PROFITABILITY MEASURES - C&EN Global Enterprise (ACS

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PROfITABILITY MEASURES Return on original investment? Return on average investment? Payout time?

Which can help the decision most?

Payout time including interest?

Present worth? Interest rate of return? 94

C & ENS E PT. 25, 1961

A major objective of any manufacturing company is to provide the greatest possible long-term profit to its stockholders. This requires that its assets be used wisely and that they be increased in dollar value at the highest possible rate. The series of decisions made by management largely determines the profits realized by the corporation. Decisions, of course, vary greatly in -importance. But they also vary in the degree to which they commit the firm to future action and to future payment of costs. Choosing a man to serve in top management is extremely important, but the choice can be withdrawn with a great deal of speed if necessary. Investing in fixed facilities, on the other hand, involves long-term commitments. Here, a positive decision implies assuming the burden of continuing depreciation and other costs for a period of years. Moreover, it limits the fluidity of the company's action greatly, should a major technological advance make the company's facilities obsolete. For these reasons, capital investment decisions must be made with great care. Nothing is more important than a series of successful capital investments in establishing a record as a profitable growth company. Profita bility is not the whole story. An informed decision on new capital expenditures requires consideration of many other factors as well. Every project has intangibles associated with it that must be considered carefully. Its size relative to the company as a whole is important, and so is the availability of funds. Integration of the proposed product with the company's existing products and with the com-

They help in capital investment decisions. But tougher competition leads to tougher decisions, and tougher decisions call for finer measuring tools. Here are six of them compared.

JAMES B. WEAVER, Atlas Chemical Industries, Inc. pany's long-term objectives should be studied. The expected growth rate in the new product's market is also important. Furthermore, the availability of company personnel to take part in the proposed program must be taken into account. The investment's profitability is considered against a total background of many factors, including these. It is generally agreed, however, that profitability is one of the very important factors—and it is the only one to be discussed in this presentation. I intend to discuss various measures available for calculating profitability and to compare them with a nonexistent ideal profitability measure. Many forecasts concerning future investments, profits, etc., resulting from a capital outlay can be expressed in numbers, and the ideal profitability measure would include everything that can be quantified. The decision maker's problem is made easier by expressing all those forecasts as simply as possible. By reducing a myriad of numbers to a few simple indicators, it permits management to focus attention on the many intangibles also involved. No profitability measure is ideal. Attempts are still being made to in-

corporate additional quantitative information into available measures so as to assist in making the decision. Particularly is this true of certain elements of risk. At present, all measures merely include forecasts on a "best estimate" basis, although they can be supplemented by some indication of the answer's sensitivity to variations from best forecasts of the major factors. But I am ahead of my story. First let us review the steps in weighing a capital expenditure, as well as the future influences impinging on all capital investments. Three Evaluation

Stages

Evaluation of capital investment can be said to pass through three stages: • One must decide what factors or future influences will essentially determine each capital investment's profitability. The number of important factors is greater than usually believed. • One must obtain forecasts of these factors over the expected life of the product or equipment. In many cases, forecasts must be made of the situation not only where the company un-

dertakes the investment, but also if the investment is not made. The new investment should only be credited with the difference in profit. • A method must be at hand for combining these forecasts into a single understandable measure of profitability. This third phase is the only subject under detailed discussion here. Before leaving the factors that influence profitability, however, a couple of additional points should be made. These factors will influence the investment's future, whether or not detailed forecasts are made. Without the forecasts, some unrecognized assumptions must be replacing a conscious attempt to foresee the future. Forecasting is not easy; and naturally, the over-all forecast of profitability cannot be achieved if the errors in the individual forecasts are significant. Nevertheless, it seems useful to make conscious assumptions rather than unconscious ones. The other point concerns the importance of time in most factors to be considered. The investments are usually made largely in the near future, so that time is not so critical. Sales and other factors determining income, however, are subject to considerable change over the investment's operating life. The timing of such changes is critical. Four elements that deal SEPT. 2 5,

