Time value, of money

Simple breakeven analysis is quite useful for getting a ballpark sense of when a given investment will start to payoff, but more sophisticated analysis will take account of the alternative uses of money and the fact that a dollar today is worth more than a dollar tomorrow. 

The key idea is to take a present amount P and account for the interest i that will compound over n periods to give some future amount F as follows  

The validity of the equation is easy to verify as in one period the amount P 

The major problems with the indicators that have been presented are that they fail to take into account the timing of payments and receipts and the magnitude of the profits. They also can give incorrect results when comparing projects having different time durations, To resolve these problems a different economic indicator 

Your roommate is going to come into a sizeable inheritance at age 25. He is now 18, and ever since he saw a James Bond movie he has felt he must have an Aston Martin. (This automobile costs 13,500 with accessories.) He currently has only 100 a month spending money and he needs the car immediately. You have access to the required money because of the death of a wealthy maiden aunt. He is willing to sign over a portion of his inheritance. What would be a reasonable amount to request from him when he reaches 25  

In 1969 this money could be placed in a savings and loan association where it would earn 5.25% interest compounded annually, with the principal guaranteed by the federal government. There is no risk in this investment. At the end of the first year the interest would be 

This would obviously be the minimum amount to request. 

The maximum amount your roommate would pay would be determined by his alternate sources of financing. If he could get a loan from a bank it would be at an interest rate of 8% or more. A loan from a finance agency would cost more. At 8% interest compounded annually 13,500 would be worth 23,100 after 7 years. To request that he pay you 23,100 on his twenty-fifth birthday in return for giving him 13,500 now would certainly be fair-especially if he let you use the car and if an ironclad Hen could be placed on his inheritance. 

The total bare-module cost for the column and its auxiliaries = 2,226,000 The annual heating steam cost for the reboiler is computed = 728,000/yr The annual cooling water cost for the two condensers = 84,000/yr The annual electricity cost for the reflux pump = 38,000/yr The total utility cost = 850,000/yr Compute the annualized cost. 

For purposes of comparison of alternatives, the bare-module cost of the distillation column and its auxiliary equipment replaces -TCl- The annual utility cost replaces the total annual production cost. 

In Example 17.15, approximate profitability measures, when applied to the MCB plant, are not favorable. However, one of the chemicals produced, MCB, is given a selling price of 0.52/lb, which is not well established by current competition. 

Solving this equation, x = selling price of MCB = 0.537/lb, which is slightly higher than the price of 0.52. Clearly, the ROI is very sensitive to the selling price of MCB. 

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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. 

Ref 91. Discounted cash-flow models account for use of capital, working capital, income taxes, time value of money, and operating expenses. Real after-tax return assumed to be 12.0%. Short-rotation model used for sycamore and poplar. Herbaceous model used for other species. Costs ia 1990 dollars. Dry tons. 

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... 

Time Value of Money A large part of business activity is based on money that can be loaned or Borrowed. When money is loaned, there is always a risk that it may not be returned. A sum of money called interest is the inducement offered to make the risk acceptable. When money is borrowed, interest is paid for the use of the money over a period of time. Conversely, when money is loaned, interest is received. 

Once the bids are tabulated for specification compliance in the form of a chart for easy review by all others involved in the project, an overall evaluation should be made, factoring in energy cost, first cost, and time value of money using an established economic equation. Most companies have a standardized formula. If the data are available, total cost of ownership can be estimated, which for larger equipment is considered a good measure for evaluation. 

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. 

Discounted cash flow (time value of money)... 

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. 

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. 

Various other evaluation schemes based on the concept of time value of money are also sometimes used. These, together with the Net Present Value and Rate of Return methods, are all grouped together under the title of discounted cash flow methods. 

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. 

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). 

Time value of money from sold products. 

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. 

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