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?

One example we will see is IRR. 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.

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:

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.

0 1 2 3

-$1,000 $400 $400 $400

IRR – NPV Profile Diagram Evaluate the NPV at various discount rates:

Rate NPV 0 $20010 -$5.320 -$157.4

At r = 9.7%, NPV = 0

-200-150-100

-500

50100150200250

0 10 20

Discount Rate

NPV

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:

This can (and does) have two IRRs.

0 1 2

-$100 $230 -$132

Pitfalls of IRR cont…

Disc.Rate 0.00% 10.00% 15.00% 20.00% 40.00% NPV -$2.00 $0.00 $0.19 $0.00 -$3.06 IRR1 IRR2

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 10 15 20 40

Discount Rate

NPV

Pitfalls of IRR cont…

-0.5

0

0.5

1

1.5

2

2.5

3

0 10 15 20 40

Discount Rate

NPV

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. Store toxic waste.B. Store fresh produce.

Let’s look at the cash flows, IRRs and NPVs.

Mutually Exclusive Projects and IRR

Project Year 0 Year 1 Year 2 Year 3A -10,000 10,000 1,000 1,000B -10,000 1,000 1,000 12,000

Project NPV @0%

NPV @10%

NPV@15%

IRR

A $2000 $669 $109 16.04%B $4000 $751 -$484 12.94%

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.

-1000

0

1000

2000

3000

4000

5000

0% 10% 15%

Discount Rate

NPV

AB

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% $363.64B -$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:

Example: Nominal Interest Rate=10% Inflation Rate=6%

rReal = (1.10/1.06) - 1 = 0.038=3.8%

111

Inf

NomReal

rrr

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.

• The nominal interest rate is 14% and expected inflation is 5%

• Using nominal quantities• NPV = -1000 + 600/1.14 + 650/1.142 = 26.47

-1000 600 650

0 1 2

• Using real quantities, the real cash flows are:

• 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!

-1000 571.43 =600/1.05

589.57 =650/1.052

0 1 2

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.