1961 C&EN

95

These influences determine the profitability of the company's investment Possible Accuracy of Forecast Installed Cost of Fixed Investment

good

Working Capital

fair

Usual Effect of Possible Error

major

Construction Period

good

minor

Initial Startup Expense

fair

intermediate

Sales Volume Forecast

poor

major

Product Price Forecast

poor

major

Cost Stream over the Project Life

good(direct) fair(overheads)

major

Economic Life

poor

intermediate

Depreciation Life

good

intermediate

Salvage Value

poor

minor

Depreciation Method

*

intermediate

Minimum Acceptable Rate of Return

*

*

Income Tax Rate

poor

major

Inflation Rates

poor

major

Risk

poor

major

General Business Conditions

fair

intermediate

* Policy choices, not forecasts.

primarily with timing are construction period, depreciation life, economic life, and depreciation method. Obviously, a company will benefit more quickly from a project with a shorter construction period. The project's economic life likewise determines how long the profits will continue coming in, while the depreciation life and method determine certain tax allowances and their timing. It is apparent that the ideal profitability measure cannot be limited to consideration of total dollars. There must be a method of incorporating differences in the timing of receipt and expenditure of cash. First let us establish a concept of what to maximize—what we want the most of—in combining the forecasts. Why Return on Investment? Profit maximization alone is not enough. The true goal is to improve the "efficiency" of profit production from a dollar of investment in an enterprise or manufacturing facility. The efficiency ratio relating profits to in96

C&EN

S E P T . 25, 1961

vestments is known as "rate of return on investment," and unquestionably this is the proper sort of relationship for studying the economic success of an enterprise. The main question asked by any stockholder or investor is, "How much profit can I get per dollar of investment?" Indeed, the goal should not be to maximize the return on investment as a ratio. The ideal is to maximize the profits that return more to the investor than the cost of the money he is required to invest. "Return on sales"—the ratio of profit to sales—is often shown as if it were an important measure. On reflection, it should be obvious that it cannot be used to measure economic performance: a very high ratio would not be good if very high investment is needed to get the profit. Needless to say, much ambiguity in terms is apparent in the field. The return-on-investment measures to be discussed give answers that vary from each other by as much as two to one. It is not surprising, then, that profitability criteria that seem unattainable

appear in the literature. This is particularly so since return on investment can be reported either before or after taxes. Therefore, the statement in a news magazine that a company accepts nothing less than 40% return on investment might indicate merely that the company calculates return on average investment before taxes. A similar calculation by return on original investment after taxes would show a return of about 10%. In this article I shall discuss, within the text and in tabular form, six of the most popular methods for calculating return on investment: return on original investment, return on average investment, pay-out time, pay-out time including interest, present worth, and interest rate of return. With regard to the table, the essential elements for comparing these on a consistent basis are their abilities to handle completely the investment, the income, and the capital recoveries of the venture. Furthermore, the factors must be covered as to timing as well as to amount—cash is more useful to the company the sooner and the longer it is available. The tabular comparison, based as it is on usual practice, indicates that certain of the factors are "not considered," although there is no technical reason why they couldn't be used. In other cases the formula under discussion simply could not be altered easily to handle a given factor, and this I have indicated where appropriate. Ease of Cahufotions

Varies

The ease of calculating return on investment by the several methods varies quite a bit. The easiest can be done with a slide rule or a scrap of paper. The hardest takes perhaps five minutes at most for the complete calculation, so the difference in the actual arithmetic is not great. The most important differences among the methods concern their abilities to handle the key factors essential to the investment decision. The calculation itself is not a significant part of the expense involved. Once you are convinced that the more sophisticated methods require information that is useful to the decision, it will not take long to learn to use any of the methods I am about to discuss.

