Chapter 11
Cash Flow Estimation
and Risk Analysis
ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS
11-1 a. Cash flow, which is the relevant financial variable, represents the actual flow of cash.
Accounting income, on the other hand, reports accounting data as defined by
Generally Accepted Accounting Principles (GAAP).
b. Incremental cash flows are those cash flows that arise solely from the asset that is
being evaluated. For example, assume an existing machine generates revenues of
$1,000 per year and expenses of $600 per year. A machine being considered as a
replacement would generate revenues of $1,000 per year and expenses of $400 per
year. On an incremental basis, the new machine would not increase revenues at all,
but would decrease expenses by $200 per year. Thus, the annual incremental cash
flow is a before-tax savings of $200. A sunk cost is one that has already occurred and
is not affected by the capital project decision. Sunk costs are not relevant to capital
budgeting decisions. Within the context of this chapter, an opportunity cost is a cash
flow that a firm must forgo to accept a project. For example, if the project requires
the use of a building that could otherwise be sold, the market value of the building is
an opportunity cost of the project.
c. Net operating working capital changes are the increases in current operating assets
resulting from accepting a project less the resulting increases in current operating
liabilities, or accruals and accounts payable. A net operating working capital change
must be financed just as a firm must finance its increases in fixed assets. Salvage
value is the market value of an asset after its useful life. Salvage values and their tax
effects must be included in project cash flow estimation.
d. The real rate of return (rr), or, for that matter the real cost of capital, contains no
adjustment for expected inflation. If net cash flows from a project do not include
inflation adjustments, then the cash flows should be discounted at the real cost of
capital. In a similar manner, the IRR resulting from real net cash flows should be
compared with the real cost of capital. Conversely, the nominal rate of return (rn)
does include an inflation adjustment (premium). Thus if nominal rates of return are
used in the capital budgeting process, the net cash flows must also be nominal.
Mini Case: 11 - 1
, e. Sensitivity analysis indicates exactly how much NPV will change in response to a
given change in an input variable, other things held constant. Sensitivity analysis is
sometimes called “what if” analysis because it answers this type of question.
Scenario analysis is a shorter version of simulation analysis that uses only a few
outcomes. Often the outcomes considered are optimistic, pessimistic and most likely.
Monte Carlo simulation analysis is a risk analysis technique in which a computer is
used to simulate probable future events and thus to estimate the profitability and risk
of a project.
f. A risk-adjusted discount rate incorporates the riskiness of the project’s cash flows.
The cost of capital to the firm reflects the average risk of the firm’s existing projects.
Thus, new projects that are riskier than existing projects should have a higher risk-
adjusted discount rate. Conversely, projects with less risk should have a lower risk-
adjusted discount rate. This adjustment process also applies to a firm’s divisions.
Risk differences are difficult to quantify, thus risk adjustments are often subjective in
nature. A project’s cost of capital is its risk-adjusted discount rate for that project.
g. Real options occur when managers can influence the size and risk of a project’s cash
flows by taking different actions during the project’s life. They are referred to as real
options because they deal with real as opposed to financial assets. They are also
called managerial options because they give opportunities to managers to respond to
changing market conditions. Sometimes they are called strategic options because
they often deal with strategic issues. Finally, they are also called embedded options
because they are a part of another project.
h. Investment timing options give companies the option to delay a project rather than
implement it immediately. This option to wait allows a company to reduce the
uncertainty of market conditions before it decides to implement the project. Capacity
options allow a company to change the capacity of their output in response to
changing market conditions. This includes the option to contract or expand
production. Growth options allow a company to expand if market demand is higher
than expected. This includes the opportunity to expand into different geographic
markets and the opportunity to introduce complementary or second-generation
products. It also includes the option to abandon a project if market conditions
deteriorate too much.
11-2 Only cash can be spent or reinvested, and since accounting profits do not represent cash,
they are of less fundamental importance than cash flows for investment analysis. Recall
that in the stock valuation chapters we focused on dividends and free cash flows, which
represent cash flows, rather than on earnings per share, which represent accounting
profits.
11-3 Since the cost of capital includes a premium for expected inflation, failure to adjust cash
flows means that the denominator, but not the numerator, rises with inflation, and this
lowers the calculated NPV.
