Present worth

P = present worth of estimated capital cost F = future worth of estimated capital cost... 

Discounted Total Capital. Because the investment can occur over a period of years, the investment flows should be discounted to the same present time and combined to give the discounted total capital (DTC). This present-worth investment parameter is the second criterion it corresponds to the investment of the earher example. 

Example The present worth (PW) of a series of cash flows at the end of year k is... 

The amount of a loan is known as the principal. The longer the period of time for which the principal is loaned, the greater the total amount of interest paid. Thus, the future worth of the money F is greater than its present worth P. The relationship between F and P depends on the type of interest used. 

In effec t, in computing the average net annual cash flow per dollar invested, the value of f p of Eq. (9-46) has been obtained for this example. From tables of the annuity present-worth factor/ p the value of the interest rate is found to be = 0.25 when f p = 0.5124 with n = 3 years. 

The value of y will for most cases be less than 0.2 and with the right apphcation may well be less than 0.1. Values for the annuity present-worth factorwill in most cases be less than 0.15. 

The tables were based upon the cost of energy at the end of the first year, a 10 percent inflation rate on energy costs, a 15 percent interest cost, and a present-worth pretax profit of 40 percent per annum on the last increment of insulation thickness. Dual-layer insulation was used for 3l/2-in and greater thicknesses. The tables and a full explanation of their derivation appear in a paper by F. L. Rubin (op. cit.). Alternatively, the selected thicknesses have a payback period on the last nominal l/2-in increment of 1.44 years as presented in a later paper by Rubin [ Can You Justify More Piping Insiilation Hydrocarbon Process., 152-155 (July 1982)]. 

The annualized capital cost (ACC) is the product of the CRF and TCC and represents the total instaUed equipment cost distributed over the lifetime of the project. The ACC reflects the cost associated with the initial capital outlay over the depreciable life of the system. Although investment and operating costs can be accounted for in other ways such as present-worth analysis, the capital recovery method is preferred because of its simplicity and versatUity. This is especiaUy true when comparing somewhat similar systems having different depreciable lives. In such decisions, there are usuaUy other considerations besides economic, but if all other factors are equal, the alternative with the lowest total annualized cost should be the most viable. 

The importance of present worth, also known as present value, lies in the fact that... 

In this formula, P is present worth or present value, F is future value, i is the interest or discount rate, and n is the number of periods. Economically, there is an additional factor at work in present value, and that factor is pure time preference, or impatience. However, this issue is generally ignored in business accounting, because the firm has no such emotions, and opportunities can be measured in terms of financial return. 

The importance of present worth, also known as present value, lies in the fact that time is money. The preference between a dollar now and a dollar one year from now is driven by the fact that a dollar in-hand can earn interest. Present value can be expressed by a simple formula ... 

Although the reasoning seems sound, opportunity costs are not really expenses. Though it is true that the cash will be unavailable for other investments, opportunity cost should be thought of as a comparison criteria and not an expense. The opportunity forgone by using the cash is considered when the project competes for funds and is expressed by one of the financial analysis factors discussed earlier (net value of present worth, pay back period, etc.). It is this competition for company funds that encompasses opportunity cost, so opportunity cost should not be accounted directly against the project s benefits. 

The money earned in any year can be put to work (reinvested) as soon as it is available and start to earn a return. So money earned in the early years of the project is more valuable than that earned in later years. This time value of money can be allowed for by using a variation of the familiar compound interest formula. The net cash flow in each year of the project is brought to its present worth at the start of the project by discounting it at some chosen compound interest rate. 

Net present worth (NPW) Estimated net cash flow in year n (NFW)... 

Discounted cash-flow analysis, used to calculate the present worth of future earnings (Section 6.10.3), is sensitive to the interest rate assumed. By calculating the NPW for various interest rates, it is possible to find an interest rate at which the cumulative net present worth at the end of the project is zero. This particular rate is called the discounted cash-flow rate of return (DCFRR) and is a measure of the maximum rate that the project could pay and still break even by the end of the project life. 

Inflation depreciates money in a manner similar to, but different from, the idea of discounting to allow for the time value of money. The effect of inflation on the net cash flow in future years can be allowed for in a similar manner to the net present worth calculation given by equation 6.9, using an inflation rate in place of, or added to, the discount rate r. However, the difficulty is to decide what the inflation rate is likely to be in future years. Also, inflation may well affect the sales price, operating costs and raw material prices differently. One approach is to argue that a decision between alternative projects made without formally considering the effect of inflation on future earnings will still be correct, as inflation is likely to affect the predictions made for both projects in a similar way. 

Net present worth NPW , As for NFW but accounts for timing of cash flows Dependent on discount rate used... 

This is found by trial-and-error calculations. The present worth has been calculated at discount rates of 25, 35 and 37 per cent. From the results shown in Table 6.8 it will be seen that the rate to give zero present worth will be around 36 per cent. This is the discounted cash-flow rate of return for the project. 

Calculate the cumulative net present worth of the project, at a discount rate of 8 per cent. Also, calculate the discounted cash flow rate of return. 

Alternative 2 has a lower present worth and O M cost than Alternative 3, but because of the additional cap required it has a higher capital cost (USD 11,200,000 versus USD 8,000,000). The cap is one of the most expensive components to construct. Alternative 4 has a higher capital, O M, and present worth cost than Alternatives 2 and 3. Alternative 5 has the highest capital (USD 34,600,000), first-year O M (USD 3,200,000), and present worth cost (USD 42,600,000) of all of the alternatives because of the incinerator component. All costs have been updated in terms of 2007 USD.68... 

P Present worth of a future sum of money ( ), or pressure (N-m 2, bar), or probability (-), or thermal effectiveness of 1-2 shell-and-tube heat exchanger (-)... 

The right-hand side of Equation (3.5) is known as the capital recovery factor or present worth factor, and the inverse of the right-hand side is known as the repayment multiplier r. 

Number of years for the net Present worth of receipts less IRR equals the interest rate i... 

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