Return on Original Investment. Since this calculation is merely a ratio of annual profits to the original invest-

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JEFFERSON CHEMICALS C & Ε Ν 97

Cash position charts show the realities A cumulative cash position chart can be used in profitability analysis to portray the realities of an investment. At any given time, it shows the project's cumulative cash effect on the company. With the help of the charts shown here, the fundamental concepts are presented. The upper chart includes most of the complexities of a normal project, except that equal annual profits and straight line depreciation are assumed for illustrative purposes. The first investment shown is that which has been made in land at a single point before time zero. This is followed by a gradual increase of fixed investment during construction. Working capital is shown as being added instantaneously at time zero— this is an approximation. Equal annual profits are assumed to start at time zero, bringing the cumulative cash position line upward at a constant slope throughout the life of the project. All of these elements can be clearly seen on the chart, and so can the construction period and economic life of the project. The value of the investment remaining on the company's accounting books can also be approximated (dash line). The introduction of compound interest increases the complexity of the chart. In order to keep the illustration as simple as possible, we will omit complicating factors such as construction period, working capital, salvage value, etc. (lower chart). The "obligation," which we defined as the changing sum that is brought about by continually adding the accumulated interest to the principal, is indicated by the dash line. Investment is increased regularly by interest on the one hand and, on the other hand, it is decreased by cash income in each time period to calculate the obligation that is shown. The lower dash line in the chart shows this obligation at the interest rate that will maintain some obligation throughout the life of the project, with the effect of reducing it to zero just at the end of the estimated economic life. The zero cash position occurs, then, at a point after the recovery of any working capital and of 98

C&EN SEPT. 2 5, 1961

any land or salvage value. This com­ pound interest is what we refer to as the interest rate of return, the interest rate paid by the project to the com­ pany for the use of company funds. All profits have been converted so as to be expressed as this interest rate. At the end of the project, the obliga­ tion of the project to the company, which has continued to be some real obligation throughout the project life, has been completely repaid. The dotted line indicates another reality of the calculation of future or terminal worth, equivalent to present worth. The procedure of discounting has been applied to the cash flows, but the discounting is not enough to reduce the total profit to zero at the end of the economic life of the proj­ ect. Rather than that, the discount rate is merely representative of the cost of capital (or minimum accept­ able rate of return) that must be earned before a project is considered worthy of further action. A project that did earn an interest rate of re­ turn that was equal to the cost of capital would show no profit after dis­ counting, and it would resemble the dash line. For projects earning more than the cost of capital, the profit line would still cross the zero cash position line as it does before the dis­ counting procedure. Except for the possibility of the recovery of land and working capital, this point in time corresponds to the payout time in­ cluding interest, which is one of the profitability methods shown in the comparative table. Applying interest rates in the posi­ tive-cash-position area is no longer a discounting procedure. The amount made available by this project after it has earned the cost of capital is as­ sumed to be invested in other projects at the cost of capital. The profits are compounded as in the illustration, so that the terminal cash position, after applying the cost of capital, may be greater than the final cash position before discounting if the project's economic life is long enough. The dot-dash line shows the relationship between this terminal worth and present worth discounted at the cost of capital.

ment, it can be done with great ease. I£ profits differ in different years, the return can be calculated for several significant years during the life of the investment. It can also be figured as the average for the investment's en­ tire economic life. The only problems encountered may be those introduced by fixed- or work­ ing-capital investments that are made after the time of original investment. It is not then clear whether calcula­ tions should be based on original or on total investment.

Return on Average Investment. This calculation is much like the one for return on original investment. Only the denominator is* different. One meets the same limitations and compli­ cations. Introducing accelerated de­ preciation brings an added complica­ tion into the calculation. The book investment reduces more rapidly when accelerated depreciation is used, and the "average investment" can no longer be assumed to be working capital plus one half the fixed investment. Pay-out Time. This is figured by a year-by-year cumulation of the sum of profits plus depreciation for the proj­ ect's initial years. The intent is to find out during which year the total of profits and depreciation surpasses the amount of original depreciable in­ vestment. A pay-out including a frac­ tional year—e.g. 3τ/2 years—can be calculated by indicating the point dur­ ing the year at which the profits and depreciation completely offset depreci­ able investment. Payout Time Including Interest. The calculation for this measure is very similar to the one for pay-out time. It differs in that profits are reduced by discounting those not gained until later years, using an appropriate in­ terest rate that has been chosen as the minimum acceptable rate of return. This reflects the time-value of money. It tends to increase the pay-out time, to represent the earning of the mini­ mum rate of return, and the measure reflects a real benefit for projects that earn most of their profits early in their lives. Continuous interest tables, which show present value factors for determining zero-time values for cash flows occurring at other than zero time, are valuable in using this method. Present Worth. Continuous interest tables are also used in the present