Mini Case: 11 - 2
Cash Flow Estimation
and Risk Analysis
ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS
11-1 a. Cash flow, which is the relevant financial variable, represents the actual flow of cash.
Accounting income, on the other hand, reports accounting data as defined by
Generally Accepted Accounting Principles (GAAP).
b. Incremental cash flows are those cash flows that arise solely from the asset that is
being evaluated. For example, assume an existing machine generates revenues of
$1,000 per year and expenses of $600 per year. A machine being considered as a
replacement would generate revenues of $1,000 per year and expenses of $400 per
year. On an incremental basis, the new machine would not increase revenues at all,
but would decrease expenses by $200 per year. Thus, the annual incremental cash
flow is a before-tax savings of $200. A sunk cost is one that has already occurred and
is not affected by the capital project decision. Sunk costs are not relevant to capital
budgeting decisions. Within the context of this chapter, an opportunity cost is a cash
flow that a firm must forgo to accept a project. For example, if the project requires
the use of a building that could otherwise be sold, the market value of the building is
an opportunity cost of the project.
c. Net operating working capital changes are the increases in current operating assets
resulting from accepting a project less the resulting increases in current operating
liabilities, or accruals and accounts payable. A net operating working capital change
must be financed just as a firm must finance its increases in fixed assets. Salvage
value is the market value of an asset after its useful life. Salvage values and their tax
effects must be included in project cash flow estimation.
d. The real rate of return (rr), or, for that matter the real cost of capital, contains no
adjustment for expected inflation. If net cash flows from a project do not include
inflation adjustments, then the cash flows should be discounted at the real cost of
capital. In a similar manner, the IRR resulting from real net cash flows should be
compared with the real cost of capital. Conversely, the nominal rate of return (rn)
does include an inflation adjustment (premium). Thus if nominal rates of return are
used in the capital budgeting process, the net cash flows must also be nominal.
Mini Case: 11 - 1
, e. Sensitivity analysis indicates exactly how much NPV will change in response to a
given change in an input variable, other things held constant. Sensitivity analysis is
sometimes called “what if” analysis because it answers this type of question.
Scenario analysis is a shorter version of simulation analysis that uses only a few
outcomes. Often the outcomes considered are optimistic, pessimistic and most likely.
Monte Carlo simulation analysis is a risk analysis technique in which a computer is
used to simulate probable future events and thus to estimate the profitability and risk
of a project.
f. A risk-adjusted discount rate incorporates the riskiness of the project’s cash flows.
The cost of capital to the firm reflects the average risk of the firm’s existing projects.
Thus, new projects that are riskier than existing projects should have a higher risk-
adjusted discount rate. Conversely, projects with less risk should have a lower risk-
adjusted discount rate. This adjustment process also applies to a firm’s divisions.
Risk differences are difficult to quantify, thus risk adjustments are often subjective in
nature. A project’s cost of capital is its risk-adjusted discount rate for that project.
g. Real options occur when managers can influence the size and risk of a project’s cash
flows by taking different actions during the project’s life. They are referred to as real
options because they deal with real as opposed to financial assets. They are also
called managerial options because they give opportunities to managers to respond to
changing market conditions. Sometimes they are called strategic options because
they often deal with strategic issues. Finally, they are also called embedded options
because they are a part of another project.
h. Investment timing options give companies the option to delay a project rather than
implement it immediately. This option to wait allows a company to reduce the
uncertainty of market conditions before it decides to implement the project. Capacity
options allow a company to change the capacity of their output in response to
changing market conditions. This includes the option to contract or expand
production. Growth options allow a company to expand if market demand is higher
than expected. This includes the opportunity to expand into different geographic
markets and the opportunity to introduce complementary or second-generation
products. It also includes the option to abandon a project if market conditions
deteriorate too much.
11-2 Only cash can be spent or reinvested, and since accounting profits do not represent cash,
they are of less fundamental importance than cash flows for investment analysis. Recall
that in the stock valuation chapters we focused on dividends and free cash flows, which
represent cash flows, rather than on earnings per share, which represent accounting
profits.
11-3 Since the cost of capital includes a premium for expected inflation, failure to adjust cash
flows means that the denominator, but not the numerator, rises with inflation, and this
lowers the calculated NPV.
Mini Case: 11 - 2
