capital budgeting and optimal timing of investments in flexible manufacturing systems

Annals of Operations Research 3(1985)35-57 35

C A P I T A L B U D G E T I N G A N D O P T I M A L T I M I N G O F I N V E S T M E N T S

IN F L E X I B L E M A N U F A C T U R I N G S Y S T E M S

N. KULATILAKA

School of Management, Boston University, Boston, Massachusetts 02215, USA

and

Energy Laboratory, MIT, Cambridge, Massachusetts 02139, USA

A b s t r a c t

This paper investigates the financial-economic decision process for investments in flexible manufacturing systems (FMS). Contrary to popular belief, we show that conventional capital budgeting techniques can be used to make such investment decisions. First, we identify the overall impact of installing an FMS and present guidelines for a cash flow forecasting model. We then present ways in which to incorporate uncertainty in these cash flows within a risk-adjusted discount rate. These expected cash flows and the discount rate are used in calculating the net present value (NPV). Once the capital budgeting analysis is completed, a critical issue facing the fh-rn is the optimal timing of the installation. We reinterpret the general results on optimal timing of investments within the special context of an FMS project. Finally, we illustrate the above technique via a stylized example.

K e y w o r d s a n d p h r a s e s

Capital budgeting for FMS, optimal timing of investments, overall impact of FMS.

I n t r o d u c t i o n

Manufacturing industries in the U.S. and in other developed nations are rapidly

increasing the use of flexible manufacturing systems (FMS) in mid-volume, mid-variety

product ion applications. This macro phenomenon is driven by firm level decisions to replace existing conventional plant and equipment with FMSs and other advanced technologies. Although much at tent ion has been devoted to the engineering feasibility

and product ion management aspects of FMSs, very little has been focused on the financial and economic considerations. Nevertheless, a firm's decision to invest in an FMS remains an economic issue.

© J.C. Baltzer A.G., Scientific Publishing Company

36 N. Kulatilaka, Capital budgeting and optimal timing

The aims of this paper are twofold: (i) to modify the capital budgeting framework by incorporating special characteristics of the FMS, and (ii) to apply recent results in the financial economics literature to obtain the optimal time to invest in an FMS. Several previous papers in the industrial engineering literature have investigated the economic implications of advanced automation. Notable among these is the MAPI method and its variants which uses engineering data in evaluating the economic feasibility of manufacturing projects 1.* More recent studies by Boothroyd [3] and Hutchinson and Holland [4] have remained within the engineering costing framework in their more sophisticated economic analysis of advanced manufacturing systems.

All of this analysis fails to bring to bear important new developments in micro- economics and modern finance theory in analyzing the radically modified risk characteristics of FMSs. The industrial engineering literature is prevailent with the misconception that FMSs can not be evaluated using conventional capital budgeting methods such as the net present value (NPV) method 2. The basic argument in these studies stems from the fact that the introduction of an FMS in one point of a production process has far-reaching ramifications throughout the plant. It is true that in such cases a local cash flow analysis will give misleading results. In two recent studies, Kulatilaka [6,7] demonstrates how, with appropriate modifications, an overall NPV analysis will be suitable for evaluating FMS projects. In the present paper we further develop the above approach and apply it specifically to FMSs.

Perhaps the most important contribution of this paper is the treatment of the optimal investment timing problem. We follow theoretical developments by Mc- Donald and Siegel [9] and cast the timing of FMS installations as an option to postpone. We use a stylized example to study the value of this option under various scenarios.

The rest of this paper is organized as follows: In the next section we identify the costs and benefits from an FMS and provide the basic guidelines of a forecasting model which will translate the non-pecuniary effects into cash flow equivalents. Section 2 provides a risk analysis of the estimated cash flows. Section 3 makes a brief statement of the capital budgeting decision criterion based on the NPV. A justification of the NPV method is presented in an appendix which also provides a tutorial on different capital budgeting techniques. Section 4 provides a discussion of the investment timing issues. In sect. 5 we present a stylized example to illustrate the techniques discussed in this paper. Finally, we make some concluding remarks.

1. Cash f low fo recas t ing

The first step in any investment analysis is to identify and estimate the various present and future cash flows resulting from the proposed project. The difficulty of

*Footnotes numbered 1 - 17 axe listed at the end of the paper, preceding the references.

iV. Kulan'laka, Capital budgeting and optimal timing 37

estimating the indirect and non-pecuniary costs and benefit components o f the FMS

complicates this task. Here we identify the various effects and provide guidelines for

estimating these in terms of cash flow equivalents. Two important caveats need mentioning at the onset. First, since most applica-

tions o f FMSs compete with fixed or semi-flexible transfer lines, we use them as the reference alternatives. Table 1 provides a brief comparison o f the characteristics of a

transfer line and of an FMS. Incremental cash flows refer to increments over such

alternatives. Second, we measure all cash flows on a 'per unit t ime ' basis.

Table 1

Comparison of characteristics: FMS and transfer line

Attribute Transfer line FMS

Number of parts per system

Production per part type

Number of interconnected tools

Degree of specialization of each tool

Handling of material flows: - across tools

- into and out of tool

Supervisory control of: - material flows

- tool parameters

1 2 - 800

very high volume 15 - 15 000

several hundred 3 - 50

single purpose multipurpose

au t oma ted au tom ated fixed sequence variable sequence

automated automated

dedicated logic hierarchial control computer control

dedicated logic hierarchial control computer control

Source: Miller [ 10], table 4.1 and figs. 4.1 and 4.2.