worth method. Present value factors in the tables are used to compound or discount all cash flows to their equiv­ alent value at time zero. Time zero can be chosen arbitrarily, but the start of operations is usually used. Since, for this method, the minimum ac­ ceptable rate of return is known in advance, multipliers for incomes or investments occurring at other than time zero can be taken directly from the table. One usually sums all cash incomes separately from all cash outlays, using discounted values, to show both sums as of time zero. Present worth is the excess of the present value of incomes over the present value of investments. It is usually shown as the difference between the two, but it can also be shown as a ratio. Interest Rate of Return. A trial and error solution is required to calculate interest rate of return, since no dis­ counting rate is available before the calculation. The cash flows are set forth before discounting, in columns showing all cash flows, much as in the present worth method. These cover the period from the start of construc­ tion to the recovery of land and work­ ing capital after the project is shut down. Discount rates are then ap­ plied to get the closest approximation to the whole percentage point which makes the present value of earnings equal to the present value of invest­ ments when it is used as the actual discounting rate. Note that the interest rate of return is earned neither on the original nor on the total amount of investment. In Text continued on page 102 (Comparison table on next page)

SUGGESTED READING Bierman, H., and Smidt, S., "The Capital Budgeting Decision," Macmillan, New York (1960). Gregory, J. C , "Interest Tables for De­ termining Rate of Return," Phila­ delphia, Penna., The Atlantic Refining Co. (1946). Ind. Eng. Chem., Monthly "Costs" fea­ ture, 1958 to date. Swalm, R. O., The Engineering Econo­ mist, 5, 45+ (Fall, 1959); 57+ (Winter, 1960); 77+ (Spring, 1960). Interest tables. Weaver, J. B., Ind. Eng. Chem., 50, 43A (March, 1958). Factors influencing investment. Weaver, J. B., and Reilly, R. J., Chem. Eng. Progr., 52, 405-12 (Correction 448), (1956). Use of interest tables. SEPT. 25, 1961 C&EN

99

Profitability measures have different capabilities Return on Original Investment

Name of Method

Return on Average Investment

Payout Time

Other Titles

Engineer's method, du Pont method, operator's method, and capitalized earning rate.

Return on book investment, accountant's method.

Pay-off period (time), cash recovery period, pay-back period (time), payout period.

Statement of Intent

A

A

Years required to recover original de­ preciable investment from profits and depreciation accruals.

Algebraic Description

Average yearly profit during earning life only Original fixed investment + working capital

percentage comparison of average annual profits over the earning life to the initial total fixed and working capital investment.

percentage comparison of average annual profits over the earning life to the average book investment including working capital.

Average yearly profit during earning

X100

Jifeonly

χ

m

Average fixed investment - f working capital

Original depreciable fixed investment Profit + yearly average depreci ation over the period

X100

Geometric Description

Avg. annual profit, earning life

Avg. annual profit, earning life

„ J Avg. investment X Book investment

y Recovery value ^ of fixed plus working capital

Handling of Investment Amount

Considers total amount.

Considers a definite fraction of original investment; fraction depends on de­ preciation method.

Considers depreciable investment only.

Handling of Investment Timing

Cannot consider construction period or later fixed or working capital invest­ ments.

Cannot consider construction period or later fixed or working capital invest­ ments.

Cannot consider land or working capital or any investments beyond payout period; could, but usually does not consider construction period.

Handling of Income

Considers average of income over earning life only. Cannot consider yearly differ­ ences; can be calculated for various fractions of capacity, or for various in­ dividual years, to show effect of operat­ ing level.

Considers average of income over earning life only. Cannot consider yearly differ­ ences; can be calculated for various fractions of capacity, or for various in­ dividual years, to show effect of operat­ ing level.

Considers income only up to end of pay­ out time.

Handling of Income Timing

Not considered; could not be utilized.

