The Cost of Capital

The funds that might be obtained from the various sources given in Section 9.4 come at very different costs - both real and virtual. If there are few sources available, then a simple calculation may be possible to determine an annual cost of the finance raised for the project, but it is more likely that a detailed analysis will have to be made. 

The capital needed for a new major project will come from two sources inside the company and outside it. The internal resources are the owners funds, and this money exists in the current assets part of the balance sheet, from which it can be drawn. New capital can be raised by the sale of already issued shares held by the company, or by the sale of bonds, or by the issuance of new shares. 

The normal external sources are loans from banks and other lending institutions at commercial rates of interest, and grants from governments or loans (also from overseas credit agencies) at lower than commercial rates of interest. The cost of a single source of borrowed money is easily determined - it is the annual rate of interest being charged on the loan. Where several different sources are used, a composite cost can be calculated (see below). 

The cost of using the company s own funds (or, actually, the owners funds) is less easily derived, because it contains an element of owners future expectations and an element of risk. It is most definitely not free , because the money can be used for a number of plans other than the one under consideration, and its cost should be set at least to equal the expected return on the most attractive of these alternatives, known as the opportunity cost . 

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As stated previously, the source of capital is often not known, and hence it is not known whether or not Eq. (A. 10) is appropiiate to represent the cost of capital. Equation (A. 10) is, strictly speaking, only appropriate if the money for capital expenditure is to be borrowed over a fixed period at a fixed rate of interest. Moreover, if Eq. (A. 10) is accepted, then the number of years over which the capital is to be annualized is unknown, as is the rate of interest. However, the most important thing is that even if the source of capital is not known, etc., and uncertain assumptions are necessary, Eq. (A. 10) provides a common basis for the comparison of competing projects. 

Caution is required in the use of the simple cashflow indicators, since they fail to take account of changing general price levels or the cost of capital (discussed in Section 13.4). It is always recommended that the definition of the indicators is quoted for clarity of understanding. 

In the above example, the discount rate used was the annual compound interest rate offered by the bank. In business investment opportunities the appropriate discount rate is the cost of capital to the company. This may be calculated in different ways, but should always reflect how much it costs the oil company to borrow the money which it uses to invest in its projects. This may be a weighted average of the cost of the share capital and loan capital of a company. 

If the company is fully self-financing for its new ventures, then the appropriate discount rate would be the rate of return of the alternative investment opportunities (e.g. other projects) since this opportunity is foregone by undertaking the proposed project. This represents the opportunity cost of the capital. It is assumed that the return from the alternative projects is at least equal to the cost of capital to the company (otherwise the alternative projects should not be undertaken). 

The example just shown assumed one discount rate and one oil price. Since the oil price is notoriously unpredictable, and the discount rate is subjective, it is useful to calculate the NPV at a range of oil prices and discount rates. One presentation of this data would be in the form of a matrix. The appropriate discount rates would be 0% (undiscounted),.say 10% (the cost of capital), and say 20% (the cost of capital plus an allowance for risk). The range of oil prices is again a subjective judgement. 

If 10% is the cost of capital to the company, then the NPV (10) represents the real measure of the project value. That is, whatever positive NPV is achieved after discounting at the cost of capital, is the net value generated by the project. The 20% discount rate sensitivity is applied to include the risks inherent in the business, and would be a typical discount rate used for screening projects. Screening is discussed in more detail in Section 13.6. 

When the sensitivities are performed the economic indicator which is commonly considered is the true value of the project, i.e. the NPV at the discount rate which represents the cost of capital, say 10%. 

The price differential at which coal becomes competitive with gas depends on plant size and the cost of capital, but based on estimates by the International Energy Agency (21) the required price ratio for gas to coal in North America falls into the range of 3.1 to 3.7 on an equivalent energy basis ( /MJ). Current prices give a gas/coal cost ratio nearer 1.5 to 2.0. As a result, all projected new methanol capacity is based on natural gas or heavy oil except for the proposed coal-based plant in China. 

In an economic comparison of these three common abatement systems, a 1991 EPA study (58) indicates extended absorption to be the most cost-effective method for NO removal, with selective reduction only matching its performance for small-capacity plants of about 200—250 t/d. Nonselective abatement systems were indicated to be the least cost-effective method of abatement. The results of any comparison depend on the cost of capital versus variable operating costs. A low capital cost for SCR is offset by the ammonia required to remove the NO. Higher tail gas NO... 

Discounted Ca.sh Flows. Because the flows below the cash flow box in Figure 1 tend to be arbitrary management decisions that are generally difficult to predict, the prediction of profitabiUty is based on the expected cash flows instead of earnings. As a result, some logical assumptions to account for the cost of capital and the recovery of the investment must be made. 

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

The NPV represents the present-value net return, because provision has been made for capital recovery and the cost of capital. In other words, the NPV is a discounted net return or profit, analogous to the net return of the example introduced earher. 

The internal return rate (IRR), a fixed point on the diagram, caimot be viewed as a measure of profitabihty, which should vary with the cost of capital (discount rate). Because the curvature of the total return curve caimot be predicted from the single IRR point, there is no way that the IRR can be correlated with profitabihty at meaningful discount rates. Even both end points, ie, the IRR and the total return at zero discount rate, are not enough to predict the curvature of the total return curve. 

Modern Measures of Profitability An investment in a manufacturing process must earn more than the cost of capital for it to be worthwhife. The larger the additional earnings, the more profitable... 