1.1. IDENTIFYING THE OVERALL IMPACT

The initial purchase o f an FMS is more complex and use-specific than an investment in a conventional machine. Some firms prefer to purchase integrated

systems, while others might purchase various design blocks from different vendors and set up the system using in-house staff. In either case, the initial expenses will exceed the direct purchase cost due to interfacing, rearranging, rescheduling, and other modifications.


In addition, more subtle and invisible costs arising from the need to retrain existing labor, to reschedule other sections of the manufacturing plant, inventories, and sales divisions will further increase the initial outlay. In some cases, the product itself has to be redesigned to make it more readily processed by an FMS.

Significant cost savings, from replacing a conventional production system with an FMS, stem from a number of sources:

(1) The substitution of old vintage capital and labor with new vintage inputs such as computers, robots, and skilled technicians.

(2) Effects of increased 'reliability', reduced 'idle time', and reduced 'in- service time '.

(3) Increased quality and reduced reject rates. (4) Tax savings and other purely financial factors. (5) Long-term strategic considerations that would improve the competitive-

ness and bargaining power of the firm.

The expected cost savings due to some of these factors (e.g. new vintage capital) are easily quantified. The effects due to others (e.g. flexibility) are more subtle and harder to quantify. Tile approach suggested in this paper is such that we give not only a point estimate of the cost but also make an assessment of the variance around that expected cash flow. When performing the capital budgeting calculations, we can account for the differing risk characteristics via the discount rates.

The most dramatic effect of installing an FMS will be due to its flexibility. The added flexibility will produce many cost savings as well as some additional costs. The sources of these effects are listed below:

(1) Economies due to faster switching times between different batch tasks 3. (2) With its ability to reroute a part through different paths within the produc-

tion process, an FMS can be serviced without shutting down the entire plant. This capability will produce strikingly lower down times for the plant 4 .

(3) The increased reliability of an FMS helps schedule upstream and down- stream processes more efficiently.

The cash flows under a plant with FMSs will be affected due to differences in the mix of inputs used by the two systems. In a simple stylized depiction, an FMS substitutes labor and old vintage capital (conventional machines) with more sophisticated forms of capital (robots and computers) and with technically skilled labor. In cases where more than one production shift is used, the amount of displaced labor will be even more significant. The operating cost savings arising from the lowering payroll, overtime, and other employee benefits will therefore depend not only on the particular application, but also on the number of shifts s.

Another variable cost component affected by the new tectmology is energy. The net effect on the use of energy is ambiguous: FMSs will use more directly costed

N. Kulatilaka, Capital budgeting and optimal timing 39

energy than replaced workers. However, the new vintage technologies are likely to be more energy efficient than the older machines which they replace. Furthermore, reductions in heating and lighting needs of the FMS (when compared to humans) will reduce indirectly costed overheads.

The impact on material usage will result from (i) reduced reject rates due to quality improvements, and (ii) reduced waste from more precise instrumentation.

1.2. PURELY FINANCIAL EFFECTS

In addition, installing an FMS can bring about several purely financial cost savings. In the decision structure of the present-day corporation, the costing analysis made by production engineers will not include tax related considerations. These are viewed as duties of the finance and accounting departments. Unless tax effects due to the higher depreciation shields and investment tax credits are considered jointly with the engineering cost data, the decision process could produce misleading con- clusions.

1.3. ELEMENTS OF A CASH FLOW FORECASTING MODEL

Now that we have identified the sources of change that might be induced by the introduction of FMSs, we must project these future cash flows under the different technological alternatives. There are numerous ways to forecast future cash flows due to the installation of FMSs. All forecasts, however, must be based on information available at the time the decision is made.

The factors that affect future cash flows can be placed in several categories:

- Those due to general economic conditions that would affect the demand conditions for the product and the inputs in an entire industry.

- Those due to firm specific factors which will depend on the competitive- ness of the firm within the industry.

- Those due to production process specific factors that can be fairly ac- curately estimated using engineering cost data.

1.4. INCREMENTAL OPERATING REVENUE

When comparing an FMS to a conventional production system, we can bench- mark the level of output to some common reference point. Although the FMS increases throughput efficiency and quality, the demand for outputs is determined exogenously.

If a firm did, in fact, consider a capacity expansion, then the relevant comparison is one between FMSs and other alternatives where each has the new capacity. Hence, the incremental operating revenues will be independent of the type of technology. However, the added reliability and quality due to an FMS could improve the output demand by providing an edge over the competition.


1.5, INCREMENTAL DIRECT COSTS

The initial investment II for the conventional plant will be the sum of the purchase price PP, cost of redesigning the product RP, interfacing costs IF, labor retraining costs LR, and the net effect of rearranging and space saving RS 6. The corresponding values for the FMS will be denoted with a superscript *. (Throughout the rest of this paper we use a superscript * to represent the values under an FMS.)

If the reference alternative is the currently operating plant, then the net incremental investment is the above sum less the salvage value of the existing plant. If instead the reference alternative is some other non-FMS technology, then the relevant incremental investment is the sum of the incremental components:

AII = App + AIF + ALR + ARS, (1)

where A denotes the difference in values under the conventional and FMS technologies. For example, APP = PP - PP*. Many of these components are known with high levels of certainty. The purchase price and some of the redesigning costs can be contractually bound with long-term contracts with suppliers. The more use-specific items can be estimated using in-house experience, costing experts, and information from other plants which have installed similar FMSs.

