Analysis of the purchase option of computers

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1 Analysis of the of coputers N. Ahituv and I. Borovits Faculty of Manageent, The Leon Recanati Graduate School of Business Adinistration, Tel-Aviv University, University Capus, Raat-Aviv, Tel-Aviv, Israel This paper presents an analysis of the of coputers in coparison with the other coon s such as rent and. The results of this analysis show that in ost cases this is not econoical fro the custoer's point of view. (Received Deceber 17) 1. Introduction In the process of coputer selection, the econoic analysis usually deals only with three alternatives of coputer acquisition:, rent and leasing (Brandon, 172; Borovits, 175; Titeck, 173). However, there is one that is overlooked and this is the. Usually, the is given by the anufacturer to the custoer who rents data processing equipent but who ay wish to it at a later date. If the custoer decides to, a certain percentage of the rental payents that have already been paid will be deducted fro the price. The coon ters for the are described in the second section. The third section shows that the analysis of the is required by a custoer involved in one of two possible decision-aking situations: 1. Before installing new equipent a custoer ay initially decide to, or rent and exercise the in future, or rent it peranently. Soeties a custoer decides to rent even when is calculated to be cheaper, in order to be allowed to return the equipent should it prove unsuitable. Analysis of the ay elicit the 'cost of decreasing risk' introduced by delaying the decision to. 2. After installing rented equipent, the custoer ay wish to re-evaluate the prior decision of renting the equipent instead of purchasing it initially. The inforation at the tie of re-evaluation is ore coplete than the inforation available at the tie of the prior decision. Thus, at this stage, the custoer ay exercise the. It is of great interest to understand the factors taken into account by the anufacturer who grants a. These are analysed in the fourth section. The fifth section presents several tables which exhibit selected nuerical results of the analysis, followed by the last section which presents conclusions derived fro the quantitative analysis. 2. The Coputer anufacturers usually grant the custoer an to the coputer after a period in which the coputer was rented. The price consists of the current price at the tie of this, inus the rent paid up to this point, ultiplied by a certain percentage which is deterined for each of the coponents. That is, C the aount of oney the custoer has to pay if he decides to exercise the after rental onths is: C = C - Rd* where: R = onthly rental price C = price d = accuulation percentage toward Exaple: If we assue that the ratio of rent to is 1 :48, R = $1, C = $48, d = 0%, and = 20, then C = 48 - (1) (20) (0.) = $3. Manufacturers usually constrain this forula with the following liitations: (a) the total accuulated onths cannot exceed M onths; or (b) the total price reduction cannot exceed P percent of the price of the equipent at the tie of the. It can be shown that these two constraints are interdependent. Using the notations denned previously the constraints are: C = C - d-r ^ PC or C(l - P)> -Rd C{\ - P) > or Rd In other words, the custoer is peritted to use the CO P) within M onths or n, onths, whichever is the sal- R' d ler. To present the ethod of analysis we oit these constraints and will bring the back at a later stage of the discussion. 3. Methods of analysis fro the custoer's point of view Let us consider a custoer who had decided to install a specific equipent and is now wishing to calculate the cost of soe alternatives such as, rent, or first rent and later. If the equipent is d the lup-su payent is certain. In this case, however, the custoer is not certain of the econoic life of the installed equipentf. In other words, the aount of tie in which the equipent could be used is unknown to the custoer. If the equipent is rented, the future payents are not certain because of at least two reasons: (a) since the econoic life of the equipent is unknown, the custoer does not know how any rent instalents will have to be paid; and (b) the rental price ight be changed by the When rental price is not constant for the whole relevant period, the correct forula should be C" = C - d. Rt where Ri is the rental price paid at onth i. For convenience purposes, we shall assue that Rt is fixed. teconoic life of coputer equipent is the period fro the instalent date up to the econoic obsolescence which is defined by Brandon (172, p. 7) as 'the point at which the syste can no longer eet the user's requireents effectively'. An alternative ter which will be used here is 'Syste Life-cycle'. Volue 21 Nuber 2 105