Not considered; could not be utilized.

Properly considered in early years; can­ not consider at all from then on.

Handling of Capital Recovery Amount

Not considered; could not be utilized.

Not considered except depreciation in­ directly as establishing investment base.

Properly considered for early years; can­ not consider later or terminal recoveries.

Handling of Capital Recovery Timing

Not considered; could not be utilized.

Not considered; could not be utilized.

Properly considered up to the end of the payout time; not afterward.

Handling of Other Elements

Often used either before or after income tax. Cannot consider economic life. Result must be compared with minimum acceptable rate of return on the same basis.

Often used either before or after income tax. Cannot consider economic life. Result must be compared with minimum acceptable rate of return on the same basis.

Taxes properly considered. Cannot consider economic life beyond payout time. Result must be compared with a maximum acceptable payout time.

Variants of System

Major variants in common use include calculation before and after income tax, with and without working capital. Martin adds depreciation to profits to give a ratio of cash generation to invest­ ment which is equivalent to the re­ ciprocal of payout time.

Major variants in common use include calculation before and after income tax, with and without working capital. Average book investment is different with sum of the years-digits deprecia­ tion, but many consider return on average investment should be calculated on one-half the initial fixed investment independent of depreciation method.

In some cases, depreciation is not added to profits so that this is essentially the reciprocal of return on original invest­ ment. Although working capital is assumed to be always recoverable and so is not usually included in the invest­ ment base for payout time, it is not really recoverable until the project is shut down. Therefore, in some cases, a cash recovery period may be called for which includes the restoration of work­ ing capital and land investments made by the company.

Major Shortcomings of System

Cannot consider timing of cash flows. Averaging of profits permits laxity in forecasting. Does not consider capital recoveries.

Cannot consider timing of cash flows. Averaging of profits permits laxity in forecasting. Does not consider capital recoveries.

Ignores later years of project on all counts. Cannot consider investments in working capital or land.

References for Further

Aries, R. S., Newton, R. D., "Chemical Engineering Cost Estimation," McGrawHill, New York, 1955. Chem. Eng. News, 33, 3676-9 (Sept. 5, 1955).

Stiles, K.. J. Accountancy, [102, 37-9 (Sept., 1956). Moller, G., Controller, 26, 107 (March,

Yanagisawa, E., Chem. Eng., 62, 185-6 (January, 1955). Aries, R. S., Newton, R. D., "Chemical Engineering Cost Estimation," McGrawHill, New York, 1955.

100

C&EN

SEPT.

2 5,

1961

1958).

Name of Method

Payout Time, Including Interest

Present Worth

Interest Rate of Return

OtherTitles

Cash recovery period.

Venture worth, incremental present worth.

Profitability index, discounted cash flow, internal rate of return, investor's method.

Statement of Intent

Years to recover original depreciable in­ vestment and a minimum acceptable rate of return from profit plus deprecia­ tion accruals.

Comparison, by difference or ratio, of the (discounted) present value of all cash flows to the project with all investments in the project.

Calculates the interest rate at which the company's outstanding investment is repaid by proceeds from the project— the maximum rate at which callable preferred stock could be issued for financing the investment in the proposed project and have it paid off in full at the end of the project's expected life.

Algebraic Description

Original depreciable fixed investment + interest* X100 Profit + yearly average de­ preciation over the period

Present worth of project earnings — (original fixed investment + working capital)

Average yearly profit during construction and earning life Average fixed investment + working capital - f interest*

X100

Geometric Description

"jt"Avg. obligation Recovery of land ^ v and working capital Investment with cost of capital

** Investment \ & proceeds with cost of capital

"^—"Obligation"; investment with interest rate of return

Handling of Investment Amount

Considers depreciable investment only.

Considers all investment amounts.

Considers all investment amounts.

Handling of Investment Timing

Cannot consider land or working capital or any investments beyond period; could, but usually does not, consider construction period.

Properly considered, including construc­ tion period and working capital.

Properly considered, including construc­ tion period and working capital.

Handling of Income Amount

Properly considered up to end of calculated period; cannot consider later income.

