Engineering Economics Blog

 
For any investment to be profi  table, the investor (corporate or individual) expects to receive more money than the amount of capital invested. In other words, a fair   rate of return,  or   return on investment,  must be realizable. The defi nition of ROR in Equation [1.4] is used in this discussion, that is, amount earned divided by the principal.
  
Engineering alternatives are evaluated upon the prognosis that a reasonable ROR can be expected.

Therefore, some reasonable rate must be established for the selection criteria (step 4) of the engineering economy study ( Figure 1–1 ).

The Minimum Attractive Rate of Return (MARR) is a reasonable rate of return established for the evaluation and selection of alternatives. A project is not economically viable unless it is   expected to return at least the MARR.  MARR is also referred to as the hurdle rate, cutoff rate, benchmark rate, and minimum acceptable rate of return.
    
Figure 1–12  indicates the relations between different rate of return values. In the United States, the current U.S. Treasury Bill return is sometimes used as the benchmark safe rate. The MARR will always be higher than this, or a similar, safe rate. The MARR is not a rate that is calculated as a ROR. The MARR is established by (fi nancial) managers and is used as a criterion against which an alternative’s ROR is measured, when making the accept/reject investment  decision.     
  
To develop a foundation-level understanding of how a MARR value is established and used to make investment decisions, we return to the term   capital  introduced in Section 1.1.   Although the MARR is used as a criterion to decide on investing in a project, the size of MARR is fundamentally connected to how much it costs to obtain the needed capital funds.   It always costs money in the form of interest to raise capital. The interest, expressed as a percentage rate per year, is called the   cost of capital.  As an example on a personal level, if you want to purchase a new widescreen HDTV, but do not have suffi cient money (capital), you could obtain a bank loan for, say, a cost of capital of 9% per year and pay for the TV in cash now. Alternatively, you might choose to use your credit card and pay off the balance on a monthly basis. This approach will probably cost you at least 15% per year. Or, you could use funds from your savings account that earns 5% per year and pay cash. This approach means that you also forgo future returns from these funds. The 9%, 15%, and 5% rates are your cost of capital estimates to raise the capital for the system by different methods of capital fi nancing. In analogous ways, corporations estimate the   cost of capital  from different sources to raise funds for engineering projects and other types of projects.

Figure 1–12 Size of MAAR relative to other rate of return  values.

In general, capital is developed in two ways—equity fi nancing and debt fi  nancing. A combination of these two is very common for most projects. Chapter 10 covers these in greater detail, but a snapshot description follows.
  
Equity fi  nancing  The corporation uses its own funds from cash on hand, stock sales, or retained earnings. Individuals can use their own cash, savings, or investments. In the example above, using money from the 5% savings account is equity fi  nancing.  
   
Debt fi  nancing  The corporation borrows from outside sources and repays the principal and interest according to some schedule, much like the plans in Table 1–1. Sources of debt capital may be bonds, loans, mortgages, venture capital pools, and many others. Individuals, too, can utilize debt sources, such as the credit card (15% rate) and bank options (9% rate) described above.  
  
Combinations of debt-equity fi nancing mean that a   weighted average cost of capital (WACC)  results. If the HDTV is purchased with 40% credit card money at 15% per year and 60% savings account funds earning 5% per year, the weighted average cost of capital is 0.4(15) + 0.6(5) =9% per year.
  
For a corporation, the   established MARR  used as a criterion to accept or reject an investment alternative will usually be equal to or   higher than the WACC  that the corporation must bear to obtain the necessary capital funds. So the inequality


 must be correct for an accepted project. Exceptions may be government-regulated requirements (safety, security, environmental, legal, etc.), economically lucrative ventures expected to lead to other opportunities, etc.
  
Often there are many alternatives that are expected to yield a ROR that exceeds the MARR as indicated in  Figure 1–12 , but there may not be suffi cient capital available for all, or the project’s risk may be estimated as too high to take the investment chance. Therefore, new projects that are undertaken usually have an expected return at least as great as the return on another alternative that is not funded. The expected rate of return on the unfunded project is called the opportunity cost.            
  
The opportunity cost is the rate of return of a forgone opportunity caused by the inability to pursue a project. Numerically, it is the   largest rate of return of all the projects not accepted (forgone) due to the lack of capital funds or other resources.  When no specifi  c MARR is established, the de facto MARR is the opportunity cost, i.e., the ROR of the fi rst project not undertaken due to unavailability of capital funds.          
  
As an illustration of opportunity cost, refer to Figure 1–12 and assume a MARR of 12% per year. Further, assume that a proposal, call it A, with an expected ROR = 13% is not funded due to a lack of capital. Meanwhile, proposal B has a ROR = 14.5% and is funded from available capital. Since proposal A is not undertaken due to the lack of capital, its estimated ROR of 13% is the   opportunity cost;  that is, the opportunity to make an additional 13% return is forgone.