The Time Value of Money

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. 

Payout time (PT), or payback period, is a measure of the time, usually in years, required to recover the investment in a scenario in which the time value of money is neglected. This can be represented by the general form... 

Expenditure on corrosion prevention is an investment and appropriate accountancy techniques should be used to assess the true cost of any scheme. The main methods used to appraise investment projects are payback, annual rate of return and discounted cash flow (DCF). The last mentioned is the most appropriate technique since it is based on the principle that money has a time value. This means that a given sum of money available now is worth more than an equivalent sum at some future data, the difference in value depending on the rate of interest earned (discount rate) and the time interval. A full description of DCF is beyond the scope of this section, but this method of accounting can make a periodic maintenance scheme more attractive than if the time value of money were not considered. The concept is illustrated in general terms by considering a sum of money P invested at an... 

A consideration of the costs of the protective Schemes 1 and 3 given in Table 9.2 indicates that the latter is significantly more expensive than the former, and it is of interest, therefore, to apply the concept of the time value of money to these two schemes for 11 of steel processed. 

Thus it can be seen that although the aggregate cost indicates Scheme 1 to be the cheaper, it is the more expensive when account is taken of the time value of money. 

The total NPW will be less than the total NFW, and reflects the time value of money and the pattern of earnings over the life of the project see Example 6.6. 

The rate of return is often calculated for the anticipated best year of the project the year in which the net cash flow is greatest. It can also be based on the book value of the investment, the investment after allowing for depreciation. Simple rate of return calculations take no account of the time value of money. 

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 future worth NFW , Simple. When plotted as cash-flow diagram, shows timing of investment and income Takes no account of the time value of money... 

The other indices to be described, net present value and discounted cash flow return, are more comprehensive because they take account of the changing pattern of project net cash flow with time. They also take account of the time value of money. 

As a more complete picture of the project emerges, the cash flows through the project life can be projected. This allows more detailed evaluation of project profitability on the basis of cash flows. Net present value can be used to measure the profit taking into account the time value of money. Discounted cash flow rate of return measures how efficiently the capital is being used. 

It should be noted that for Example 10-4 none of the evaluation methods that did not take into account the time value of money could differentiate between these plants, but the net present value method not only could differentiate but determined which was best. 

This chapter includes a discussion of how to formulate objective functions involved in economic analysis, an explanation of the important concept of the time value of money, and an examination of the various ways of carrying out a profitability analysis. In Appendix B we cover, in more detail, ways of estimating the capital and operating costs in the process industries, components that are included in the objective function. For examples of objective functions other than economic ones, refer to the applications of optimization in Chapters 11 to 16. 

So far we have explained how to estimate capital and operating costs. In Example 3.3, we formulated an objective function for economic evaluation and discovered that although the revenues and operating costs occur in the future, most capital costs are incurred at the beginning of a project. How can these two classes of costs be evaluated fairly The economic analysis of projects that incur income and expense over time should include the concept of the time value of money. This concept means that a unit of money (dollar, yen, euro, etc.) on hand now is worth more than the same unit of money in the future. Why Because 1000 invested today can earn additional dollars in other words, the value of 1000 received in the future will be less than the present value of 1000. 

For an example of the kinds of decisions that involve the time value of money, examine the advertisement in Figure 3.1. For which option do you receive the most value Answers to this and similar questions sometimes may be quickly resolved using a calculator or computer without much thought. To understand the underlying assumptions and concepts behind file calculations, however, you need to account for cash flows in and out using the investment time line diagram for a project. Look at Figure 3.2. 

Payback period (PBP)—how long a project must operate to break even ignores the time value of money. 

Two other measures of profitability that take into account the time value of money are... 

Does not properly consider the time value of money and distributed investments or cash flows... 

In Example 3.3 we developed an objective function for determining the optimal thickness of insulation. In that example the effect of the time value of money was introduced as an arbitrary constant value of r, the repayment multiplier. In this example, we treat the same problem, but in more detail. We want to determine the optimum insulation thickness for a 20-cm pipe carrying a hot fluid at 260°C. Assume that curvature of the pipe can be ignored and a constant ambient temperature of 27°C exists. The following information applies ... 

What is the minimum cost for the optimal thickness of the insulation List specifically the objective function, all the constraints, and the optimal value of t. Show each step of the solution. Ignore the time value of money for this problem. 

