Ch.8

Risk Analysis, Real Options, and Capital

Budgeting

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Real-world practitioners often wonder how much confidence they should place in NPV calculations.

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Chapter Outline

8.1 Decision Trees

8.2 Sensitivity Analysis, Scenario Analysis,

and Break-Even Analysis

8.3 Monte Carlo Simulation

8.4 Real Options

8.1 Decision Trees

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A fundamental problem in NPV analysis is dealing with uncertain future outcomes.

Warning 1: Perhaps a higher discount rate should have been used for the initial test-marketing decision.

Warning 2: It is hard for decision trees to capture all of the managerial options in changing environments.

8.2

Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis

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The projected cash flow often goes unmet in practice, and the firm ends up with a money loser.

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Sensitivity Analysis and Scenario Analysis

Sensitivity analysis examines how sensitive a particular NPV calculation is to changes in underlying assumptions.

Revenue: Depends on three assumptions - market share, size of jet engine market, and price per engine.

Cost: Total cost before taxes =Variable cost + Fixed cost

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Sensitivity Analysis and Scenario Analysis

A table such as Table 8.3 can be used for a number of purposes: It can indicate whether NPV analysis should be trusted It shows where more information is needed

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Sensitivity Analysis and Scenario Analysis

The effect of incorrect estimates on revenues is so much greater than the effect of incorrect estimates on costs, more information on the factors determining revenues might be needed.

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Sensitivity Analysis and Scenario Analysis

However, sensitivity analysis suffers from some drawbacks: It may unwittingly increase the false sense of security

among managers; it treats each variable in isolation. Managers frequently perform scenario analysis to

minimize this problem.

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Break-Even Analysis

This approach determines the sales needed to break even.

It is a useful complement to sensitivity analysis, because it also sheds light on the severity of incorrect forecasts.

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Break-Even Analysis

Accounting Profit (Fixed costs + Depreciation)*(1-Tc)

(Sales price-Variable costs)*(1-Tc) Contribution margin: It is the amount that each

additional engine contributes to after-tax profit.

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Break-Even Analysis

EAC = Initial Investment / 5-year annuity factor at 15%

(Fixed costs + Depreciation)*(1-Tc) = Fixed costs *(1-Tc) + Depreciation)*(1-Tc) = Fixed costs *(1-Tc) + 【 Depreciation - Depreciation*Tc 】

Fixed costs *(1-Tc) + 【 EAC - Depreciation*Tc 】

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Break-Even Analysis

Present Value Break-Even Point:

Fixed costs*(1-Tc) + 【 EAC -Depreciation*Tc 】 (Sales price-Variable costs)*(1-Tc)

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Break-Even Analysis

The EAC of $447.5 million is greater than the yearly depreciation of $300 million, because we implicitly assume that the $1,500 million investment could have been invested at 15%.

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Break-Even Analysis

Depreciation understates the true costs of recovering the initial investment. Thus Companies that break even on an accounting basis are really losing money. They are losing the opportunity cost of the initial investment.

8.4

Real Options

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NPV analysis ignores the adjustments that a firm can make after a project is accepted. These adjustments are called real options. Thus, NPV underestimates the true value of a project.

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One of the fundamental insights of modern finance theory is that options have value.

Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation.

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Options

The Option to Expand Has value if demand turns out to be higher than

expected.

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The Option to Abandon Managers also have the option to abandon existing

projects. Abandonment can often save companies a great of money.Thus, the option to abandon increases the value of any potential project.

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Timing Options They have value if the underlying variables are

changing with a favorable trend.

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