Abandonment value, economic life of an asset and buying time alternatives

Shareholders value maximization: abandonment value, economic life of an asset and buying time alternatives

Bhavesh Patel


This concept paper is focused on the determination of the economic life of an asset from the angle of maximization of the shareholder value. The paper considers options of buying used assets, as the used assets can be sold in the market. The options of buying new as well as old assets have been verified under the assumptions of one-time investment plans and also under the assumption of chain of repeat investment plans. The shareholder value creation is measured in terms of net present value because the reinvestment assumption of the net present value method of evaluation is more realistic and sound especially in evaluation mutually exclusive investment plans. The model developed proves that as there exists good opportunity for risk-adjusted value maximization through abandonment timing decision, there also exists value maximizing opportunities through the decision of buying used assets of right age.


The theory of capital budgeting evolved considerably between ’50s and ’70s of the last century. Many academicians and researchers made valuable contributions in the development of the capital budgeting theory during this period. Many ideas were mooted and lateral thinking initiated. Discounted cash flow approach got wide acceptance during this period. Academic soundness of net present value (NPV) method was established.

The introduction of abandonment value concept in capital budgeting is an important contribution in capital budgeting theory during this period. Contributions of Robicheck and Van Horne [10, 1967], and Dyl and Long [2, 1969] provided basic algorithms, demonstrating how premature disposal of an investment project can affect project feasibility. The purpose of this paper is to extend their work further to bring into discussion the concept of economic life of an investment project, and also evaluating the option of buying an old asset with the purpose of enhancing profitability. Dimension of risk is also added for the verification of impact of decision on risk-return trade-off.


Shillinglaw [13, 1959] and Moore [9, 1964) initiated the concept of replacement and abandonment. While discussing how to measure the abandonment value they concluded that abandonment value is assumed to represent the net disposal value of the project that would be available to the company in either cash or cash savings. Robichek and Van Horne (RV-H) [10, 1967] first introduced the application of abandonment value concept in capital budgeting for maximization of NPV. They submitted, “A project should be abandoned at that point in time when its abandonment value exceeds the net present value of the project’s subsequent expected future cash flows discounted at the cost of capital rate.” This decision rule is formulated below:

If NPV[tau],[alpha] [less than or equal to] AV[tau] then abandon at time [tau], otherwise don’t abandon

RV-H also considered uncertainty in their algorithm to check the effect of abandonment value on risk-returns trade-off. They observed that “much of the down side risk can be eliminated, if the project is abandoned when events turn unfavorable. R-VH, however, considered abandonment value as a risk-free variable.

Dyl and Long (D-L) [2, 1969] observed that R-VH model answered only a question ‘whether to abandon’ a project or not, but it does not answer the question ‘when to abandon a project’. D-L contributed a newer approach to the decision making, which can answer the question ‘when to abandon’ a project if it is currently accepted. They observed that down side risk is further reduced and expected NPV increased, if abandonment value is considered for determining the timing of abandonment at the time of investment. In a way D-L model determines the economic life of an asset, whereas R-VH model is only an abandonment model. However, we believe that the R-VH model cannot be considered as a foolproof abandonment model, because a project that is worth abandoning to day may be held now, and profitably abandoned on a future date. R-VH model will work only if there is no future abandonment option before the completion of project.

R-VH and D-L both took the abandonment value as certainty. The abandonment value can be safely taken as risk-free variable in R-VH model because abandonment value is the present-day-variable for their model, and that only helps in deciding whether to now abandon or hold the asset. D-L, on the contrary, considers an estimate of abandonment value as it is considered at the time of investing in asset, and it is meant for deciding whether the asset should be abandoned at some future point in time. D-L considered an option of future abandonment; hence uncertainty is associated with abandonment value.

R-VH in their reply [11, 1969], pointed out the uncertainty of the abandonment value especially in D-L model. While accepting the D-L modifications, they suggested that the first model of R-VH should be applied to the revised estimates of the cash flows and the abandonment value in determining whether to abandon, after the investment is made as per D-L model.

