RISK ANALYSIS, REAL OPTIONS, AND
Answers to Concept Questions
Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows.
The danger is greatest with a new product because the cash flows are probably harder to predict.
With a sensitivity analysis, one variable is examined over a broad range of values. With a scenario
analysis, all variables are examined for a limited range of values.
It is true that if average revenue is less than average cost, the firm is losing money. This much of the
statement is therefore correct. At the margin, however, accepting a project with marginal revenue in
excess of its marginal cost clearly acts to increase operating cash flow.
From the shareholder perspective, the financial break-even point is the most important. A project can
exceed the accounting and cash break-even points but still be below the financial break-even point.
This causes a reduction in shareholder (your) wealth.
The project will reach the cash break-even first, the accounting break-even next and finally the
financial break-even. For a project with an initial investment and sales after, this ordering will
always apply. The cash break-even is achieved first since it excludes depreciation. The accounting
break-even is next since it includes depreciation. Finally, the financial break-even, which includes
the time value of money, is achieved.
Traditional NPV analysis is often too conservative because it ignores profitable options such as the
ability to expand the project if it is profitable, or abandon the project if it is unprofitable. The option
to alter a project when it has already been accepted has a value, which increases the NPV of the
The type of option most likely to affect the decision is the option to expand. If the country just
liberalized its markets, there is likely the potential for growth. First entry into a market, whether an
entirely new market, or with a new product, can give a company name recognition and market share.
This may make it more difficult for competitors entering the market.
Sensitivity analysis can determine how the financial break-even point changes when some factors
(such as fixed costs, variable costs, or revenue) change.
There are two sources of value with this decision to wait. Potentially, the price of the timber can
increase, and the amount of timber will almost definitely increase, barring a natural catastrophe or
forest fire. The option to wait for a logging company is quite valuable, and companies in the industry
have models to estimate the future growth of a forest depending on its age.