Perhaps the most significant impact of an FMS is due to modified operating costs. These effects depend on the technology and on the price of inputs. We will denote the vector of input quantities under the reference alternative by Q, (Qi, i = 1, . . . ,n). In the above framework, an input i can also include in-process and input/output inventories. The corresponding vector for the FMS is denoted Q*. Both Q and Q* are determined primarily by the level of output and the technical specifica- tions of the production process. Although these values are time dependent, we omit the time argument for simplicity of notation except in places where explicit treatment of time is essential.

Information on the the mix of variable inputs can be obtained from guidelines provided by the FMS manufacturer and other in-house knowledge of the manufacturing process. We denote the technologies by transformation matrices q, qi, j, i = 1 . . . . ,n ; f = 1, . . . ,m , and q*, which represents the input levels needed to produce a unit vector of outputs 7. In other words qi./gives the quantity of input i needed to produce a unit of output f. Then the total utilization of input i, Qi = Zqi , /Y j , where Yi is the level of output f, If we denote input prices by Pt, i = 1 . . . . ,n, the variable input cost due to the i th input is VCi = QiPt. Similarly, the input i cost under the FMS is VC~ = * *. Qi P~

Some of these variable inputs will be purchased on contractual agreements and, thus, can be predicted with a high degree of precision. Others, however, may depend


on general levels of inflation and obtaining these requires independent estimates of future inflation. In these cases, forming expectations of uncertain future prices and outputs is no less or no more complex than with any other capital budgeting problem. The only added complication is that with an FMS the technology itself introduces uncertainty (i.e. qid values will be uncertain). However, as the technology becomes more widespread, the earlier systems can be used to learn about the technological properties. We will discuss the learning effects in our treatment of uncertainty in sect. 2.

We can write the incremental total operating costs (i.e. cost savings due to an FMS) at any future time during the life of the FMS as

v c = Z [vc; - v c 7 I.

1.6. PURELY FINANCIAL EFFECTS

The total operating profits will be taxed at the marginal corporate profit tax rate. Any increase in the cost of production will bring about a tax saving, while a cost saving will bring about a tax liability. The after-tax incremental operating cost saving is simply (1 - rc)AVC, where r c is the marginal corporate tax rate.

An increase in capital base also provides a corresponding increase in the depreciation tax shield. The exact amount of the tax shield will depend not only on the size of the investment, but also on the type of depreciation scheme being used 8. In general, the depreciation tax shield in year t for an initial investment AII is DTS t = ra, tAII , where ra, t is the depreciation rate at time t. The investment tax credit is trivially computed as ITC =riII , where r i is the rate of investment tax credit (currently 10%*). In some cases, major overhauling of FMSs can qualify as capital investment and, thus, contributes depreciation tax shields and further investment tax credits. Hence, the initial investment net of tax effects is £xIIr i + PV(DTS), where PV(DTS) is the present value of the depreciation tax shield.

2. Analys is o f u n c e r t a i n t y in cash f low p ro jec t ions

As with any capital budgeting problem, the key issue after identifying the expected cash flows is to arrive at a discount rate which properly reflects the risk associated with each cash flow. Intuitively, risky projects are, ceteris paribus, less desirable than safe ones and should demand higher rates of returns. Since different cash flows have different risk characteristics, it is imperative to carefully analyze these and to find ways to incorporate risk into the capital budgeting decision. Our discussion highlights the differences between:

- total risk which is reflected by the variance of the cash flows; - systematic risk which is, for example, measured by the 'beta' of the cash

flow.

*In the USA

42 iV. Kulatffaka, Capital budgeting and optimal timing

Project analysts often underestimate the importance of an accurate evaluation of the risk in the opportunity cost of capital. Using too low a discount rate results in accepting 'bad' projects. Conversely, too high a discount rate results in rejecting 'good' projects.

A development of modem finance theory, the capital asset pricing model (CAPM), provides a rigorous and an intuitively appealing way to quantify the risk return tradeoff. In an economy with well-developed capital markets, a publicly held firm need only be concerned with the systematic risk.

2.1. IMPACT ON VARIANCE OF PROJECTED CASH FLOWS: TOTAL RISK

Suppose that the cash flow projections for FMSs and a conventional technology give identical point estimates, but the cash flows under FMSs are less risky. How then should we account for this in our capital budgeting calculations? Our intuition suggets that, ceteris paribus, projects with higher levels of risk will be domi- nated by those with lower levels of risk. Therefore, when the projected cash flows have widely different risk characteristics, it is important to study the impact of the risk on the decision criterion. The confidence level of the decision will hinge critical- ly on the variance of this measure.

For example, consider the effect on cash flow due to the changed input mix and the resulting changes in substitution elasticities. The sensitivity of a firm's costs and revenues to factor price variablility will depend on the substitution elasticity between the various input prices. 9 Furthermore, the changed input mix will also affect the plant's ability to respond to (temporary) shortages of inputs. Since a temporary shut-down of an FMS-equipped plant incurs fewer costs than one that uses a conventional technology, installing an FMS will improve a plant's ability to react to volume variability. These effects can be modeled as reductions in the variance of forecasted cash flows.

The forecasting model suggested here will require independent estimates on the variance of the different cash flow components. Therefore, every cash flow estimate derived in the previous section will have a corresponding variance term. In practice, estimating these variances will be extremely difficult. However, as Jaikumar and Cooper [5] point out, the increased ability to monitor the performance of FMSs will be helpful in obtaining such information. Obviously, such data can only be available after several years of experience with a new technology. This also highlights the learning value of systems that are installed earlier on. Since cash flows enter the capital budgeting criterion in fairly complex and often nonlinear ways, we can use Monte Carlo simulations to evaluate the impact of uncertainty.