Later on Maurice [7, 1976] tried to bring out basic difference between R-VH algorithm and D-L preposition. He concluded that R-VH is good for accept-reject type of projects, whereas D-L is good for mutually exclusive projects or in capital rationing situation. But, the mutually exclusive alternatives are automatically generated with the introduction of the abandonment value in the investment proposal. Therefore, at the time of investment decision D-L model is superior, though R-VH can be applied later to decide whether to abandon, provided that it is the last opportunity of abandonment before the completion of the asset life.

Kee and Feltus [5, 1982] observed that R-VH and D-L model both make ‘”explicit assumption that the firm is not constrained by capital rationing”. The authors prepared a comprehensive table, which can explain D-L rules in a better way. The table effectively explains the changes in NPV over time. However, risk elements are excluded from the whole analysis.

George McCabe and George Sanderson [8, 1984] suggested rollback decision-tree model as simple alternative to Kee-Feltus approach. However, value maximization should be the central concern behind the investment decision and not the simplicity.


It is a foregone conclusion that the recognition of abandonment value in investment decision improves shareholder value. A value conscious firm will accept an asset and run it for the period as signified by its economic life. The result still may be sub-optimal if, (a) buying-time alternatives are not evaluated, and (b) the nature of investment–whether one-time or repetitive–is not suitably considered in the evaluation. This paper introduces these two dimensions, first under the assumption of certainty, and then verifies the impact of these two dimensions on risk-return profile. Both these dimensions are evaluated for one-time investment plan as well as for repetitive investment plan.

We have considered net present value method for measuring returns from investment plans because this analysis involves the evaluation of many mutually exclusive alternatives, and it is a foregone conclusion that NPV is better method for evaluation of mutually exclusive alternatives than internal rate of return for its reinvestment assumption. We have calculated expected returns and measured the risk in terms of standard deviation of returns. The risk-return trade-off is evaluated with the help of coefficient of variation (CV). Being aware of limitations of CV as the decision rule (that it ignores the fact that the indifference curve of a rational investor is concaved and not a sloping line), we plotted the maximum and minimum NPV on a graph and observed the downside risk for all alternatives. Semi-variance cannot effectively help in measuring the downside risk and compare across the mutually exclusive alternatives. The simulation method could have been used for having a better look at the downside risk across the mutually exclusive alternatives for better choice but we did not apply it because it would have hardly changed the concept that we propagate.


All previous authors have so far assumed that the firms buy only new assets. The used assets can also be bought as they can be sold. A firm should consider buying a used asset instead of new one, if it wanted to maximize shareholders value. Let us take an example to see the effect of considering buying old asset on net present value.

A firm is considering buying construction equipment. This equipment has a life of six years and it can be sold any time during its life. We have considered abandonment at the end of each year, and also buying of an old equipment at the beginning of any year. We have considered the discount rate of 15 percent.

The Problem

The purchase price, operating cash flows and abandonment values along with their probabilities are given below:

Purchase Price at Year 0

Probability Purchase Price

0.6 112,000

0.4 115,000

The solution is considering the purchase value of the used asset equal to the abandonment value in the respective period. This assumption can be easily relaxed, without hampering what we prorogate here.

If new equipment is bought, it can be abandoned any time during its six years’ life. If we consider for simplicity that the asset can be abandoned at the end of every year, we get six options for evaluation. More options are developed if the firm considered option of buying used equipment. Buying one year old machine will have five options, buying of two year old machine will offer four options and so on. That way 21 mutually exclusive options will be available. List of the options is given below:




New 1-year old 2-year old 3-year old

[M.sub.0,6] [M.sub.1,6] [M.sub.2,6] [M.sub.3,6]

[M.sub.0,5] [M.sub.1,5] [M.sub.2,5] [M.sub.3,5][M.sub.0,4] [M.sub.1,4] [M.sub.2,4] [M.sub.3,4][M.sub.0,3] [M.sub.1,3] [M.sub.2,3][M.sub.0,2] [M.sub.1,2][M.sub.0,1]

New 4-year old 5-year old

[M.sub.0,6] [M.sub.4,6] [M.sub.5,6][M.sub.0,5] [M.sub.4,5][M.sub.0,4][M.sub.0,3][M.sub.0,2][M.sub.0,1]

The Solution

We first present two solutions both based on an assumption that it is a one-time investment and the firm will not go for the chain of replacement. In the first solution we assume certainty and in the other we consider uncertainty. Table 2 presents the net present values of all alternatives under the assumption of certainty. We considered all values at second probability as certain values, and Table-3 presents the NPVs, standard deviations and coefficient of variations for all alternatives. Both the tables use presentation style developed by Kee and Feltus.

