Cost of capital

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. 

At discount rates less than 18%, Proposal 1 is more favourable in terms of NPV, whereas at discount rates above 18%, Proposal 2 is more attractive. NPV is being used here as a ranking tool for the projects. At a typical cost of capital of, say, 10%, Proposal 1... 

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%. 

Wells are worked over to increase production, reduce operating cost or reinstate their technical integrity. In terms of economics alone (neglecting safety aspects) a workover can be justified if the net present value of the workover activity is positive (and assuming no other constraints exist). The appropriate discount rate is the company s cost of capital. 

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. 

Various i Interest rate per period, usually annual, often tbe cost of capital Dimensionless... 

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... 

Cumulative discounted-cash-flow or (NPV) curve for a discount rate of 10 percent per year or other agreed aftertax cost of capital... 

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 ... 

With a cost of capital of 10 percent the various cash flows can be discounted and summed. Thus for the base cases Z Af = 2,815,600, Z Ajp/d = 754,716, Z Aofd = 614,457, and Z C c/d = 61,446. With corporate taxes payable at 50 percent the aftertax cash flows of the first three items are (1 — 0.50) of the sums calculated above. The discounted working capital and the fixed-capital outlay are not subject to tax. These most probable values are listed and summed in Table 9-11 and, after adjustment for tax, give the modal value of the (NPV) as 276,224. 

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. 

As an example, let us calculate the required risk rate for a projec t that is described by the following (I) risk strategy is equivalent to an (MSF) of 99 percent, (2) payback of risk capital is 3 years, (3) cost of capital i is 10 percent, and (4) probabibty of complete success of the projec t is estimated as 95 percent. 

The same money invested in a project with a (DCFRR) of 10 percent would, by Eq. (9-108), obtain an entrepreneurial return i = 8.37 percent on the whole investment, i.e., 8.37/ 100. Investment of the entrepreneur s own money would only achieve an aftertax return of (0.1)(1 — 0.40) = 6 percent on 50, or 3/ 100 of total investment. The incentive to the entrepreneur to manage the projeci thus corresponds to a tax-free income of 5.37/ 100 of total investment. In practice, money is borrowed from more than one source at different interest rates and at different tax liabihties. The effective cost of capital in such cases can be obtained by an extension of the above reasoning and is treated in detail by A. J. Merrett and A. Sykes Capital Budgeting and Company Finance, Longmans, London, 1966, pp. 30 8). 

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. 

Example 18 Risk-Free Cost of Capital A company requires an investment of 100,000 in new plant to maintain its present sales. Let us determine the current cost of capital to the company and the risk-free cost of capital that it should assign to the plant-replacement project, given the following data. 

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. 

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