Discount factors

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 ... 

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)... 

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. 

Net Present Va.Iue, Each of the net annual cash flows can be discounted to the present time using a discount factor for the number of years involved. The discounted flows are then all at the same time point and can be combined. The sum of these discounted net flows is called the net present value (NPV), a popular profit criterion. Because the discounted positive flows first offset the negative investment flows in the NPV summation, the investment capital is recovered if the NPV is greater than zero. This early recovery of the investment does not correspond to typical capital recovery patterns, but gives a conservative and systematic assumption for investment recovery. 

Fig. 2. Venture A Input data and profitabifity analysis. For profitabifity analysis, DTC equals line 8 multiphed by the discount factor [1 -...

Prevailing interest rates probably tend to reflect an estimate of future inflation and contain a component that can be attributed loosely to inflationary expectations. However, the classical treatment is to assume that an inflation-free interest rate, r and average inflation rate, r, over the project lifetime can be identified. A discount factor (1 + r) can be modified (25) so that... 

Values for the discount factors are readily available in tables which show that it will take 7.3 years for the principal to double in amount if compounded annually at 10 percent per year and 14.2 years if compounded annually at 5 percent per year. 

Time is taken into account by using the annual discounted cash flow Adcf, which is related to the annual cash flow Acf and the discount factor by... 

NOTE Aqf is net annual cask flow, Aqcf is net annual discounted cask flow,/ is discount factor at stated interest, lative discounted cask flow. 

We shall calculate for these data the net present value (NPV) for the following depreciation methods and discount factors ... 

TABLE 9-5 Annual Cash Flows, Straight-Line Depreciation, and 10 Percent Discount Factor... 

Atc = total annual capital expenditure. Acf Aci — Aij — Atc net annual cash flow. f = discount factor at 10%. 

The net annual cash flows Acp and cumulative discounted annual cash flow X Aocf discount factor of 10 percent are hsted in Table 9-7 for the two projec ts. At the end of Year 9, the net present values are... 

Both projects have lives of 10 years and constant positive net annual cash flows Acf of 2069 and 1558 for projec ts J and K respec tively. The corresponding (NPV)s at a discount factor of 10 percent are + 2710 and + 2560 respectively. These data are summarized as follows ... 

Example 3 Sensitivity Analysis The following data describe a project. Revenue from annual sales and total annual expense over a 10-year period are given in the first three columns of Table 9-5. The fixed-capital investment Cfc is 1 million. Plant items have a zero salvage value. Working capital C c is 90,000, and the cost of land Ci is 10,000. There are no tax allowances other than depreciation i.e., is zero. The fractional tax rate t is 0.50. For this project, the net present value for a 10 percent discount factor and straight-line depreciation was shown to be 276,210 and the discoiinted-cash-flow rate of return to be 16.4 percent per year. 

We shall use these data and the accompanying information of Table 9-5 as the base case and calculate for straight-line depreciation the net present value (NPV) with a 10 percent discount factor and the discoiinted-cash-flow rate of return (DCFRR) for the project with the following situations. 

Year, n Net capital expendihire, Atc Revenue from sales, Total expenses. Ate Cash income, Aci Depreciation charge. Ad Taxable income, Aci - Ad) Amount of tax at t = 0.5, A,t Net cash flow, Acf Discount factor at i = 10%, f. Discounted net cash flow, Adcf Net present value (NPV)... 

First, the project s anticipated benefit and cost are tabulated for each year of the project s lifetime. Then, these values are converted to present values by using the present-value equation, with the company s discount rate plugged in as the discount factor. Finally, the cumulative total of the benefits (at present value) and the cumulative total of the costs (at present... 

Mass transfer Generalized model of Bravo, et al. [113], with discount factors for wetted surfaces. 

There are various ways of discounting, i.e. net present value (NPV) or internal rate of return (IRR). Discounting should ideally be carried out over the whole life of the project but generally, after 10 years, the discount factors are small and make little difference. 

The selection of the discount factor depends on the financial policy of the business, but is usually 2-3 per cent above the current interest rates. Use of discounting methods will determine whether the project cost will produce a better return than by simply investing the capital involved at the highest compound interest rate or, if the capital cost has to be borrowed, whether the rate of return is much higher than the cost of borrowing. 

In order to analyse the balance in view of the threat of exclusion from public financing, the author devises a demand equation with a two-stage budget allocation. The first step is to choose a therapeutic group, and the second is to choose the differentiated products. The co-payment acts as the price. The main conclusion is that when the product is included in public financing the health service can receive a discount if the political decisions are price-sensitive and the fixed cost of market entry in the event of inclusion is lower than the fixed cost of exclusion. In his study of price-cap regulation, the author insists that the mechanism should be continued in the long term, and that therefore it is necessary to account for the entire lifetime of the product and consider a discount factor. All this takes as its point of departure Abbott s 1995 model. 

The objective function is the net present value, NPV (sum of the discounted cash flows), using a discount rate of 10 percent. All flows except capital were assumed to be uniformly distributed over the year working capital was added or subtracted instantaneously at the beginning of each year, and fixed capital was added only in the zero year. The continuous discounting factors were... 

Year Fixed capital Discount factor Discounted cash flow ... 

Year Discount factor Discounted cost flow at 10% discount rate... 

Sulphur content of crude oils has always been regarded as a discounting factor and as environmental restrictions on sulphur emissions have been tightened, the need to desulphurise refinery... 

How does this entrapment come about It cannot come about if all choices are done with full information about all the future consequences of one s choices and with a stable exponential discount factor. Both of these requirements can, however, be relaxed. (Becker and Murphy do not discuss this point.)... 

As the discount factor at delay t = 0 should be equal to 1, we can— without loss of generality—set p = 1. Ainslie has no theory of interindividual or intraindividual variations in the parameter a and seems to conceive a as fixed. Obviously, a depends on the units of measurement for time. Hence, as long as we are not making interpersonal comparisons, we may choose the time unit so that a reward delayed one time unit is valued as half of its instantaneous value. This implies that a = 1, and we obtain... 

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