Properly considered.

Properly considered.

Handling of Income Timing

Properly considers up to end of calculated period ; cannot consider later.

Properly considered.

Properly considered.

Handling of Capital Recovery Amount

Properly considered up to end of calculated period; cannot consider later or. terminal recoveries.

Properly considered.

Properly considered.

Handling of Capital Recovery Timing

Properly considered up to end of calculated period; cannot consider later or terminal recoveries.

Properly considered.

Properly considered.

Handling of Other Elements

Taxes properly considered. Cannot con­ sider full economic life, but may be use­ ful for comparison with economic life since minimum acceptable rate of re­ turn has already been earned. Requires determination of minimum acceptable rate of return before calculation.

Taxes properly considered. Considers total economic life. Requires deter­ mination of minimum acceptable rate of return on the same basis before calcula­ tion.

Taxes properly considered. Considers total economic life. Must be compared against minimum acceptable rate of return on the same basis.

Variants of System

Cost of capital may be substituted for minimum acceptable rate of return as discounting rate.

Cost of capital may be substituted for minimum acceptable rate of return as a discounting interest rate. Present worth is usual y expressed as the difference remaining when present value of invest­ ments is subtracted from the present value of all cash generations. Ratio of cash flow to investment is also suggested as a criterion. The combination can give some idea of the total magnitude of the project.

Present worth is itself considered a variant of this system by some. System as described by some does not include consideration of land, working capital, construction period.

Major Shortcomings of System

Not as informative an answer as present worth, interest rate of return. Ranking with limited funds by this method would not maximize future worth of company. Cannot consider working capital or land.

Result does not indicate magnitude of project. Most generally suitable of systems presented. Choosing projects with highest present worth will maxi­ mize future worth of company if as­ sumptions hold.

Multiple answers can be obtained for certain unusual cash flow patterns. Does not properly compare projects of differing project lives. Does not indicate total magnitude of project. Adequate for evaluations not involving competi­ tion for funds.

References for Further Detail

Scheuble, P. Α., Harvard Business Re­ view, 33,81-94 (Sept.-Oct., 1955). Happel, J., Chem. Eng. 58, 146-8 (Oct., 1951).

Happel, J., Chem. Eng. Progr., 51, 533-9 (December, 1955). Winn, F. W., Petroleum Refiner, 35, 199-

Weaver, J. B., and Reilly, R. J., Chem. Eng. Prog., 52, 405-12 (Correction 448) (1956). Dean, J., Harvard Business Review, 32, 120-130 (Jan.-Feb., 1954).

210 (July, 1956).

Interest charged on both fixed and working capital to reflect time value of money. SEPT.

2 5, 1 9 6 1 C & E N

101

Continued from page 99 efiFect, the discounting procedure alters the principal invested in the project by the amount of interest. Interest accumulated over each compounding period is added to the principal that existed at the start of that period to obtain the new principal for the following period. The term "obligation" has been used frequently to refer to this changing sum and avoid confusion with the original principal sum.

Obligation denotes the total indebtedness of the project to the investor, including all capital outlays and accrued interest at a given time. Cumulative Cash Position A chart of cumulative cash position is an excellent tool for associating the realities of an investment's status relative to the company with the various mathematical models for estimating its

profitability. As the name implies, it also shows the cumulative cash efiFect of the project on the company. This chart uses time as the horizontal scale and cash position as the vertical scale. Zero on the ordinate scale is the line of zero cash position, indicating a balance of funds between the company and the project, no investment and no profit. Points in the "negative cash position" area, below the zero line, indicate investment by

Continuous interest tables* give more realistic picture to task position (Factors for determining zero-time values for cash flows which occur at other than zero time.) Compounding of Cash Flows which Occur: A. In an Instant V2 year before 1 " " 17s" " 2 " " 3 " " B. Uniformly until Zero Time From y 2 year before to 0 time 11

11 it

1

"

" "" "

lVi "

"

" " "

O

it

U

11 It

« q

"

"