2 anufacturer in the future. To siplify the analysis we shall assue: (a) the custoer has an estiate of the econoic life of the equipent (b) the custoer assues that rental price will reain unchanged during the econoic life of the equipent (c) the custoer's price of capital ( of interest) is known and constant (d) when future resort to the is considered, the current price at the date of is assued to be equivalent to the existing price. Once the preceding assuptions have been ade, the coparison between the alternatives should be ade on the basis of the results of the following calculations. Deterine the actual cash flow of each of the following alternatives and discount it in accordance with the predeterined interest. The ain cost eleents of these alternatives are as follows: 1. : 2. al: Initial cost Maintenance cost Insurance cost Monthly rental payents Overtie payents 3. : Monthly rental payents up to the tie of Maintenance cost after the tie cost at the tie of resorting to the In analysing the, it is possible, of course, to change the tie of the, and then to analyse the results on the basis of the anufacturer's constraints and the assuptions entioned earlier. It should again be noted that this analysis does not take into consideration the uncertainty about the future and rental prices. Soe of the anufacturers quote the aintenance and rental prices sepaly. In such cases the analysis ay exclude the aintenance price, and use only the pure onthly rental price i.e. onthly rent inus onthly aintenance price. To illust the ethod of analysis, an exaple is now given. Assue the following data: price (C) $48 Monthly rent (/?) $l ( pur e rent) Cuulative percentage for the (d) 0% Estiated econoic life (A/*) 0 onths Rate of interest (/) 0% Then, the coparison of the three alternatives will yield the following : : $48 (excluding insurance cost) : 0 x 1 = $0 1. First the constraint on the should be calculated. If we assue that the axiu accuulated nuber of onths cannot exceed 3, and the deduction should not exceed % of the price, then 48 x (1-0-5) _ = onths 1 x 0- which indicates that the should be ade within 3 onths. 2. If the is exercised after 1 year the total cost is 10 al payents cost Total cost 3. After two years al payents cost Total cost 4. After three years al payents cost X 1 = 48 - x 0 = $ $-8 $ X 1 = $ x 0' = $33- $57-3 X 1 = $ x 0- = $2-4 Total cost $2. 4 It is clear that if the econoic life of the coputer is greater than the -to-rent ratio, the coputer should be d (Brandon, 172). For higher s of interest this breakeven point oves further in favour of the rent alternative. If we assue an interest of zero percentage, then the rental cost is: C R {) = R- The cost of the after onths is: C 0 () = C R () + C - dc R (ni) = C + C R ()(l - d) = C + R{\ - d) Substituting M*, the econoic life of the coputer, indicates the axiu nuber of onths for which the is econoical: For our exaple C R {M*)> C + R{\ -d) RM* > C + R--(I ~ d) which yields R(\ - d) 1 x 0-48 = 30 onths 1 x (1-0-) which eans, that it is econoically correct to exercise this up to 30 onths of rent. This equation shows that when the interest equals zero, the is not econoical if the expected life of the equipent is less than or equal to the -to-rent ratio. In other words, the is econoical only when the alternative was econoical initially. If we denote the interest as / per onth, the total discounted rental cash flow is: M'-l C R (M\ I) = Therefore, the cost of the in onth is -l r ( i\ "V 7 = 0 R c ~ d--r The breakeven point for can now be obtained, as it was done before. Now let us exaine the reconsideration of a custoer's prior decision to rent coputer equipent. Possible reasons for reconsidering this decision ight be: (a) changes in the The Coputer Journal

3 estiation of the econoic life of the equipent (the reaining utilisation period); (b) change in the onthly rental price; (c) change in the current price; or (d) change in the interest. In such cases the custoer ay choose either to continue the rental contract, or to exercise the. The choice can be ade by a coparison between an iediate payent of agnitude C", and a sequence of future payents with estiated aounts, ters and of interest. (A ore sophisticated custoer ay use odels of decision theory under uncertainty.) C, the iediate lup su which has to be paid in a can be easily calculated as C = C - d-r(or C = C - d- i), where C is the current price; the rental payents already disbursed, -R (or Rj), and the accuulation percentage, d, are known. Assuing that the current onthly rental price is constant (when better inforation is not available) and that the econoic life has been revised, the custoer has a siple to rent proble which was widely discussed by Brandon (172), Borovits (175) and others. 4. Method of analysis fro the anufacturers point of view The anufacturer is free to anipulate soe of the paraeters of the, while for the custoer these paraeters are fixed. Therefore, in addition to the present value analysis which is the sae for both custoer and anufacturer it is interesting to analyse the anufacturer's stgy in setting these paraeters. The paraeters are: d The accuulation percentage (the percentage of the rent payents that will be deducted fro the price) M The axiu nuber of onths that can be accuulated P The upper liit of the aount that can be deducted It can be assued that the anufacturer estiates the expected period of rent, and then, based on this estiation and on the of interest, coputes the onthly rent in such a way that the profit fro renting the equipent will not be less than the profit fro selling the equipent. Therefore, there is a rental period in which the anufacturer is indifferent between renting and selling the equipent. The rental payents include four coponents: (a) al payent for the equipent (b) Maintenance cost (c) 'Risk payent' which has to cover the custoer's privilege of returning the equipent at any tie which akes its re-renting or its selling uncertain (d) The interest on the investent. In calculating the accuulation percentage (d), the anufacturer will deduct at least the portion which includes the last three coponents. Exercising the when 1 d is higher than the su of these three coponents yields a higher profit. In order to illust this, let us take the exaple presented previously: Table 1 Net present value coparison of rent v. syste life cycle of 3 onths 3 cost 48 0 accuulate 1 year years years Volue 21 Nuber 2 107