The simplified application of D-L rule would conclude that the economic life of the proposed machine is four years. Option [M.sub.0,4] offers maximum NPV of $30,736. This value is obtained by taking maximum NPV value from the first row. However this is not a value-maximizing alternative. Buying one-year-old asset and using it for three more years before abandoning when it is four-year-old asset would maximize the value. This [M.sub.1,4] option offers NPV of $32,597, which is highest among all 21 alternatives.

When risk is incorporated the option [M.sub.0,4] is considered best for the efficient risk-return trade-off measured through CV and decided using the least CV as the best option.


Twenty-one options evaluated in the example do not have equal lives. The life discrepancy can be ignored if repeat investment is not required. But, many investment decisions evaluated by the firm are repetitive by nature undergoing the chain of replacement at the end of every life of it. The investment in a machine is usually repetitive type because it is the part of a major project, which goes on for longer period than one life of its configuration parts like machine. In that case life discrepancy among mutually exclusive alternatives must be recognized, because the future dependent investment option and returns from it, both are known. The mutually exclusive repetitive alternatives with varying lives can be evaluated by any of the three alternative solution methods, namely; the uniform annual series method, the least common multiple method, and the infinite chain of replacement method. We have calculated NPVs for the chain of replacement.

Total of NPV during the infinite life with chain of replacement can be calculated with the following equation:

Total NPV([M.sub.[lambda],[varies]]) = NPV([M.sub.[lambda], [varies]])/1-[1/[(1+r).sup.([varies]-[lambda])]]

where, [lambda] is year in which investment is made [varies] is year in which investment can be abandoned

The Table-4 gives the NPVs for the options we considered earlier, if they undergo infinite chain of replacement under the assumption of uncertainty.

In case of the repetitive option, 15% discount rate, and certainty situation it is economically advisable to abandon the equipment after using it for four years, if bought new. But that would create the value of $71,772 only as against a potential value creation of $101,333 from repeating the chain of buying two years old asset and abandoning it after one more year (option [M.sub.1,2]).

When we consider risk also along with the chain of replacement, option [M.sub.3,4] must be selected, as its risk-return profile is most attractive at 0.14 coefficient of variation. This is the least risk for every unit of return offered by any alternative.

Downside Risk

Robicheck-Van Horne [10, 1967] proved through the mathematical analysis that much of the downside 9risks can be eliminated, if the project is abandoned when the events turn favorable. This model adds a point that the downside risk can be further reduced and value can be further increased if the firm also combines buying time alternatives along with the abandonment options.

Coefficient of variation measures the risk per unit of return. It cannot throw light on the downside risk. Perusal of tables 3 and 5 show that the CV is minimum if four year old asset is bought and used for either one or two years. But both these alternatives ([M.sub.4,5] and [M.sub.4,6]) have negative net present values. Their downside risk is very high despite the CV being the least mathematically. Semi-variance also cannot give better idea of downside risk because it measures the chance of getting return less than its mean.

We calculated net present value for each options under two scenarios each, one most favorable situation where the equipment is bought at the least price, operating cash flows are received at maximum and abandonment value is maximum. Two, most unfavorable situation where purchase price is the maximum, operating cash flow is the least and abandonment value is also the least. The first calculation gives us upper end of potential NPV and the second calculation gives us the lower end of the potential NPV. These values for all alternatives are plotted in graph-1.


The graph-1 shows that the option [M.sub.0,4] has the least minimum NPV. Coincidentally it also offers the highest maximum NPV among all. The next best is [M.sub.1,4]. One may use simulation and account for all possible outcome along with their respective probabilities and get better profile of risk-return. In case of economic life decision, however, one may not use that most difficult model and still get good decision guide-line because the mutually exclusive alternatives in such problem are not very much different it terms of outcomes and their respective probabilities except the timing factor. One can use graph of maximum and minimum NPVs and still get useful decision support.