The cost of capital may also be considered as the interest rate at which money can be invested instead of putting it at risk in a manufacturing process. Let us consider the process data listed in Table 9-4 and plotted in Fig. 9-10. If the cost oi capital is 10 percent, then the appropriate discounted-cash-flow curve in Fig. 9-10 is abcdef. Up to point e, or 8.49 years, the capital is at risk. Point e is the discounted breakeven point (DEEP). At this point, the manufacturing process... 

Plot of capital-return ratio (CRR) against time over the life of the projec t for a discount rate at the cost of capital... 

These (NPV) data are plotted against the cost of capital, as shown in Fig. 9-12. The discounted-cash-flow rate of return is the value of i that satisfies Eq. (9-5). From Fig. 9-12, (NPV) = 0 at a (DCFRR) of 11.8 percent for project C and 14.7 percent for project D. Thus, on the basis of (DCFRR), project D is more profitable than project C. 

The (NPV) of project C is equal to that of project D at a cost of capital i = 9.8 percent. If the cost of capital is greater than 9.8 percent, projec t D has the higher (NPV) and is, therefore, the more profitable. If the cost of capital is less than 9.8 percent, project C has the higher (NPV) and is the more profitable. 

When to Scrap an Existing Process Let us suppose that a company invests 50,000 in a manufacturing process that has positive net annual flows (after tax) Acp of 10,000 in each year. During the third year of operation, an alternative process becomes available. The new process would require an investment of 40,000 but would have positive net annual cash flows (after tax) of 20,000 in each year. The cost of capital is 10 percent, and it is estimated that a market will exist for the product for at least 6 more years. Should the company continue with the existing process (project H), or should it scrap project H and adopt the new process (project 1) ... 

Comparisons on the Basis of Capitalized Cost A machine in a process generates a positive net cash flow of 1000. Two alternatives are available machine L, costing 2000, requires replacement every 4 years, and machine M, costing 3000, requires replacement every 6 years. Neither machine has any scrap value. The cost of capital is 10 percent. Which machine is the more profitable to operate ... 

Capital is at risk until the breakeven point has been reached. It is common practice to give consideration to the discounted breakeven point (DEEP), the time at which the (NPV) is zero when discounting at the cost of capital. At any time after the (DEEP), the project will have recovered its cost and provided a greater return on the capital than the cost of capital. It is customary for management to spread risk by diversifying the activities of a company among a portfoho of projects. 

It is an advantage to a company to be listed on a stock exchange since its investors can more easily sell their stock if they decide to do so. This increased hquidity makes investors more willing to accept a lower rate of return, which effectively lowers the cost of capital to the company. 

Cost of Capital The value of the interest rate of return used in calculating the net present value (NPV) of a project is usually referred to as the cost of capital. It is not a constant value since it depends on the financial structure of the company, the policy of the company toward a particular project, the local method of assessing taxation, and, in some cases, the measure of risk associated with the particular projec t. The last-named fac tor is best dealt with by calculating the entrepreneurs risk allowance inherent in the project i from Eq. (9-108), written in the form... 

In the absence of a rislc allowance the cost of capital becomes a technical financial computation based on sources of funds and company policy. As such it will usually be presented as a figure specified For use in a particular appraisal and is therefore of little concern to the projec t assessor. However, the following resume indicates the lands of Factors to be considered. 

Since this project is essential if current production is to be maintained, many companies would assess the cost of capital at somewhere near the lower value. Values of cost of capital in the region of 10 percent are to be expected in developed countries at the present time. 

As has been stated, it is alternatively possible to assign to the cost of capital the best risk-free return available on the money. The assessment then proceeds as discussed in connection with Eq. (9-108). 

Where the process is a labor intensive, low-cost workers are required in numbers (for example, textiles and clothing). The cost of capital has little effect on the choice of location as capital sources can be from anywhere. The ability, however, to repatriate profits and the proceeds from the sales of assets and exposure to foreign exchange risk are important if the location options are abroad. This factor becomes more relevant, the greater the capital intensity of the project. 

Fixed costs are those elements of piece cost that are a function of the annual production volume. Fixed costs are called fixed because they typically represent one-time capital investments (buildings, silos, processing machines, etc.) or annual expenses unaffected by the number of products produced (building rent, engineering support, administrative personnel, etc.). Typically, these costs are distributed over the total number of products produced in a given period. For plastics processes the principal elements are main machine cost, auxiliary equipment cost, tooling cost, building cost, overhead labor cost, maintenance cost, and the cost of capital. 

The capital cost of air separation machinery is linked to both the size of the beds (which dictates the cost of piping valves), of course to molecular sieve inventory and to the size of the compressor required to run the process. A low product recovery may have little impact on the bed size factor but it has an enormous effect on the amount of gas required and on the cost of compressing that gas. Thus the recovery and bed size factors have direct links to the cost of capital and operations of air separation machines. 

The minimum acceptable rate of return (MARK) for a venture depends on a number of factors such as interest rate, cost of capital, availability of capital, degree of risk, economic project life, and other competing projects. Management will a(bust the MARK depending on any of the above factors to screen out the more attractive ventures. When a company invests in a venture, the investment must earn more than the cost of capital and should be able to pay dividends. 

Equation (9-22) may be solved graphically or analytically by an iterative trial-and-error procedure tor the value of i, which is the discounted cash flow rate of return. It has also been known as the profitability index. For a project to be profitable, the interest rate must exceed the cost of capital. 

Economic value added The period dollar profit above the cost of capital. It is a means to measure an organization s value and a way to determine how management s decisions contribute to the value of a company. 

Minimum acceptable rate of return (MARR) The level of return on investment, at or above the cost of capital, chosen as acceptable for discounting or cutoff purposes. 

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