N. Kulat i laka, Capital budge t ing and op t ima l t iming 43

2.2. IMPACT ON COVARIANCE OF CASH FLOWS WITH GENERAL ECONOMIC CONDITIONS: SYSTEMATIC RISK

The systematic risk measures the component of total risk that is due to move- ments in general market conditions. In a well functioning capital market, the investors need only reward a firm for taking systematic risk. The unsystematic part (i.e. specific to the project) can be diversified via the portfolio decisions of individual investors.

Each cash flow component is associated with a level a systematic risk. For example, the depreciation tax shield will have nearly zero systematic risk. Some regulated inputs such as electric power will have very small levels of systematic risk. The prices of certain other production inputs (e.g. steel) can be highly correlated with general economic conditions and, thus, will have very high levels of systematic risk. Precise measures of systematic risk of the various cash flow components are unlikely to be feasible. In our illustrative example (see sect. 5), we use a constant, 5% risk premium to discount cash flows stemming from all input costs and a risk-free rate for evaluating the present value of the depreciation tax shield.

Although the above component-by-component analysis is theoretically elegant, it is rarely used in practice due to data limitations. Hence, the forecasted net cash flows are discounted at the firm's opportunity cost of capital. The most dramatic change in the firm's systematic risk profile stems from the increased operating leverage. The substitution of capital for labor raises the fixed costs as a fraction of total costs and thus the operating leverage. An application of the CAPM shows how the project's required rate of return is proportional to the ratio of present value of fixed costs to the present value of the project. The proportionality constant will be the ~ of the revenues. In equations we can express these relationships as follows:

~FMS = ~revenue [1 + PV(fixed costs)/PV(fms)] , (2)

where PV(. ) denotes the present value. The/3 of any asset i is given by

t3 i = 0(5) p ( r , r . ) l o ( r ) , (3)

where r i and r m denote the rates of return on the asset i and a well-diversified market portfoliol°; p ( r m , ri) is the correlation coefficient between r i and r m ; o ( r m ) and a(r i ) are the standard deviations o f r m and r i, respectively.

We can now rely on the CAPM to link the/3 with the risk-adjusted required rate of return:

rFM S = r F + /3FM s [ E ( r ) - r v ] , (4)


w h e r e r F is the rate of return on a risk-free asset such as a treasury bill. We stress two observations about rFM S :

(I) The ratio of present values of fixed costs to that of the FMS [second term in the square brackets in eq. (2)] will be quite high for a capital intensive project like an FMS. Therefore, the rate of return on such a project will be much higher than that of its revenues.

(2) The risk-adjusted discount rate depends on the variance of the cash flows o~. Hence, if FMSs reduce the variance of the cash flows (without reducing the expected cash flows), then they will also reduce the discount rate.

3. The capi ta l b u d g e t i n g rule

Information derived in the above analysis forms the inputs for the capital budgeting decision rule. Among the many alternative investment decision rules, we restrict this discussion to the NPV method. A detailed description of the various altemative methods, their relative merits and drawbacks, and a justification of the NPV method are given in the appendix.

The incremental NPV of the project (compared to the reference alternative) can be expressed in the most general terms as

ANPV = QitPit(1 + 5) -t = i = 1

- AII(1 - 5 ) + PV(DTS)] ,

-Q;eT(1 +,.*r (1-0

(5)

where

r. = discount rate for the i th cash flow t

P/t = the vector of input prices at time t

Qit = the vector of input quantities at time t

T = the economic life of the project

N = number of input categories

r e = marginalcorporate tax rate

r. = investment tax credit l

PV(DTS) = present value of the depreciation tax shield.

All values with a superscript * correspond to the FMS case.

N. KulatT"laka, Capital budgeting and opt imal t iming 45

4. O p t i m a l t iming o f i n v e s t m e n t s

The analysis thus far asserted that an investment should be undertaken if the NPV is greater than zero. This is true when choosing between mutually dependent projects. However, when choosing between mutually exclusive alternatives, one must choose the project with the highest NPV. A particularly interesting case of mutually exclusive projects is that of investing in the 'same' project at different points in time. This is the investment timing problem.

In order to gain insight, let us suppose that the capital budget works out favorably (i.e. positive NPV). If we ignore timing effects, then the firm should under- take the investment in an FMS immediately. However, since the firm can always postpone the installation, the correct decision must compare the value of investing today with the present value of the option of investing at all possible future times. Although this point has long been acknowledged in investment models, none have dealt with an explicit solution. In a recent paper, McDonald and Siegel [9] attack this problem using option pricing models of modern finance theory.

Here we look more closely at the investment timing problem within the FMS setting and interpret the implications of the McDonald-Siegel results. At any time t, when the firm is considering an FMS investment, it can pay a known cost I t and install the technology. The present value of the cash flows from undertaking this project at time t is V r V t is based on information available at time t using the forecasting and discounting procedures described above.

If the firm accepts the project at time t, then it foregoes the option to postpone, incurs the cost I t and receives the present value V t. If the firm decides to postpone the investment, then it foregoes the cash flows it would have received from the project but retains the option to invest at some future date. Depending upon the evolution of the economy and technological developments, the project can become more or less attractive in the future. The postponement decision is motivated by the possibility of an improvement in future cash flows or a reduction in costs.

The solution to this problem is derived from noticing its analogy to a call option on a dividend-paying stock. The maturity of the option is the time at which the investment opportunity expires. If the option to invest lasts a very long time, then it can be treated as an infinitely lived option. Since the net cash flows are the dividends earned by owning the underlying asset, which in this case is the project itself, the foregone benefits from postponement are analogous to foregone dividends. As with a call option on a stock, the option of waiting to invest gives the firm down- side protection while allowing for full play on the upside swing.

