Capital Budgeting Applications
Implementing the NPV Rule
Ocean Carriers



January 2001, Mary Linn of Ocean Carriers is
evaluating the purchase of a new capesize
carrier for a 3-year lease proposed by a
motivated customer.
Ocean Carriers owns and operates capesize
dry bulk carriers that mainly carry iron ore
and coal worldwide.
Ocean Carriers’ vessels were commonly
chartered on a time charter basis for 1-, 3-,
or 5-year periods, however the spot charter
market was also used.
Sensitivity, Scenario, and
Breakeven analysis.


The NPV is usually dependent upon assumptions and
projections. What if some of the projections are off?
Breakeven analysis asks when do we see zero NPV?


Sensitivity analysis considers how NPV is affected by
our forecasts of key variables.


Examines variables one at a time. Consider for example a
one standard deviation change in expected inflation.
Scenario analysis accounts for the fact that some
variables are related.


One example we will see is IRR.
In a recession, the selling price and the units sold may both
be lower than expected.
Simulation is the granddaddy of them all, you will
learn about this technique in your Ops course.
Internal Rate of Return


Definition: The discount rate that sets the NPV of a
project to zero is the project’s IRR.
 Conceptually, IRR asks: “What is the project’s rate
of return?”
Standard Rule: Accept a project if its IRR is greater
than the appropriate market based discount rate,
reject if it is less. Why does this make sense?



This is where the term “hurdle rate” comes from.
IRR is completely internal to the project. To use the
rule effectively we compare the IRR to a market rate.
For independent projects with “normal cash flow
patterns” IRR and NPV give the same conclusions.
IRR – “Normal” Cash Flow Pattern

Consider the following stream of cash flows:
0
-$1,000


1
$400
2
$400
3
$400
Calculate the NPV at different discount rates
until you find the discount rate where the
NPV of this set of cash flows equals zero.
That’s all you do to find IRR.
IRR – NPV Profile Diagram

Evaluate the NPV at various discount rates:
Rate NPV
0
$200
10
-$5.3
20
-$157.4

At r = 9.7%,
NPV = 0
250
200
150
100
NPV 50
0
-50 0
-100
-150
-200
10
20
Discount Rate
The Merit to the IRR Approach



The IRR is an approximation (assumes
reinvestment of payouts at the IRR) for the
return generated over the life of a project on
the initial investment.
The IRR is based on all incremental cash
flows and (by comparison to the appropriate
discount rate, r) takes proper account of the
time value of money (and risk).
In short, it can be useful.
Pitfalls of the IRR Approach

Multiple IRRs


There can be as many solutions to the IRR
definition as there are changes of sign in the time
ordered cash flow series.
Consider:
0
1
2
-$100

$230
-$132
This can (and does) have two IRRs.
Pitfalls of IRR cont…
Disc.Rate 0.00% 10.00% 15.00% 20.00% 40.00%
-$2.00 $0.00 $0.19 $0.00 -$3.06
NPV
IRR2
IRR1
0.5
0
NPV
-0.5 0
10
15
-1
-1.5
-2
-2.5
-3
Discount Rate
20
40
Pitfalls of IRR cont…
3
2.5
NPV
2
1.5
1
0.5
0
-0.5 0
10
15
Discount Rate
20
40
Pitfalls of IRR cont…
Mutually exclusive projects:



IRR can lead to incorrect conclusions
about the relative worth of projects.
Ralph owns a warehouse he wants to fix
up and use for one of two purposes:
A.
B.
Store toxic waste.
Store fresh produce.
Let’s look at the cash flows, IRRs and NPVs.
Mutually Exclusive Projects and IRR
Project
A
B
Year 0 Year 1 Year 2 Year 3
-10,000 10,000 1,000
1,000
-10,000 1,000
1,000
12,000
Project
NPV @
0%
$2000
$4000
A
B
NPV @ NPV@
10%
15%
$669
$109
$751
-$484
IRR
16.04%
12.94%
5000
A
B
4000
NPV
3000
2000
1000
0
-1000
0%
10%
15%
Discount Rate



At low discount rates, B is better. At high discount
rates, A is better.
But A always has the higher IRR. A common mistake
to make is choose A regardless of the discount rate.
Simply choosing the project with the larger IRR
would be justified only if the projects’ intermediate
cash flows could be reinvested at the IRR instead of
the actual market rate, r, for the life of the project.
Project Scale and the IRR


Because the IRR puts things in terms of
a “rate” it may not tell you what really
interests you; which investment will
create the most “wealth”.
Example:
Project Investment
Time 1
IRR
NPV at 10%
A
-$1,000
+$1,500
50%
$363.64
B
-$10,000
+$13,000
30%
$1,1818.18
Summary of IRR vs. NPV

IRR analysis can be misleading if you don’t fully
understand its limitations.






