Making Investment Decisions with the Net Present Value Rule
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Transcript of Making Investment Decisions with the Net Present Value Rule
Making Investment Decisions with the Net Present Value
Rule
Chapter 6
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
Do not confuse average with incremental payoffs
Include all incidental effectsDo not forget working capital requirementsForget sunk costsInclude opportunity costsBeware of allocated overhead costs
Points to “Watch Out For”
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
INFLATION RULEINFLATION RULE
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 real interest rate = 1+nominal interest rate1+inflation rate
Inflation
Example - nominal figures
Year Cash Flow PV @ 10%
1 8000
2 8000x1.03 = 8240
8000x1.03 = 8240
8000x1.03 = 8487.20
80001.10
2
3
7272 73
6809 92
3 6376 56
4 5970 78
429 99
82401 108487 20
1 108741 82
1 10
2
3
4
.
.
.
.
$26, .
..
..
.
Inflation
Example - real figures
Year Cash Flow [email protected]%
1 = 7766.99
2 = 7766.99
= 7766.99
= 7766.99
80001.03
7766.991.068
82401.03
8487.201.03
8741.821.03
2
3
4
7272 73
6809 92
3 6376 56
4 5970 78
26 429 99
7766 991 068
7766 991 068
7766 991 068
2
3
4
.
.
.
.
..
..
..
= $ , .
IM&C’s Guano Project
Revised projections ($1000s) reflecting inflation
IM&C’s Guano Project
NPV using nominal cash flows
$3,519,000or 519,3
20.1
444,3
20.1
110,6
20.1
136,10
20.1
685,10
20.1
205,6
20.1
381,2
20.1
630,1000,12
76
5432
NPV
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 ProjectTax 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.
Equivalent annual cost =present value of costs
annuity factor
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.
Year
Machine 1 2 3 4 PV@6% EAC
A 15 5 5 5 28.37 10.61
B 10 6 6 21.00 11.45
Equivalent Annual Cost
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.
tr
t
)1(
date of as valuefutureNet NPVCurrent
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?
9.411.915.420.328.8 valuein change %
109.410089.477.564.450($1000s) Net FV
543210
YearHarvest
Timing
Example - continuedYou 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?
5.581.10
64.41 year in harvested if NPV
Timing
Example - continuedYou 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?
5.581.10
64.41 year in harvested if NPV
67.968.367.264.058.550($1000s) NPV
543210
YearHarvest
Fluctuating Load Factors
$30,00015,0002machines twoofcost operating PV
$15,0001,500/.10pachineper cost operating PV
$1,5007502machineper cost Operating
units 750machineper output Annual
MachinesOld Two
Fluctuating Load Factors
$27,000500,132machines twoofcost operating PV
$13,500750/.106,000pachineper cost operating PV
$7507501machineper cost Operating
000,6$machine pecost Capital
units 750machineper output Annual
esNew Machin Two
Fluctuating Load Factors
000,26..$..............................machines twoofcost operating PV
$16,000.10/000,16,000$10,000,000/.101pachineper cost operating PV
$1,000000,11$1,0005002machineper cost Operating
000,6$0machine pecost Capital
units 1,000units 500machineper output Annual
eNew Machin One MachineOld One