At any time t, the values for I s and Vs, where s > t, are not known with certainty. In a rapidly changing industry as the vending of FMSs, the price and the technological capabilities will also be changing. We can represent the inter-temporal evolution of the purchase price I t by a stochastic process:

46 N. Kulati laka, Capital budge t ing and o p t i m a l t iming

d I / I = a I d t + a i d z I , (6)

where a I and a I are the growth rate and standard deviation of I, and z I is a standard Wiener process with zero expected value.

The present value of future cash flows V t can also be modeled as a similar stochastic process. However, technological breakthroughs or some other firm specific event can make this project infeasible at some random time in the future. In other words, we allow for the possibility that the present value of net future cash flows can drop to zero at once. Under such assumptions we can write the continuous time stochastic process for V t as

d V / V = a v d t + a v dz v + d q , (7)

where dq = - I with probability X dt, and dq - 0 with probability 1 - X dt. The Poisson process dq, with parameter X, presents an absorbing barrier to the geometric Brownian motion process and, thus, stops the V t process when the Poisson event o c c u r S .

Under these assumptions for stochastic processes of V and I, the firm's problem is to find an optimal boundary where the investment will be undertaken upon the first passage of V t across this boundary. Suppose the investment opportunity expires at T. If the project has not already been undertaken at T, then it is optimal to do so

"It if V T > I T . This defines the terminal point of the boundary, C r = I r . McDonald- Siegel use stochastic dynamic programming to solve, backwardly, for C* such that if the investment is still not undertaken at t, then it will be optimal to do so if V t > C t .

The gist of this result is that the investment criterion now becomes:

- If V t > I t + 'option value of waiting to invest then invest at time t'. - If the inequality is reversed then it is optimal to wait.

The firm will be willing to invest at V t = I t only if o v = 0 or a v tends to negative infinity. For very reasonable parameter values, a v = 0, r = a~. = 0.02, the value of waiting to invest becomes equal to the cost of investment I t. Even if V is expected to decline at 25% per year, a t = -0 .25 , it can be optimal to defer investments until V exceeds /by as much as 20%.

Closed form solutions for the option value can be obtained only in the case of infinitely lived option. For finite maturities, the option has to be solved numerically by discretizing the continuous time differential equations. The results for the finite time problem are similar to the infinite life case, but the option value is somewhat smaller than under infinite maturity 11

We now turn to the sensitivity of the waiting option to changes on model parameters. Perhaps the most interesting comparative static is that with respect to


variance. McDonald-Siegel show that a partial derivative of the option value with respect to variance is positive; thus, an increase in variance, holding V fixed, will raise the value of the option to invest. This is a standard result of option pricing. It stems from the fact that increased variance increases the deviations of V from its expected path. However, investors are not hurt any more by larger negative swings than by smaller ones, since in both cases they will opt not to invest. This is the down- side protection offered by a call option. On the other hand, the investor can take advantage of large positive deviations of V and thus reap all upside benefits.

An increase in the risk-free interest rate r F tends to lower the value of the option. Since r F does not enter into the distribution of the first passage distribution, it does not affect the optimal time to invest. The value of the option is affected only via the discounting effect where an increased r F reduces the present value of any particular passage. This result is contrary to the standard option pricing result where the option value is raised with increasing values o f rF 12

An increase in a v will increase the value of the option, while an increase in a I will decrease the option value 13, The obvious intuition is that when the benefits from the investment will be greater in the future, it is better to wait; when the FMS is expected to cost more in the future, it is better to invest today.

The impact due to jump probabilities (i.e. values of the Poisson parameter )t) is identical to the effects due to the risk-free interest rate.

5. A n i l lustrat ive e x a m p l e

5.1. CAPITAL BUDGETING

The aim of this stylized example is to elucidate the above capital budgeting decision process. For simplicity we normalize all cash flows and make the following assumptions:

(1) The plant produces equal amounts of two output goods whose prices are independent of the production method, i.e. Y1 = 1, Y2 = 1. The goods differ in their input mix characteristics and their relative performance under FMSs. Furthermore, the prices of these outputs are independent of the type of production process and are normalized at 1. Therefore, revenues will remain unchanged between the reference alternative and FMSs. Hence, a comparison of incremental cost (savings) with incremental initial investment is sufficient.

(2) The price of inputs is unaffected by the introduction of FMSs, i.e. Pi = P~" Kulatilaka and Marks [8] show that a flexible technology will increase the firm's bargaining power in its negotiations with input suppliers and thus lead to lower input prices. Hence, this assumption depicts a worst case scenario.

(3) The cash flow components are roughly representing the average value weights in aggregate U.S. manufacturing: labor = 0.25, energy = 0.15, non-energy

48 N. Kutatilaka, Capital budget ing and op t imal t iming

Table 2

Incremental cash flow computations

qi, 1 qi,2 qi, l qi,2 Pi Pi = Pi

Materials (I) Materials (II) Materials (III) Energy (PI) Energy (PII) Energy (HLE) Labor (I) Labor (II) Labor (III) Inventory (IP) Inventory (I/O) Maintenance Reputation effect

100 100 90 90 5 0.05 100 100 50 90 2 0.05 100 100 50 90 0.5 0.05 100 100 90 95 2 0.05 100 100 150 150 0,5 0.05 100 100 50 50 0.2 0.05 100 100 90 75 1 0.05 100 I00 110 100 2 0.05

10 10 10 10 4 0.05 100 100 80 90 0.2 0.05 100 100 80 90 0.2 0.05

10 10 15 15 1 0.05 100 100 80 50 0.1 0.05

Table 2 (continued)

