Engineering Economic Analysis

AdjustingMARRto Account forRiskand Uncertainty 479

SELECTING A MINIMUM ATTRACTIVE RATE OF RETURN

Focusing on the three concepts on the cost of money (the cost of borrowed money, the

cost of capital, and opportunity cost), which, if any, of these values should be used as the

minimum attractive rate of return (MARR) in economic analyses?

Fundamentally,we know that unless the benefits of a project exceed its cost, we cannot

add to the profitability of the firm. A lower boundary for the minimum attractive rate of.

return must be the cost of the money investedin the project. It would be unwise, for example,

to borrow money at 8% and invest it in a project yielding a 6% rate of return.

Further, we know that no firm has an unlimited ability to borrow money. Bankers-

and others who evaluate the limits of a firm's ability to borrow money-look at both the

profitability of the firm and the relationship between the components in the firm's capital

structure. This means that continued borrowing of money will require that additional stock

must be sold to maintain an acceptableratio between ownership and debt. In other words,

borrowing for a particular investment project is only a block of money from the overall

capital structure of the firm. This suggests that the MARR should not be less than the cost

of capital. Finally, we know that the MARR should not be less than the rate of return on the

best opportunity forgone. Stated simply,

Minimum attractive rate of return should be equal to the largest one of the following:

cost of borrowed money, cost of capital, or opportunity cost.

ADJUSTING MARR TO ACCOUNT FOR RISK AND UNCERTAINTY

We know from our study of estimatingthe future that what actually occurs is often different

from the estimate. When we are fortunate enough to be able to assign probabilities to a set of

possible future outcomes, we call this a risk situation.We saw in Chapter 10that techniques

like expected value and simulation may be used when the probabilities are known.

Uncertainty is the term used to describe the condition when the probabilities arenot

known. Thus, if the probabilities of future outcomes are known we haverisk,and if they

are unknown we haveuncertainty.

One way to reduce the likelihood of undertaking projects that do not produce satis-...

factory results is to pass up marginal projects. In other words, no matter what projects

are undertaken, some will turn out better than anticipated and some worse. Some undesir-

able results can be prevented by selecting only the best projects and avoiding those whose

expected results are closer to a minimum standard: then (in theory, at least) the selected

projects will provide resultsabovethe minimum standard even if they do considerably

worse than anticipated.

In projects accompanied by normal business risk and uncertainty, the MARR is used

without adjustment. For projects with greater than average risk or uncertainty, some firms

increase the MARR. A preferable way deals explicitly with the probabilities using the

techniques from Chapter 10.This may be more acceptable as an adjustment for uncertainty.

When the interest rate (MARR) used in economic analysis calculations is raised to adjust

for risk or uncertainty, greater emphasis is placed on immediate or short-term results and

less emphasis on longer-term results.