Discount rate

As pointed out in Chapter 3.3.2 the company s cost of capital should be used to discount cash flows to their present value. As a company encounters different costs for equity and debt, the respective costs have to be identified as a prerequisite for calculating the cost of capital. 

The costs of debt can generally be deduced from the terms of credit contracts or corporate bonds issued by the company. Alternatively, if a credit rating is available, the interest rate corresponding to the credit rating of the company can be used (cf. Koller et al. 2005, pp. 319-320). 

The use of uniform costs of capital to evaluate all investment projects of a company implies that the risk associated with each individual investment equals the company s average risk. As this is often not the case in diversified companies, the use of more differentiated business unit or project specific cost of capital has been suggested in literature (cf. Brealey et al. 2006, pp. 215-218). 

In the design of a global production network for a specific value chain additional risk stems from factors such as exchange rate exposure or political risks associated with international investments. Following the differen- 

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Discounted cash-flow rate of return. Discounted cash-flow rate of return is defined as the discount rate i which makes the NPV of a project zero (curve 3 in Fig. A.2) ... 

Keywords economic model, shareholder s profit, project cashflow, gross revenue, discounted cashflow, opex, capex, technical cost, tax, royalty, oil price, marker crude, capital allowance, discount rate, profitability indicators, net present value, rate of return, screening, ranking, expected monetary value, exploration decision making. 

Corporate Planning Forecast oil and gas prices Discount rates, hurdle rates Exchange rates Inflation forecast Market factors Political risk, social obligations... 

What we have calculated is the present value (at a particular reference date) of a future sum of money, using a specified discount rate. In any discounting calculation, it is important to quote the reference date and the discount rate. 

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). 

Once the concept of discounting is accepted, the procedure becomes mechanical. The general formula for discounting a flow of money cooccurring in tyears time to its present value Cq assuming a discount rate r is... 

The total undiscounted cash surplus (the ultimate cash surplus) is 190 m. The total discounted cash surplus ( 24.8 m) is called the net present value (NPV) of the project. Since in this example the discount rate applied is 20%, this figure would be the 20% NPV also annotated NPV(20). This is the present value at the beginning of Year 1 of the total project, assuming a 20% discount rate. 

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. 

The IRR column is the internal rate of return of the project at the relevant oil price, and is a measure of what discount rate the project can withstand before the NPV is reduced to 0. This indicator will be discussed in a moment, but is included here as a recommended part of this presentation format. 

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. 

As the discount rate increases then the NPV is reduced. The following diagram shows the cashflow from the previous example (assuming an oil price of 20/bbl and ignoring the effect of inflation) at four different mid-year discount rates (10%, 20%, 25%, 30%). 

At a specific discount rate the net present value (NPV) is reduced to zero. This discount rate is called the internal rate of return (IRR). 

Another useful profitability indicator is the internal rate of return (IRR), already introduced in the last section. This shows what discount rate would be required to reduce the NPV to zero. The higher the IRR, the more robust the project is, i.e. the more risk it can withstand before the IRR is reduced to the screening value of discount rate. Screening values are discussed below. 

One way of calculating the IRR is to plot the NPV against discount rate, and to extrapolate/ interpolate to estimate the discount rate at which the NPV becomes zero, as in the Present Value Profile in Figure 13.16. The alternative method of calculating IRR is by... 

The PV Profile can be used to select the more attractive proposal at the appropriate discount rate if the primary indicator is NPV. Figure 13.17 illustrates that the outcome of the decision may change as the discount rate changes ... 

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. 

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. 

A logical choice for the discount rate is the average capital cost rate, where capital includes both the equity and debt capital. The estimation of a suitable value for the discount rate is not straightforward (23), but financial speciaUsts always seem ready to provide a number. 

Internal Return Rate. Another rate criterion, the internal return rate (IRR) or discounted cash flow rate of return (DCERR), is a popular ranking criterion for profitabiUty. The IRR is the annual discounting rate that makes the algebraic sum of the discounted annual cash flows equal to zero or, more simply, it is the total return rate at the poiat of vanishing profitabiUty. This is determined iteratively. 

The total annual return rate on investment is the sum of both the capital cost rate, ie, discount rate, and the net return rate (NRR). Any given numerical value can represent a low capital cost rate and a high net return rate, or a high capital cost rate and a low net return rate. The IRR, as the discounting rate that gives a vanishing net return, cannot be related to the total return rate at appropriate discount rates because of the nonlinear nature of the discounting step. 

Profitability Diag rams. Profitabihty diagrams of the type shown in Figure 3a for Venture A provide insight into venture profitabihty. Total return rate is defined as the sum of the discount rate and the net return rate (NRR). The discount rate, net return rate, and total return rate are all shown on the diagram as functions of the discount rate. Because the NPV is a nonlinear function of the discount rate, the NRR and total return rate are also nonlinear. The NRR, as a measure of the profitabihty, correctly decreases as the discount rate increases. 

Fig. 3. Profitabihty diagram for Venture A. (a) Simple diagram. NRR is net return rate IRR, the internal rate of return, is a given fixed point, (b) Three NRR cutoff lines for Venture A where B, C, and D represent NRR values of 15, 10, and 5%/yr, respectively. For example, at a discount rate of 10% per year, the NRR cutoff for Venture A could be as high as 10.74% per year for marginal acceptance (point X). Acceptable levels are to the left of NRR cutoff...

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. 

An NRR cutoff level can be selected to reflect the minimum acceptable profitabihty level. Lines of constant cutoff rate can be drawn on a profitabihty diagram, as shown in Figure 3b for NRR cutoff rates of 5, 10, and 15% per year. The acceptable region changes with discount rate and relative venture risk, ie, cutoff rate. 

Fig. 4. Effect of NPV on profitabihty where investment and lifetime are the same for all Ventures (see Table 4). (a) Sale revenues for Ventures B and C have been selected so that at a discount rate of 10% per year Ventures A, B, and C each have the same NPV and NRR. IRR values are as given and do not relate to NPV, NRR, or total return rate (TRR). The diagram indicates that at discount rates less than 10%, Venture C has the largest NRR, but the IRR indicates Venture B is the choice for all discount rates, (b) Sale revenues for Ventures D and E have been selected so that Ventures A, D, and E each have a different NPV at a discount rate of 10% per year, but all three have the same IRR. The diagram indicates that at the selected discount rate of 10%, the...

Fig. 5. Effect of lifetime on profitability. Venture F has a shorter operating lifetime than Venture A, but the same investment and IRR (see Table 4) the NPV is the same at the 10% discount rate. The diagram indicates that the profitabiUty of Venture F is higher than that of Venture A at all discount rates the shorter lifetime leads to a higher annual net return rate (NRR). The IRR rate does not indicate this difference in profitabiUty.

Fig. 7. Sensitivity analysis, (a) Changes in discount rate as indicated by a sensitivity diagram. At center axis the discount rate i = 10% and NRR = 10.74% ...

The ways of assessing profitabihty to be considered in this section are (1) discounted-cash-flow rate of return (DCFRR), (2) net present value (NPV) based on a particiilar discount rate, (3) eqmvalent maximum investment period (EMIP), (4) interest-recovery period (IRP), and (5) discounted breakeven point (DEEP). 

FIG. 9-10 Effect of discount rate on cumulative cash flows. 

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... 

The (DCFRR) is the discount rate that satisfies Eq. (9-57) in the final year of the project. We can approximate the (DCFRR) for each projec t as follows ... 

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