Uc i oc i np o i np o i Anp o i

Materials (I) 540 486 2047.0 1842.3 204.7 Materials (II) 216 151.2 818.8 573.2 245.6 Materials (III) 54 37.8 204.7 143.3 61.4 Energy (PI) 216 199.8 818.8 757.4 61.4 Energy (PII) 54 81 204.7 307.1 - 102.4 Energy (HLE) 21.6 10.8 81.9 40+9 40.9 Labor (1) 108 89.1 409.4 337.8 71+6 Labor (II) 216 226,8 818.8 859,8 - 40.9 Labor (III) 43.2 43.2 163.8 163,8 0.0 Inventory (IP) 21.6 18.36 81,9 69,6 12.3 Inventory (I/O1 21,6 18.36 81.9 69+6 12.3 Maintenance 10.8 16.2 40.9 61.4 - 20.5 Reputation effect 10+8 7.02 40.9 26.6 14.3

PV(DTS) = 407.0

ANPV = 67.9

N. Kulatilaka, Capital budget ing and op t imal t iming 4 9

Formulae

VCi, t =

npv. =

2

j = l

5

E VCi,o {(1 + g ) / [ ( 1 + r F) (1 + pi)l }-r t= l

2

oc,,, -- Z a;*, Y, P:, . - j = l

5

npo. = E VCi,o {(l + g~) / t ( l + r F ) ( I + p T ) ] } - t

t = l

&np~ = n p ~ - n p ~

PV(DTS) = E IAtIT"d,r} - t t = l

ITC = A I I T/

N

/ ~ P V = - z2xII + ITC + PV(DTS) + E ~npoi i = 1

Parameter values

&II = 1000 g = g = 0.05

7" c = 0.46 r / = 0.10

Pi = Pi = 0.05 for i E (1 . . . . . N )

]11 = Y2 = l a n d i s i n d e p e n t o f t

r i = r i = ( l + r F ) ( l + p i ) - 1

N = n u m b e r of input categories = 13 .

r F = 0 .10

7"d, t = ACRS 5 - years schedule


materials = 0.60. The breakdown within the aggregate inputs is arbitrarily chosen. For example, the cost component of heat, light and electricity [energy (HLE)] for producing a unit of output type 1, under the conventional technology, is 20 (100× 0.2). We assume that this value drops by 50% (10 = 50× 0.2) when FMSs are installed. In the cases of certain other inputs (e.g. maintenance), the introduction of FMSs can increase the cost components. In practice, qi,j and qi,*j will be estimated as described in sect. 1. Once again, thisrepresents a worst case scenario.

(4) Each cash flow has an associated risk premium (required rate of return over the risk-free rate). The changed risk premia could result either from a change in the correlation with the market or from reduced variance (see the discussion in sect. 2). For simplicity we hold the risk premia constant between conventional and FMS plants and across all inputs, i.e. r z. = r/* = r, i = 1 , . . . , n.

(5) The economic life of the project is assumed to be five years, after which it is scrapped and has no salvage value.

(6) The entire incremental initial investment is depreciated over five years on an ACRS schedule.

(7) All cash flows grow at a nominal rate, g = g* = 5 percent per year. (8) The nominal risk-free interest rate r F is 10% and the risk premia Pi = Pi

= percent for all incremental cash flows. Thus, the cash flows form a five year annuity which is discounted at t0%.

(9) The incremental initial investment is 1000. There is a 10% investment tax credi t ' r /= 0.1.

The detailed cash flows and computations leading to the capital budgeting rule are given in table 2 1 4 . The example analyzed in this table highlights several interesting points. The FMS can increase the cost of certain input components while reducing the cost on others. The net cost savings bring about the economic rationale for FMSs. Purely financial aspects such as investment tax credits and the present value of the depreciation tax shield are shown to be significant. Therefore, ignoring these would lead to the rejection of good projects. This analysis does not allow for changes in input prices or changes in risk premia due to FMSs. Since it is very likely that FMSs will reduce the risk premia and also often reduce the input prices (due to improved bargaining power with input suppliers), this analysis gives a worst case scenario. Should this information be available, the above analysis can be trivially modified to accommodate this information.

This example depicts a situation where an investment of 1000 gives an NPV of 67.9. The question then is whether to make the investment now or to postpone it in the hope of lower initial costs or greater cost savings in the future. The answer to this question rests on the solution to the optimal timing problem.


5.2. OPTIMAL TIMING

In table 3 we list the critical values of C* [ = 1 + (ANPV/AII)] at which it is optimal to invest. Several comments about the interpretation of C* are in order. Clearly, C* must always be greater than or equal to 1. The equality will hold only in a world of complete certainty (i.e. o~ = cr] = 0) or if 6 v = o0 (i.e. infinite 'excess appreciation' of V Is). The base case calculations assume the following

~ . = 0 - the 'jump' probability is zero,

8i,(Sv = 0.1 the 'excess appreciation' of both V andlprocesses is 10%. For example, an actual growth rate (appreciation) of 0.15 and a required rate of return of 0.05.

2 2 o2,o v = 0.05 - these values represent the average variance of unlevered equity in U.S. manufacturing industries 16

The value of C* under the above assumptions is 2.0. This means that the present value of benefits from the project must be twice the size of the initial investment, or, in our notation, ANPV must be equal to AII, before it becomes optimal to invest. Table 3 investigates the sensitivities of C* to parameter changes. The comparative statics mentioned in sect. 4 are illustrated by these numerical results. For example, as the variances increase the value of the waiting option increases, and thus the critical value increases (see column 1). Increases in X reflect a higher probability that the project would become worthless. Therefore, the value of the waiting option and C* decreases with increasing X (see column 2). At small values of 8 i , the sensitivity of C* to 5 v is large; at larger values of fix, this sensitivity is reduced.