For individual projects with normal cash flows NPV and IRR
provide the same conclusion.
For projects with inflows followed by outlays, the decision
rule for IRR must be reversed.
For Multi-period projects with several changes in sign of the
cash flows multiple IRRs exist. Must compute the NPVs to
see what decision rule is appropriate.
IRR may give incorrect evaluation when comparing projects.
Suffers from a reinvestment assumption.
I recommend NPV analysis, using others as a way to
communicate if necessary.
NPV and Microeconomics


One ‘line of defense’ against bad decision making is to
think about NPV in terms of the underlying economics.
NPV is the present value of the project’s future ‘economic
profits’.




Economic profits are those in excess of the ‘normal’ return on
invested capital (i.e. the opportunity cost of capital).
In ‘long-run competitive equilibrium’ all projects and firms earn
zero economic profits.
In what way does the proposed project differ from the
theoretical ‘long run competitive equilibrium’?
If no plausible answers emerge, any positive NPV is likely
to be illusory.
Dealing With Inflation


Interest rates and inflation:
The general formula (complements of Irving
Fisher) is:
(1 + rNom) = (1 + rReal)  (1 +rInf)

Rearranging:
rReal

Example:



1  rNom

1
1  rInf
Nominal Interest Rate=10%
Inflation Rate=6%
rReal = (1.10/1.06) - 1 = 0.038=3.8%
Cash Flow and Inflation



Cash flows are called nominal if they are
expressed in terms of the actual dollars to
be received or paid out. A cash flow is
called real if expressed in terms of a
common date’s purchasing power.
The big question: Do we discount real or
nominal cash flows?
The answer: Either, as long as you are
consistent.


Discount real cash flows using real rates.
Discount nominal cash flows using nominal rates.
• Example: Ralph forecasts the following nominal
cash flows for an investment project.
0
1
2
-1000
600
650
• The nominal interest rate is 14% and expected
inflation is 5%
• Using nominal quantities
• NPV = -1000 + 600/1.14 + 650/1.142 = 26.47
• Using real quantities, the real cash flows are:
0
-1000
1
571.43 =
600/1.05
2
589.57 =
650/1.052
• The real interest rate is:
rreal = 1.14/1.05 - 1 = 0.0857 = 8.57%
• NPV = -$1000 + $571.43/1.0857 + $589.57/1.08572
= $26.47
• Which method should be used?
– The easiest one to apply!
Brief Introduction to Real Options


Is it useful to consider the option to
defer making an investment?
Project A will generate risk free cash flows of
$10,000 per year forever. The risk free rate
is 10% per year. Project A will take an
immediate investment of $110,000 to launch.
NPV = 10,000/(.10) - 110,000 = 100,000 - 110,000
= -$10,000


Someone offers you $1 for the rights to this
project. Do you take it?
Hint: Do gold mines that are not currently
operated have a zero market value?
The Deferral Option

No! Suppose that one year from now interest rates
will be either 8% or 12% with equal probability.
However, the cash flows associated with this project
are not sensitive to interest rates --- they will be as
indicated above. Next year:

NPV=10,000/.08-110,000=125,000-110,000 = $15,000
or


NPV=10,000/.12-110,000=83,333-110,000 = -$26,666
Don’t give up the rights to the project yet! You can wait
until next year, and then commence the project if it proves
profitable at the time. There is a 50% chance the project
will be worth $15,000 next year! As a consequence,
ownership of the project has a positive value today due to
the deferral option (option to delay).
The Option to Abandon
• To initiate a particular project will require an
immediate investment of $80,000.
• If undertaken, the project will either pay
$10,000 per year in perpetuity or $5,000 per
year in perpetuity, with equal probability.
• The outcome will be resolved immediately,
but only if the investment is first made.
• We’ll assume that the project has an
appropriate discount rate of 10%.
The Option to Abandon
•
•
NPV = -80,000 + [.5(10,000)/.10 +
.5(5,000)/.10]
= -80,000 + [.5(100,000) + .5(50,000)]
= -80,000 + [75,000] = - $5,000
Suppose that the assets purchased to initiate this
project have a liquidation value of $70,000 (i.e.
you can sell them for use elsewhere after they
are purchased). Then, the payoff to making the
80,000 initial investment is the maximum of the
value from operating the project or $70,000.
So…
The Option to Abandon
•
•
•
NPV = -80,000 +
[.5(Max(100,000 or 70,000))
+ .5(Max(50,000 or 70,000))].
= -80,000 + [.5(100,000) + .5(70,000)]
= -80,000 + [85,000] = $5,000***
Recognizing the value contained in the option to
abandon changes the NPV from negative to
positive.
Real options such as the options to defer,
abandon, or expand can make up a considerable
portion of any project’s value.