" " «

11

1%

5%

10%

1.005 1.010 1.015 1.020 1.030

1.025 1.051 1.078 1.105 1.162

1.051 1.105 1.162 1.221 1.350

1.002 1.013 1.025 1.005 1.025 1.052 1.008 1.038 1.079 1.010 1.052 1.107 1.015 1.079 1.166

90% 100%

80%

35%

40%

50%

60%

70%

80%

1.078 1.105 1.133 1.162 1.221 1.284 1.252 1.350 1.455 1.350 1.492 1.649 1.568 1.822 2.117

1.162' 1.350 1.568 1.822 2.460

1.191 1.221 1.419 1.492 1.690 1.822 2.014 2.226 2.858 3.320

1.284 1.649 2.117 2.718 4.482

1.350 1.822 2.460 3.320 6.050

1.419 2.014 2.858 4.055 8.166

1 .492 2 .226 3 .320 4 .953 11 .023

1.568 2.460 3.857 6.050 14.880

1.649 2.718 4.482 7.389 20.086

1.038 1.052 1.065 1.079 1.107 1.136 1.121 1.166 1.213 1.166 1.230 1.297 1.263 1.370 1.489

1.079 1.093 1.107 1.166 1.197 1.230 1.263 1.315 1.370 1.370 1.448 1.532 1.622 1.769 1.933

1.136 1.166 1.197 1.297 1.370 1.448 1.489 1.622 1.769 1.718 1.933 2.182 2.321 2.805 3.412

1 .230 1 .532 1 933 2 471 4 176

1.263 1.622 2.117 2.805 5.141

1.297 1.718 2.321 3.194 6.362

.497 .247 .122 .061 .030 .001

449 202 091 041 018

.407 .165 .067 .027 .011

.368 .135 .050 .018 .007

...

..

... ...

...

.659 .268 .109 .044 .018 .007 .003 .001

.632 .232 .086 .032 .012 .004 .002 .001

15%

20%

25%

Discounting of Cash Flows which Occur: . C. In an Instant 1 year later

.951 .905 .861 .819 .779 .606 .472 .368 .286

.905 .819 .741 .670 .606 .368 .223 .135 .082

.861 .741 .638 .549 .472 .223 .105 .050 .024

.819 .670 .549 .449 .368 .135 .050 .018 .007

.779 .606 .472 .368 .286 .082 .024 .007 .002

.741 .549 .407 .301 .223 .050 .011 .002 .001

.705 .497 .350 .247 .174 .030 .005 .001

.670 .449 .301 .202 .135 .018 .002

...

...

D. Uniformly over Individual Years 1st year 2nd " 3rd " 4th " 5th " 6th " 7th " 8th " 9th " 10th "

.995 .985 .975 .966 .956 .946 .937 .928 .918 .909

.975 .928 .883 .840 .799 .760 .723 .687 .654 .622

.952 .861 .779 .705 .638 .577 .522 .473 .428 .387

.929 .799 .688 .592 .510 .439 .378 .325 .280 .241

.906 .742 .608 .497 .407 .333 .273 .224 .183 .150

.885 .689 .537 .418 .326 .254 .197 .154 .120 .093

.864 .640 .474 .351 .260 .193 .143 .106 .078 .058

.844 .595 .419 .295 .208 .147 .103 .073 .051 .036

E. Uniformly over 5 Year Periods 1st five years 6th thru 10th year 11th thru 15th year 16th thru 20th year 21st thru 25th year

.975 .928 .883 .840 .799

.885 .689 .537 .418 .326

.787 .477 .290 .176 .106

.704 .332 .157 .074 .035

.632 .232 .086 .032 .012

.571 .164 .047 .013 .004

.518 .116 .026 .006 .001

F. Declining to Nothing at Constant Rate 1st 5 years .983 11 .968 10 " 11 .952 15 " 11 20 " .936 11 .922 25 "

.922 .852 .791 .736 .687

.852 .736 .643 .568 .506

.791 .643 .536 .456 .394

.736 .568 .456 .377 .320

.687 .506 .394 .320 .269

.643 .456 .347 .278

CNJ

.990 .980 .970 .961 .951 .905 .861 .819 .779

3 4 5 10 15 20 25

" « " " " " "

* Condensed

102

" « " " " " "

from tables compiled

C&EN

SEPT.