In our illustrative example, C* = 1.0679. Based on the results in table 3, it will be optimal to invest immediately only if the variances of ANPV and AII are very small, the 'excess appreciation' 8 v is very large, and fit is very small.

6. Conc lud ing r e m a r k s

In this paper we show that the economic justification of FMSs can be obtained using standard capital budgeting techniques such as the net present value (NPV) method. In order for such a method to give unbiased results, we must consider the 'overall' impact of installing an FMS. The paper deals with cash flow forecasting and risk analysis aspects that form the basis for the capital budget. Although any cash flow forecastingmodel will be extremely case specific, we point to the special characteristics of FMSs and suggest general guidelines that must underlie such models.

5 2 N. Kulatilaka, Capital budgeting and optimal timing

Table 3

Critical values (C*) of the investment criterion

6 V

0.05 0.1 0.25

0.001 1.96 1.11 1.01 0.01 2.35 1,37 1.03 0.02 2.64 1.56 1.06 0.05 3.41 2.00 1.29 0.1 4.56 2.62 1.29 0.2 6.70 3.73 1.54 0,3 8.77 4.79 1.77

X

0 3,41 2.00 1.29 0.05 2.37 1,77 1.27 0.1 2.00 1.64 1.26 0.25 1,61 1,46 t .23

0.001 2.01 1.50 1.20 0.01 2,10 1.53 1.21 0.05 2.62 1.71 1.24 0.1 3.41 2.00 1,29 0.25 6.19 3.22 t.56

Base case: 02V = 4 = 0.05, ~,= O, 51 = 6V = 0.1,

C * = e / ( e - 1),

where e= {[((61 - 6v ) /C r 2) - 0.51 2 + 2(a l /O2)}0.5

Decision rule: Invest if 1 + ANPV/zMI I> C*

Postpone if 1 + ANPV/AII ~< C*

Reject if ANPV ~< 0

+ 1o.5 - (a I - av)/O2].


The second major issue we address is the timing of FMS installations. When facing uncertainties regarding the benefits from the FMS and the cost of the FMS, it is non-trivial to decide on the optimal time to invest. Even if the NPV turns out to be positive under most circumstances, it will be optimal for the firm to wait.

Finally, we demonstrate the methodology with a stylized example.

A c k n o w l e d g e m e n ts

Comments from two anonymous referees has much improved the quality of this paper. Any remaining errors are my own responsibility. Financial support from the School of Management, Boston University is gratefully acknowledged.

F o o t n o t e s

1 See Terborgh [13] and Abbot and Ring [1]. 2 For example, see Arbel and Seidmann [2] and Michael and Millen [1 1]. 3 In contrast to major retooling of conventional production systems, FMSs facilitate switching with

minor modifications. 4 The down time of sophisticated technologies, although less frequent, may be more prolonged

and would result in increased operating costs. 5 Employee benefits such as pension fund contributions, insurance, and social security contribu-

tions will amount to a significant fraction of the directly costed payroll. In addition, there will also be some reduction in the support staff handling matters of personnel and administration duties.

6 Not all of these costs are incurred during the initial period. For simplicity of the discussion, we treat it entirely as an initial period cost.

7 Some of the qi,j values may be zero. 8 The percentage depreciation under the existing accounting scheme, accelerated cost recovery

scheme (ACRS) is given below:

1 2 3 4 5 6 7 8 9 10 11 -15

3 year 25 38 37 5 yew 15 22 21 21 21

10 yew 8 14 12 10 10 10 9 9 9 15 yew 5 10 9 8 7 7 6 6 6 6 6

9 See Kulatilaka [6] for a detailed discussion and examples of this effect. l °For example the return on the S#P 500. l lSee Myers and Majd [12]. 12McDonald _ Siegel explain this apparent disparity by showing how the option models assume the

dividend rate to increase at the rate of interest, while in the investment model the 'dividend' is unaffected by changes in r F.


13Th e return in excess of that warranted by asset's systematic risk 6 is the more interesting variable. The behavior of 6 is similar to that of c~.

14Fo r clarity and completeness, we restate the formulae used in the computation of values follow- hag the table.

15When a project is under operation, the capital gains plus cash flow less depreciation equal the required rate of return. For an uninstalled project, the depreciation is zero. Hence, its expected price appreciation is less than the required rate of return by the cash flow net of foregone depreciation. The 'excess appreciation', therefore, can be measured as the earnings-to-price ratio.

16See McDonald and Siegel [9] for sources. 17Se e section 3.

References

[1] R.A. Abbot and E.A. Ring, The MAPI method - its effect on produtivity: An alternative is needed, Journal of Manufacturing Systems 2, No. 1 (1983).

[2] A. Arbel and A. Seidmann, Selecting an FMS: A decision framework, Proc. lst ORSA/TlMS Special Interest Conf on Flexible Manufacturing Systems; Operations Research Models and Applications, Ann Arbor, Michigan, USA, t984.

[3] G. Boothroyd, Economics of assembly systems, Journal of Manufacturing Systems 1, No. 1 (1983).

[4] G.K. Hutchinson and J.R. Holland, Economic value of flexible automation, Journal of Manufacturing Systems 1, No. 2 (1983).

[5] R. Jaikumar and R. Cooper, Production variance analysis in the flexible machining system, mimeo, Harvard Business School, 1984.

