Transcript No Slide Title

Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Making Investment Decisions with
the Net Present Value Rule
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 6
©The McGraw-Hill Companies, Inc., 2000
6- 2
Topics Covered
 What To Discount
 IM&C Project
 Project Interaction
Timing
 Equivalent Annual Cost
 Replacement
 Cost of Excess Capacity
 Fluctuating Load Factors

Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 3
What To Discount
Only Cash Flow is Relevant
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 4
What To Discount
Only Cash Flow is Relevant
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 5
What To Discount
Points to “Watch Out For”
Do not confuse average with incremental
payoff.
Include all incidental effects.
Do not forget working capital requirements.
Forget sunk costs.
Include opportunity costs.
Beware of allocated overhead costs.
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 6
Inflation
INFLATION RULE
 Be consistent in how you handle inflation!!
 Use nominal interest rates to discount
nominal cash flows.
 Use real interest rates to discount real cash
flows.
 You will get the same results, whether you
use nominal or real figures.
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 7
Inflation
Example
You own a lease that will cost you $8,000 next year,
increasing at 3% a year (the forecasted inflation
rate) for 3 additional years (4 years total). If
discount rates are 10% what is the present value
cost of the lease?
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 8
Inflation
Example
You own a lease that will cost you $8,000 next year,
increasing at 3% a year (the forecasted inflation
rate) for 3 additional years (4 years total). If
discount rates are 10% what is the present value
cost of the lease?
1+ nominal interest rate
1  real interest rate =
1+inflation rate
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 9
Inflation
Example - nominal figures
Year Cash Flow
1
2
8000
8000x1.03 = 8240
3
4
8000x1.032 = 8240
3
8000x1.03 = 8487.20
PV @ 10%
 7272.73
 6809.92
8000
1.10
8240
1.102
8487 .20
1.103
8741.82
1.104
 6376.56
 5970.78
$26,429.99
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 10
Inflation
Example - real figures
Year
1
2
3
4
Irwin/McGraw Hill
Cash Flow
8000
1.03
8240
1.032
8487.20
1.033
8741.82
1.034
= 7766.99
= 7766.99
= 7766.99
= 7766.99
[email protected]%
7766.99
1.068
7766.99
1.0682
7766.99
1.0683
7766.99
1.0684
 7272.73
 6809.92
 6376.56
 5970.78
= $26,429.99
©The McGraw-Hill Companies, Inc., 2000
6- 11
IM&C’s Guano Project
Revised projections ($1000s) reflecting inflation
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 12
IM&C’s Guano Project
 NPV using nominal cash flows
1,630 2,381 6,205 10,685 10,136
NPV  12,000 




2
3
4
1.20 1.20 1.20 1.20 1.205
6,110 3,444


 3,519 or $3,519,000
6
7
1.20 1.20
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 13
IM&C’s Guano Project
Cash flow analysis ($1000s)
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 14
IM&C’s Guano Project
Details of cash flow forecast in year 3 ($1000s)
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 15
IM&C’s Guano Project
Tax depreciation allowed under the modified accelerated cost
recovery system (MACRS) - (Figures in percent of
depreciable investment).
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 16
IM&C’s Guano Project
Tax Payments ($1000s)
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 17
IM&C’s Guano Project
Revised cash flow analysis ($1000s)
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 18
Timing
 Even projects with positive NPV may be
more valuable if deferred.
 The actual NPV is then the current value of
some future value of the deferred project.
Net future value as of date t
Current NPV 
t
(1  r )
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 19
Timing
Example
You may harvest a set of trees at anytime over the
next 5 years. Given the FV of delaying the harvest,
which harvest date maximizes current NPV?
0
1
Net FV($1000s) 50 64.4
% changein value
28.8
Irwin/McGraw Hill
Harvest Year
2
3
77.5
20.3
4
5
89.4 100 109.4
15.4 11.9 9.4
©The McGraw-Hill Companies, Inc., 2000
6- 20
Timing
Example - continued
You may harvest a set of trees at anytime over the next 5 years. Given the
FV of delaying the harvest, which harvest date maximizes current NPV?
64.4
NPV if harvested in year 1 
 58.5
1.10
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 21
Timing
Example - continued
You may harvest a set of trees at anytime over the next 5 years. Given the
FV of delaying the harvest, which harvest date maximizes current NPV?
64.4
NPV if harvested in year 1 
 58.5
1.10
Harvest Year
0
1
2
3
4
5
NPV ($1000s) 50 58.5 64.0
67.2 68.3 67.9
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 22
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 23
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
present value of costs
Equivalent annual cost =
annuity factor
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 24
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost
machine using equivalent annual cost method.
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 25
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost machine
using equivalent annual cost method.
Machine
A
B
Irwin/McGraw Hill
Year
1
15
10
2
5
6
3
5
6
4
5
PV@6%
28.37
21.00
EAC
©The McGraw-Hill Companies, Inc., 2000
6- 26
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost machine
using equivalent annual cost method.
Machine
A
B
Irwin/McGraw Hill
Year
1
15
10
2
5
6
3
5
6
4
5
PV@6%
28.37
21.00
EAC
10.61
11.45
©The McGraw-Hill Companies, Inc., 2000
6- 27
Machinery Replacement
Annual operating cost of old machine = 8
Cost of new machine
Year:
0
15
1
5
2
5
3
5
NPV @ 10%
27.4
Equivalent annual cost of new machine =
27.4/(3-year annuity factor) = 27.4/2.5 = 11
MORAL: Do not replace until operating cost
of old machine exceeds 11.
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 28
Cost of Excess Capacity
A project uses existing warehouse and requires a new one to be built in
Year 5 rather than Year 10. A warehouse costs 100 & lasts 20 years.
Equivalent annual cost @ 10% = 100/8.5 = 11.7
0 . . . 5
With project 0
0
6 . . . 10
11.7
11.7
11 . . .
11.7
Without project
0
0
0
0
11.7
Difference
0
0
11.7
11.7
0
PV extra cost = 11.7 + 11.7 + . . . + 11.7 = 27.6
(1.1)6 (1.1)7
(1.1)10
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 29
Fluctuating Load Factors
T wo Old Machines
Annual output per machine
750 units
Operatingcost per machine
2  750  $1,500
P V operatingcost per pachine
1,500/.10 $15,000
P V operatingcost of two machines 2  15,000 $30,000
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
6- 30
Fluctuating Load Factors
Two New Machin es
Annual output per machine
Capital cost pe machine
Operating cost per machine
PV operating cost per pachine
PV operating cost of two machines
Irwin/McGraw Hill
750 units
$6,000
1  750  $750
6,000  750/.10  $13,500
2  13,500  $27,000
©The McGraw-Hill Companies, Inc., 2000
6- 31
Fluctuating Load Factors
Annual output per machine
Capital cost pe machine
Operating cost per machine
PV operating cost per pachine
PV operating cost of two machines
Irwin/McGraw Hill
One Old Machine
One New Machin e
500 units
0
2  500  $1,000
1,000/.10  $10,000
................................$26,000
1,000 units
$6,000
1  1,000  $1,000
6,000  1,000 / .10  $16,000
©The McGraw-Hill Companies, Inc., 2000