The economic life model suggested in this paper is based on few assumptions. They are;

1. Abandonment (liquidation) value of an asset and the acquisition (replacement) value of the asset both are equal.

2. The life cycle of an asset remains constant irrespective of its use and maintenance.

3. The net cash flow from asset is the function of asset efficiency, as determined by the phases of life cycle, and not by the other factors external to the asset.

4. There is no gestation period or installation and de-installation period.

5. The firm does not operate under the situation of capital constraint.

6. A meaningful rate of cost of capital can be calculated.

7. The firm is aiming at maximizing the shareholder value.

Practically the abandonment value is lower than acquisition value due to the transaction costs incurred by both buyer and seller. The asset life cycle is also a function of maintenance of the asset. Negligence in preventive maintenance may shorten the life of an asset and also cause damage to the earning potential of it. The third assumption given above implies that the machine utilization is not the function of upstream or down stream activities or it is not subject to the factors like non-availability of manpower and other resources or absence of demand. The gestation period may be very negligible in the case of movable assets like vehicles, ships, wagons and other rolling stock. In some other cases it may be long. This will be reflected in the possible abandonment points during the life.

The fifth assumption is necessary for two reasons; one, in case of capital rationing a firm is compelled to take sub-optimal decision, and two, the cost of capital (discount rate) is likely to change especially when the capital constraint is external. The result measured in terms of net present value is sensitive to the discount rate. More so if the cash flow over the period is quite volatile. The economic life (and for that matter all the capital budgeting) models will become redundant if a meaningful rate of cost of capital cannot be calculated.

And finally, the firms pursuing an objective different than the shareholders value maximization will adopt different decision criteria.

Some assumptions can be modified and incorporated in this economic life model for making the model quite pragmatic. Transaction cost can be easily built in the model. It is safe to assume that the decision make would be aware of the firm’s preference for life cycle of an asset and she would pay attention to it while considering any old asset for purchase. Cash flow being affected by the factors other than the asset efficiency is really not an issue here because in that case the cash flow of all alternatives will be equally affected. Cash flow potential of asset.


Conventional capital budgeting models assume that the abandonment value of an asset at any time during the whole life of it will be equal to the present value of the remaining future cash flow stream at that point of time. In reality, for several reasons the abandonment value of an assets could be greater than the present value of its future cash flow, without depriving the buyer of the used asset of her share of value creation. Differences in cost structure, cost of capital, use of asset, risk contribution by an asset in total business risk, funds availability and host of other factors make it a win-win situation for the seller and the buyer of a used asset.

The previous contributions regarding the economic life models were based on the assumption of the certainty of cash flow except the proof given by Robicheck-Van Horne [10, 1967] that the downside risks can be eliminated, if the project is abandoned when the events turn favorable. This model not only incorporates risk analysis in the abandonment value concept, but also considers buying time options as well as the need for asset either for a single life or for a chain of perpetual replacement. The concept of risk is built into the analysis. Probabilities of cash flows are estimated. It is concluded that the decision of economic life (under any assumption, whether single life or perpetual chain of replacement) increases the expected return and reduces the risk, and thereby maximizes the value of the firm.

The economic life model is applied at the time of investment planning. The decision regarding abandonment time taken at the planning stage must be reviewed occasionally during the currency of investment. The unfolded situation must be incorporated with the improved assumptions and revised data. The economic life itself may get revised in the process. The opportune time for value maximization is hunted through such process of continuous review of economic life of an asset. The economic life model can be easily and readily applied for the assets where market for used asset is quite active, like used machine, vehicles, wagons, escalators, ships and other rolling stocks have ready market. This model can also be applied for determining the economic life and value maximizing time of selling a brand or business.