4 price $48 Monthly rent $ 1 Accuulation percentage 0% Rate of interest 0% In the above data % of the onthly rent is represented by the of interest, aintenance and risk. Now, since our analysis relates to pure rent (without aintenance price) and the interest is zero, the risk is counted as % of the rent. Using this data, it follows that the anufacturer estiates the equipent life as = 80 onth r^4 - o^ Another possible interpretation is that the anufacturer ay want to gain higher profits when the is exercised (assuing that the probability of the custoer returning the equipent is relatively sall). The other two constraints set by the anufacturer which were previously entioned contribute, obviously, to profit increase. These two constraints prevent the custoer fro buying the equipent for a very sall aount after a long period of renting. They induce the custoer to replace the old equipent by a new one. The anufacturer's policy is clear because by the tie the custoer exercises the ost or all of the investent will be covered, so finding another usage for the old equipent ay result in higher profit. 5. Suggestive nuerical results To put our analysis to work we present soe calculations using the following values: / The interest is %, % and % per year (/ = 0, 0, -) copounded onthly R The pure rent is $1 (R = 1) C The price is $3, $48 and $0 (since various coponents have different rent-to- ratios) M* Three lengths of econoic life are 3, 48 and 0 onths (M* = 3, 48, 0) Three rental periods used for the ( = 24, 3) d The accuulation percentage is -4, -5, - (since various coponents have different accuulating percentages). The results of the calculations are shown in Tables 1, 2 and 3.. Conclusions The analysis yields the following conclusions for the custoer (all paraeters are held constant): 1. The rentability of the increases with the increase in the accuulation percentage. 2. The rentability of the definitely increases with the increase in the interest. However, since the net present value of the rent is decreased, the decision should also be based upon the difference between these two values. Table 2 Net present value coparison of rent v. syste life cycle of 48 onths cost accuulate 1 year years years The Coputer Journal

5 Table 3 Net present value coparison of rent v. syste life cycle of 0 onths 3 cost 48 0 accuulate 1 year years years The later the date of the the less econoical this is. 4. The value of the is not affected by the value of the econoic life cycle of the equipent. However, the net present value of life cycle increases. 5. Exercising the the rent becoes increases as the less econoical as the cost of the equipent increases.. As the ratio between the expected econoic life to the cost increases, the becoes ore econoical. For exaple: when cost is held constant at $3, the rent alternative is ore attractive than the "or an econoic life of 3 onths. When the expected econoic life is 48 onths there is an econoic breakeven point (the breakeven point for the date of the is between and 24 onths). The becoes ore attractive than the rent alternative as the econoic life reaches 0 onths. Usually it is not worthwhile to analyse the in the case where the rent alternative is initiall)' less attractive than purchasing. However, any custoers hesitate to the data processing equipent, especially when it is the first installation in their organisation, or when it is an unfailiar equipent, even if the alternative is better than rent. Our analysis coputes the 'cost of hesitation' to these custoers. References BRANDON, D. H. (172). Coputer Acquisition Method Analysis, Dataation, Vol. 1, No.. BOROVITS, I. (175). Coputer Selection and Acquisition, Data Processing Journal, Vol. 17, No. 2. TIMMRECK, E. M. (173). Coputer Selection Methodology, ACM Coputing Surveys, Vo. 5, No. 4. Volue 21 Nuber 2 10

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