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Chapter 6
Making Investment Decisions
with the Net Present Value
Rule
Topics Covered
 What To Discount
 IM&C Project
 Project Interaction
Equivalent Annual Cost
 Replacement
 Project Interaction
 Timing
 Fluctuating Load Factors

What To Discount
Only Cash Flow is Relevant
What To Discount
Points to “Watch Out For”
Do not confuse average with incremental
payoffs
Include all incidental effects
Do not forget working capital requirements
Forget sunk costs
Include opportunity costs
Beware of allocated overhead costs
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
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
Inflation
Example - nominal figures
Year Cash Flow
1
2
8000
8000x1.03 = 8240
3
4
8000x1.032 = 8240
8000x1.033 = 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
Inflation
Example - real figures
Year
1
2
3
4
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
IM&C’s Guano Project
Revised projections ($1000s) reflecting inflation
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
IM&C’s Guano Project
Cash flow analysis ($1000s)
IM&C’s Guano Project
Details of cash flow forecast in year 3 ($1000s)
IM&C’s Guano Project
Tax depreciation allowed under the modified accelerated cost
recovery system (MACRS) (Figures in percent of
depreciable investment)
IM&C’s Guano Project
Tax Payments ($1000s)
IM&C’s Guano Project
Revised cash flow analysis ($1000s)
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
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
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
Year
1
15
10
2
5
6
3
5
6
4
5
PV@6%
28.37
21.00
EAC
10.61
11.45
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 )
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
Harvest Year
2
3
77.5
20.3
4
5
89.4 100 109.4
15.4 11.9 9.4
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
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
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
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
750 units
$6,000
1  750  $750
6,000  750/.10  $13,500
2  13,500  $27,000
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
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