Operating Cash Flows (OCF)

Year-1 Year-2 Year-3 Year-4


0.3 55,000 0.2 62,000 0.4 33,000 0.3 21,000

0.5 50,000 0.6 60,000 0.5 30,000 0.6 20,000

0.2 48,000 0.2 55,000 0.01 28,000 0.1 18,000

Year-5 Year-6


0.2 2,200 0.1 14,000

0.5 20,000 0.6 12,000

0.3 17,000 0.3 10,000

Abandonment Values (AV)

Year-1 Year-2 Year-3 Year-4


0.3 88,000 0.3 55,000 0.3 50,000 0.1 48,000

0.5 85,000 0.5 52,000 0.5 45,000 0.5 45,000

0.2 82,000 0.2 48,000 0.2 42,000 0.4 42,000

Year-5 Year-6


0.3 28,000 0.2 20,000

0.4 25,000 0.6 18,000

0.3 23,000 0.2 15,000




End of … 1 2 3 4

Beginning of year …

1 2,391 13,166 23,161 30,736

2 12,391 23,885 32,597

3 13,217 23,236

4 11,522




End of … 5 6

Beginning of year …

1 27,380 27,921

2 28,737 29,359

3 18,798 19,513

4 6,418 7,240

5 (5,870) (4,924)

6 1,087





Abandoned at the 1 2 3 4

end of year …

Investment in the

beginning of year …

NPV 5,409 15,545 21,119 28,294

1 SD 1,853 2,020 2,435 2,305

CV 0.34 0.13 0.12 0.08

NPV 11,657 22,594 14,319

2 SD 1,756 2,352 2,171

CV 0.15 0.10 0.15

NPV 12,578 21,210

3 SD 2,469 2,240

CV 0.20 0.11

NPV 12,548

4 SD 1,794

CV 0.14


5 SD



6 SD



Abandoned at the 5 6

end of year …

Investment in the

beginning of year …

NPV 25,032 26,805

1 SD 2,878 2,906

CV 0.11 0.11

NPV 24,454 24,605

2 SD 2,940 2,913

CV 0.12 0.12

NPV 14,717 14,891

3 SD 3,196 3,163

CV 0.22 0.21

NPV 2,459 2,660

4 SD 3,177 3,133

CV 1.29 1.18

NPV (9,487) (9,256)

5 SD 3,431 2,973

CV (0.36) (0.32)

NPV 265

6 SD 1,343

CV 5.06




End of … 1 2 3 4

Beginning of year …

1 18,333 53,992 67,625 71,772

2 95,000 97,946 95,178

3 101,333 95,287

4 88,333




End of … 5 6

Beginning of year …

1 54,453 49,185

2 67,105 58,388

3 54,887 45,564

4 26,318 21,139

5 (45,000) (20,194)

6 8,333




Abandoned at the 1 2 3 4

end of year …

Investment in the

beginning of year …

NPV 41,467 63,746 61,665 66,068

1 SD 14,207 15,489 18,670 17,669

CV 0.34 0.24 0.30 0.27

NPV 89,367 92,653 41,810

2 SD 13,466 18,029 16,642

CV 0.15 0.19 0.40

NPV 96,433 86,976

3 SD 18,931 17,170

CV 0.20 0.20

NPV 96,200

4 SD 13,750

CV 0.14


5 SD



6 SD



Abandoned at the 5 6

end of year …

Investment in the

beginning of year …

NPV 49,783 47,218

1 SD 22,067 22,279

CV 0.44 0.47

NPV 57,102 48,934

2 SD 22,540 22,330

CV 0.39 0.46

NPV 42,970 34,772

3 SD 24,504 24,248

CV 0.57 0.70

NPV 10,084 7,766

4 SD 24,357 24,016

CV 2.42 3.09

NPV (72,733) (37,958)

5 SD 26,308 22,795

CV (0.36) (0.60)

NPV 2,033

6 SD 10,293

CV 5.06


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Bhavesh Patel, Myers University, Cleveland, Ohio

Dr. Bhavesh Patel earned his doctorate degree from SP University, India in 1990. He published many research papers, conducted executive training and consulting assignments, and authored three books. He is Assistant Professor of Finance and Economics and the Chair of Business Division at Myers University, Cleveland, Ohio, USA.

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