Net present value (NPV) the present value (including the time value of money) of initial and future cash flows given by Equation (13.4). 

The two key elements of any biotech story are the importance of the medical need and the rationale for why this idea is likely to work when previous efforts have failed. While the time value of money should theoretically be important, given the long timelines for drug development, in practice estimates of successful drug valuations and technical risks usually overshadow the risk-free time cost of money. 

Where CF is the cash flow from operation, HR is the hurdle rate or required minimum return and II is the initial investment. Advantages of NPV are that it accounts for the time-value of money, provides a value estimate for the lifetime of the project (10 years) and can always be calculated (unlike IRR). Hurdle rates are set by central finance groups or, in some cases, the project team. If a positive NPV is obtained at a given hurdle rate a project is considered profitable and should be executed based on competing priorities. 

Is this a good investment Let us introduce the basic concept that money on hand is worth more than future money, or the time value of money. The net present value NPV is defined to be... 

In business, money is either borrowed or loaned. If money is loaned, there is the risk that it may not be repaid. From the lender s standpoint, the funds could have been invested somewhere else and made a profit therefore, the interest charged for the loan is compensation for the forgone profit. The borrower may look upon this interest as the cost of renting money. The amount of interest charged depends on the scarcity of money, the size of the loan, the length of the loan period, the risk that the lender feels that the loan may not be repaid, and the prevailing economic conditions. Engineers involved in the presentation and/or the evaluation of an investment of funds in a venture, therefore, need to understand the time value of money and how it is applied in the evaluation of projects. 

Although there have been many quantitative measures suggested through the years, some did not take into account the time value of money. In today s economy, the following measures are the ones most companies use ... 

This model does not take into account the time value of money, and no consideration is given to cash flows that occur in a project s later years after the depreciable investment has been recovered. A variation on this method includes interest, called payout period plus interest (POP + I) and the net effect is to increase the payout period. This variation accounts for the time value of money. 

Net Present Worth In the net present worth method, an arbitrary time frame is selected as the basis of calculation. This method is the measure many companies use, as it reflects properly the time value of money and its effect on profitability. In equation form... 

Other parameters are more difficult to calculate. However, they can be very much more useful because they take into account two other important aspects. Firstly, the pattern of flow of money into and out of the business (cash-flow) since items of income (revenue) and expenditure (outgoings) can vary a lot with time. For instance, as can be seen in Figure 13.5, initially expenditure greatly exceeds income, whereas later on once the plant is operating and product is being sold income exceeds expenditure. Secondly there is the time value of money , that is money received now is more valuable than the same sum of money received in a years time, as it can be invested and interest will have accmed on it by the end of the year. Hence, early income to a business is valuable as it can be invested in the business and so saves having to borrow money to buy equipment, pay wages, etc. Thus the value of money is not completely absolute, but is a function of time. 

Like NPVs and nnlike ROI, DCFR allows for the time value of money. That is the money invested in a project only produces profits after that period of time needed to carry ont R D, bnild and commission a manufacturing plant, establish a distribution network and a sales organisation and make appreciable sales etc. Whereas if that money had been invested in a bank throughout that period it would have been steadily earning interest at a snbstantial rate with very little risk incurred. 

The chapter considered the engineer s fear of financials and attempted to overcome it with a straightforward discussion of cash flow, income, and balance statements. The mathematics of these statements is simple arithmetic, but the confusion seems to come from not understanding a few key terms. The chapter also considered the utility of ratio analysis—what engineers might call dimensional analysis for companies—breakeven analysis, and the basics of the time value of money. Although a full discussion was beyond the scope of this chapter, the discussion served up the basics and may also serve to introduce more careful treatments in other courses or texts. 

Traditionally, investment decisions have been guided by tools such as the net present value (NPV), which takes into account the time value of money and is formally defined as the difference between the present value of cash inflows and cash outflows using a certain annual discount rate. The NPV is easy to calculate, but, as Dixit and Pyndick have pointed out, it is frequently wrong [11,12] since the NPV analysis is based on faulty assumptions. Either the investment is reversible and can be undone when conditions change, or if it cannot be changed, the investment has to be done now-or-never. This binary approach is not always applicable, and the ability to delay profoundly affects the investment decision. A richer framework is necessary to account for the gray area between the binary possibilities. 

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