Discount factors tables

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. 

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. 

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

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... 

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. 

Table 6.8 illustrates example 6. It is straightforward to show that these people always hit in this situation, whether they are sophisticated or naive. How impatient would time-consistent people have to be to always hit in this situation It can be shown that time-consistent people with discount factor 8 always hit only if 5. 99., and since 6 is the per-period... 

As indicated in the footnote for Eq. (12), the common interest expressions can be written in simplified form by using discount-factor and compound-interest-factor notation. Following is a summary showing the significance and meaning of the compounding factors presented in Table 3, Derivations of the factors are presented in the text. 

This discount factor, dnis the amount that would yield one dollar after n years if invested at an interest rate of i The discounted-cash-flow rate of return can be determined by the trial-and-error method illustrated in Table 1, where the annual cash flows are discounted by the appropriate discount factor to a total present value equal to the necessary initial investment. ... 

Example 2 Discounted-cash-flow calculations based on continuous interest compounding and continuous cash Row. Using the discount factors for continuous interest and continuous cash flow presented in Tables 5 to 8 of Chapter 7, determine the continuous discounted-cash-flow rate of return r for the example presented in the preceding section where yearly cash flow is continuous. The data follow. 

Lines 1, 2, and 3 (investments) in Table 2 would normally only be filled in for the first column (discount factor of 1.000) which is designated as the zero year for the operation, with the unit actually going into operation at the start of the so-called first year. It is assumed that working capital and salvage value will be recovered in a lump sum at the end of the estimated service life, so these values are listed on lines 1, 2, and 13 as positive (incoming funds) numbers in the end-of-life column. Since these are lump-sum instantaneous values, the discount factor to apply to them is the finite (year-end) cash flow factor as shown in line 14 in the end-of-life column. 

Because the compounded annual flow to the project is constant for each year at ( 310,OOOX(er - l)/r], the year-by-year use of the discount factor, as illustrated in Table 1 of this chapter, can be replaced by a one-step process wherein the equivalent present value is determined horn Eq. (25) of Chap. 7, P = R[(ern - 1 )/rern], with R = 310,000, so that... 

Dichotomous search, 407 Dimensionless numbers, definitions of 468-469 DIPPR, 117 Direct costs, 210 in capital investmenf 167 Direct production costs, 197-204,210 Discounf definition of, 226 Discount factors definition of 223/i 236-237, 303 tables of 219, 234-235, 240-246... 

Figure 9-2 shows the cumulative net present values stages in a project. Tables 9-2 through 9-5 are the discount factors for computing the net present value. 

Discount Factors. This Table Shows the Present Value of Unity Discounted for Different Numbers of Years and at Different Rates of Discount... 

For a given discount rate, calculate the discount factor during the operating life of the project. Multiply the discount factor by the cash flow and obtain the net present value and the net return rate. Valle-Riesta [8] has listed alternative methods of calculating cash flow, as shown in Table 9-6. 

When the liquid has foaming tendencies, additional residence time must be allowed for phase disengagement. System discount factors, recommended by Koch-Glitsch, Inc. on the basis of field experience, are shown in Table 12.7. As an example, the maximum allowable velocity of 0.1 m/s would be multiplied by the discount factor so as to provide adequate downcomer volume. 

TABLE 5.7-3 Downflow Capacity Discount Factors, Foaming Systems... 

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