of return, create a
present value worksheet and show the net present value.

Period
0
1
2

Irwin/McGraw Hill

Discount
Factor
1.0
1
1.07 .935
1
1.07  2

.873

Cash
Flow
 150,000
 100,000

Present
Value
 150,000
 93,500

 300,000
 261,900
NPV Total  $18,400

©The McGraw-Hill Companies, Inc., 200


3- 14

Short Cuts
 Sometimes there are shortcuts that make it
very easy to calculate the present value of an
asset that pays off in different periods. These
tolls allow us to cut through the calculations
quickly.

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 15

Short Cuts
Perpetuity - Financial concept in which a cash
flow is theoretically received forever.

cash flow
Return 
present value
C
r
PV

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 16

Short Cuts
Perpetuity - Financial concept in which a cash
flow is theoretically received forever.

cash flow
PV of Cash Flow 
discount rate
C1
PV 
r
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 17

Short Cuts
Annuity - An asset that pays a fixed sum each
year for a specified number of years.

1
1 

PV of annuity C  
t
 r r 1  r  

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 18

Annuity Short Cut
Example
You agree to lease a car for 4 years at $300 per month.
You are not required to pay any money up front or at the
end of your agreement. If your opportunity cost of capital
is 0.5% per month, what is the cost of the lease?

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 19

Annuity Short Cut
Example - continued
You agree to lease a car for 4 years at $300 per month.
You are not required to pay any money up front or at the
end of your agreement. If your opportunity cost of

capital is 0.5% per month, what is the cost of the lease?

 1

1
Lease Cost 300 

48 
 .005 .0051  .005  
Cost $12,774.10
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 20

Compound Interest
i
ii
Periods Interest
per
per
year
period

iii
APR
(i x ii)

iv
Value
after
one year

v
Annually
compounded
interest rate

1

6%

6%

1.06

2

3

6

1.032

= 1.0609

6.090

4

1.5

6

1.0154 = 1.06136

6.136

12

.5

6

1.00512 = 1.06168

6.168

52

.1154

6

1.00115452 = 1.06180

6.180

365

.0164

6

1.000164365 = 1.06183

6.183

Irwin/McGraw Hill

6.000%

©The McGraw-Hill Companies, Inc., 200


3- 21

FV of $1

Compound Interest
18
16
14
12
10
8
6
4

2
0

10% Simple
10% Compound

Number of Years
Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 22

Inflation
Inflation - Rate at which prices as a whole are
increasing.
Nominal Interest Rate - Rate at which money
invested grows.
Real Interest Rate - Rate at which the
purchasing power of an investment increases.

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 23

Inflation

1+nominal interest rate
1  real interest rate =
1+inflation rate

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 24

Inflation
1+nominal interest rate
1  real interest rate =
1+inflation rate

approximation formula

Real int. rate nominal int. rate - inflation rate

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200


3- 25

Inflation
Example
If the interest rate on one year govt. bonds is 5.9%

and the inflation rate is 3.3%, what is the real
interest rate?
Savings
Bond

Irwin/McGraw Hill

©The McGraw-Hill Companies, Inc., 200