[6] N.H. Kulatilaka, (1984a), Financial, economic and strategic issues concerning the decision to invest in advanced automation, International Journal of Production Research 22, No. 6 (1984)949.

[7] N.H. Kulatilaka, (1984b), A managerial decision support system to evaluate investments in flexible manufacturing systems, Proc. 1st ORSA/TIMS Special lnterest Conf. on Flexible Manufacturing Systems; Operations Research Models and Applications, Ann Arbor, Michigan, USA, 1984.

[8] N.H. Kulatilaka and S. Marks, The strategic value of flexible manufacturing in a world of certainty, mimeo (1984).

[9] R. McDonald and D. Siegel, The value of waiting to invest, National Bureau of Economic Research,Working paper no. 1019, Nov. 1982 (revised version Aug. 1984).

[ t0] S.M. Miller, An overview of recent developments in robotics and flexible manufacturing systems, Working paper, Graduate School of Industrial Administration, Carnegie-Mellon University, 1984.

[t 1] G.J. Michael and R. Millen, Economic justification of modern computer-based factory automation equipment: A status report, Proc. Ist ORSA/TIMS Special Interest Conf. on Flexible Manufacturing Systems; Operations Research Models and Applications, Ann Arbor, Michigan, USA, 1984.

[12] S. Myers and S. Majd, Calculating the abandonment value using option pricing theory, Sloan School of Managment, MIT, Working paper No. 1462-83, 1984.

[13] G. Terborgh, Business Investment Management (Machinery and Allied Products Institute, Washington D.C., 1967).


A p p e n d i x

A TUTORIAL ON CAPITAL BUDGETING TECHNIQUES

A capital budgeting analysis is used to determine whether the benefits stemming from investments in a real asset (such as plant and equipment) are worth more than the cost of the asset. Although theoretical reasoning clearly indicates that the proper treatment of the capital budgeting decision should be based on the net present value (NPV) of the project, in practice several methods are used in project analysis. The most commonly used ones are:

payback period, average return on book value, net present value, internal rate of return, profitability index.

We highlight the intuition behind these methods, point out some common misconceptions regarding their use and make a case for our preferred NPV method.

1. The payback rule: The merit of the payback method lies in its extreme simplicity. Once management decides on an ad hoc critical payback period, the decision rule is simple:

'If the sum of the expected net positive cash flows during the critical payback period is greater than the initial cost, then accept the project; otherwise reject the project.'

The major drawback of this method also stems from its simplicity. It ignores the order of cash flows within the payback period and ignores all subsequent cash flows after the payback period. The result is a strong bias toward short-lived projects. Furthermore, since it does not account for time value of money, inflation, and the risk characteristics of cash flows, this method can lead to accepting 'bad' projects as well as rejecting 'good' projects with long lives.

2. The average return on book value: This method is in many respects similar to the payback method. In addition to ignoring the order of cash flows (and hence the opportunity cost of capital), this method introduces arbitrariness via the book value. The resulting accounting measures produce even larger biases than those under the payback rule.

3. The net present value method: Once there are estimates for expected future cash flows and the opportunity cost of capital r, the NPV can be computed


by discounting the cash flows at the rate r to obtain the present value. The NPV is obtained by subtracting the initial investment costs from this present value:

T

NPV = - C F o + Z CFt(1 + r ) - t , t = l

where C F t is the cash flow in year t. The decision rule is intuitive and simple:

If NPV > 0, then accept the project;

If NPV < 0, then reject tile project.

A critical step in NPV analysis is to obtain the correct opportunity cost of capital 17. Nevertheless, these approximate measures are better than either of the above methods which entirely ignore the opportunity cost of capital.

4. The internal rate of return: The IRR method has a strong economic founda- tion and if used appropriately will yield correct results. The IRR is defined as the discount rate at which the NPV is zero. The decision rule is:

If opportunity cost of capital > IRR, then reject the project;

If opportunity cost of capital < IRR, then accept the project.

A common misconception regarding the IRR method is that it can be used without knowing the elusive opportunity cost of capital. Although IRR can be computed without knowledge of r, the decision rule contains r. In a sense, the IRR method reaches the same decision but with many more computations (than the NPV method). Perhaps the popularity of the IRR method is because managers have notions about what the opportunity cost of capital is and feel more comfortable in comparing the IRR with their subjective evaluation of the opportunity cost of capital. This is no different to using a less accurate measure for the discount rate in NPV calculations.

In addition, the IRR suffers from four major pitfalls:

- The rule applies only if the project generates negative cash flows followed by positive ones. If this order is reversed, the decision rule should be reversed: projects with an IRR less than r should be accepted, while those with an IRR greater than r should be rejected.

- If there is more than one change in the sign of cash flows, then there could be multiple IRR or no IRR at all.

- Unlike NPVs, IRRs do not add. Hence, when comparing mutually exclusive projects, comparing IRRs does not make sense, whereas comparing NPVs is still correct.


- When using the IRR, the discount rate is assumed to be constant over the economic life of the project. When short-term rates are not equal to long-term ones (i.e. when the term structure of interest rates is not flat), the discount rate can not be finessed. In an NPV calculation we can easily account for this by using different discount rates for different cash flows.

5. The profitability index: This is a variant of the NPV rule where the index is defined as:

rr = PV(future cash flows)/CF 0 .

The decision rule is:

If n > 1, then accept the project;

If rr < 1, then reject the project.

The drawback with this approach is that comparing the index is not suitable for comparing projects. Since the computations needed to obtain 7r are exactly the same as those for the NPV, it is pointless to use this method.

capital budgeting and optimal timing of investments in flexible manufacturing systems

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