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**Capital Budgeting Applications**

Implementing the NPV Rule

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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 coal and iron ore worldwide. Ocean Carriers’ vessels were mainly chartered on a time charter basis for 1-, 3-, or 5-year periods, however the spot charter market was occasionally used.

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**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 have seen already is IRR. Sensitivity analysis considers how NPV is affected by our forecasts of key variables. Examines variables one at a time. 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. We will use Ocean Carriers’ decision as an example.

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Breakeven Analysis Again, how far off can projections be before we hit zero NPV? In the Ocean Carriers case the discount rate, growth in shipments, and expected inflation are the main uncertainties related to NPV. For a US ship the discount rate is 6.6%. For a ship registered in HK it is %. Breakeven inflation rate is 3.49%. Breakeven growth in shipments is %

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Sensitivity Analysis This is very similar to breakeven analysis except that it considers the consequences for NPV for “reasonable” changes in the parameters. A 5% increase in expected inflation decreases NPV by 30% and a 5% decrease increases NPV by 29%. More informatively you would look at a one standard deviation change in inflation (or the relevant variable of interest). This gives a much more precise look at the uncertainty inherent in the forecast. A 5% increase in iron ore shipments increases NPV by 57%. A 5% decrease, decreases NPV by 56%. A 5% decrease in the discount rate increases NPV by 171%. A 5% increase decreases NPV by 161%.

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Scenario Analysis Suppose iron ore shipments and expected inflation are negatively related. As prices in general go up there is less demand for iron ore. If expected inflation increases by 5% when iron ore shipments decrease by 5% relative to the stated expectations the NPV is decreased by 85%. More naturally we would expect the opposite relation. Professor Vossen has presented an extension of this process called “simulation” that is a powerful tool but that has yet to be adopted by a wide set of firms.

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**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.

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**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%

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**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.

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

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 = / /1.142 = 26.47 1 2 650 600 -1000

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**Using real quantities, the real cash flows are:**

The real interest rate is: rreal = 1.14/ = = 8.57% NPV = -$ $571.43/ $589.57/ = $26.47 Which method should be used? The easiest one to apply! 1 2 -1000 = 600/1.05 = 650/1.052

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**Example: Inflation and Capital Budgeting**

Ralph’s firm is considering investing $300,000 in a widget producing machine with a useful life of five years. The machine would be depreciated on a straight-line basis and would have zero salvage. The machine can produce 10,000 widgets per year. Currently, widgets have a market price of $15, while the materials used to make a widget cost $4. Widget and raw material prices are both expected to increase with inflation, which is projected to be 4% per year. Ralph has considers a real discount rate of 5% per year to be appropriate. The tax rate is 34%.

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**Ralph’s Widget Machine: Nominal Cash Flows**

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**Ralph’s Widget Machine: Real Cash Flows**

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**Is the NPV sensitive to projected inflation?**

Does depreciation depend on inflation? If not then with real cash flows shouldn’t we see this?

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**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, , = -$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?

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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/ ,000=125, ,000 = $15,000 or NPV=10,000/ ,000=83, ,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).

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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%.

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**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…

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**The Option to Abandon NPV = -80,000 + [.5(Max(100,000 or 70,000))**

= -80,000 + [.5(100,000) + .5(70,000)] = -80,000 + [85,000] = $5,000 The option to abandon is worth $10,000 ($20,000 if exercised, with a .5 probability of exercise), which swings the NPV from -$5000 to $5000. Real options such as the options to defer, abandon, or expand can make up a considerable portion of a project’s value.

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