Discounting

Time is taken into account by discounting the annual cash flow Acf with the rate of interest to obtain the anitual discounted cash flow -Adcf- Thus, at the end of year 1,... 

The sum of the annual discounted cash flows over n years SAdcf is known as the net present value (NPV) of the project ... 

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) ... 

The value of i given by this equation is known as the discounted cash-flow rate of return (DCFRR). It may be found graphically or by trial and error. 

A suitable maintenance strategy should be developed for equipment by considering the criticality and failure mode, and then applying a mixture of the forms of maintenance described above. In particular, the long-term cost of maintenance of an item of equipment should be estimated over the whole life of the project and combined with its capital cost to select both the type of equipment and form of maintenance which gives the best full lifecycle cost on a discounted basis), while of course meeting the technical, safety and environmental specifications. 

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... 

The proflt-to-investmentratio (PIR) may be defined in many ways, and is most meaningful when deflated and discounted. On an undeflated and undiscounted basis, the PIR may be defined as the ratio of the cumulative cash surplus to the capital investment. This indicates the return on capital investment of the project, is simple to calculate, but does not reflect the timing of the income/investment in the project. 

The project cashflow discussed so far follows a pattern typical of E P projects a number of years of expenditure (giving rise to cash deficits) at the beginning of the project, followed by a series of cash surpluses. The annual cashflows need to be evaluated to incorporate the timing of the cash flows, to account for the effect of the time value of monef. The technique which allows the values of sums of money spent at different times to be consistently compared is called discounting. 

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... 

Since this is a purely mechanical operation it can be performed using the above equation, or by looking up the appropriate discount factor in discount tables. Two types of discount factors are presented for full year and half year discounting. 

If the reference date is set at the beginning of the year (e.g. 1.1.98) then full year discount factors imply that t is a whole number and that cashflows occur in lump sums at the end of each year. If the cashflow occurs uniformly throughout the year and the reference date is the beginning of the year then mid-year discount factors are more appropriate, in which case the discounting equation would be ... 

Discounting can also be performed, of course, using a programmable calculator or a spreadsheet such as Lotus 1-2-3 or Microsoft Excel. 

The cashflow discussed in Section 13.2 did not take account of the time value of money, and was therefore an undiscounted cashflow. The discounting technique discussed can now be applied to this cashflow to determine the present value of each annual cashflow at a specified reference date. 

The following example generates the discounted cashflow (DCF) of a project using 20% mid-year discount factors. 

Year Cash Surplus ( m) Discount Factor (mid year) Discounted Cashflow ( m)... 

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). 

This may be more useful if the cashflow items are discounted e.g. 10% NPV... 

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... 

It is often more useful to use the discounted values, to allow for the time effect of money, hence... 

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. 

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