2 5,

by J. C . Greg*ory9 The Atlantic

1961

I .231

Refining

.606 .368 .223 .135 .082 .007 .001

.549 .301 .165 .091 .050 .002

...

...

.824 .552 .370 .248 .166 .112 .075 .050 .034 .022

.787 .477 .290 .176 .106 .065 .039 .024 .014 .009

.752 .413 .226 .124 .068 .037 .020 .011 .006 .003

.719 .357 .177 .088 .044 .022 .011 .005 .003 .001

688 309 139 062 028 013 006 002 001

.472 .082 .014 .002

.432 .058 .008 .001

.367 .030 .002

.317 .016 .001

.277 .008

245 004

.603 .413 .309 .245 .203

.568 .506 .377 1 .320 .278 .231 .219 .180 .180 1 .147

Co,

...

.. .220 .002

.199 .001

... ... .456 .278 .198 .153 .124

.413 .245 .172 .133

.108 1

.377 .219 .153 .117 .095

.347 .198 .137 .105 .085

.320 .180 .124 .095 .077

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SEPT. 25, 1961

the company in the project. Points of "positive cash position," above the zero line, indicate a profit position has been reached; i.e., no residual invest­ ment by the company in the project. Zero on the horizontal time scale is usually chosen as the start of produc­ tion. The zero cash position between the project and the company usually occurs somewhat before this time as investment in the project starts. The company's cumulative cash position relative to the project starts out as zero. A single line then shows the project's cumulative cash status at each time indicated throughout the con­ struction period and economic life. As investment occurs before time zero, the line slopes downward from the zero cash position toward increasing negative cash position. After income starts the investment of the company is gradually reduced to zero. ( Except for the effect of recoveries of land, working capital, etc., the crossing of the zero line represents payout time.) As profits continue to come in, a net profit has been realized over the life, and the slope continues upward into increasingly positive cash position. At the project's end, the recovery of land and working capital adds a final por­ tion of cash to establish the final cash position.

Conclusion Although the concept of return on investment is reasonably well accepted in the chemical industry, there is much less agreement on the method of cal­ culating return on investment. Those who first saw the importance of the general concept started fairly simple calculating procedures within their own companies. The companies have been eminently successful, using the simple measures such as return on original investment. Possibly because of their success, or because of some resistance to change and the difficulty of explaining the more sophisticated methods, many still use the very simple return on investment relationships for profitability evaluation. Other companies have converted recently to techniques that will con­ sider more of the essential variables in comparing alternatives. Perhaps this is a result of their desire to do still better than their already-success­ ful competitors. More likely, how­ ever, it has become clear to manage­ ment that the period of easy growth in the chemical industry may be be­

hind us. With hearty competition on all sides, there has naturally been a great increase in emphasis on cost and profitability estimation of all sorts. The general feeling is that better tech­ niques can lead to better decisions and enable a company to do better at charting a profitable future for itself. To make good decisions, we must not fail to consider all the significant vari­ ables.

James B. Weaver is director of Atlas Chemical Industries' development ap­ praisal depart­ ment, charged with the com­ pany's economic evaluation, long range forecasting, op­ erations research, and marketing re­ search. He received his B.S. and M.S. in chemical engineering from MIT in 1944 and 1947, respectively. He was associated with Godfrey L. Cabot, Inc. from 1945-50 as assistant to the director of research and development. This was followed by four years at Olin Industries, first as a technoeconomist and then as section chief of staff services for the company's re­ search department. In 1954 he joined Atlas Powder Co., and has held his present position since 1958. Mr. Weaver is author or coauthor of many publications and has been a contributing editor on "Costs" for In­ dustrial & Engineering Chemistry since 1958. Besides being a registered pro­ fessional engineer in Delaware and a member of ACS, he is a fellow in AIC and a member of AIChE, ASEE, AFS, AACE, and NSPE. He also be­ longs to Phi Gamma Delta, Alpha Chi Sigma, and Sigma XL

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