# Paper Example on NPV technique

Published: 2021-07-01
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The establishment of a project value to ascertain the best option is imperative in the investment decision. The assessment of the two alternatives of purchasing an additional machine or replacing the old one is a critical decision for the company. First of all, the initial cost of replacing the machine is higher than the old machine which is to up for upgrading. Additionally, the operation costs are also higher for the new machine. Nonetheless, the added value of the new machine indicating it can produce better quality irrespective of its high expenses. However, the credibility of the observation is the to test through the Present Value technique to determine which alternative is the best. The present value (PV) entails the calculation of a net discounted value for either of the project options and subsequently comparing the values.

The PV approach incorporates the calculation the equivalent amount of future value for the equipment to determine the feasibility of the available alternatives to investment (Miles, 2015). The net present value entails the difference between PV of cost and the cash flows or benefits. Considering that the machines both have a utility life of four years, the NPV approach is precisely relevant for the assessment of the machines. The methodology entails the calculation of NPV regarding costs including initial investment and operating cost as negatives while the added value as positives. The positives depict the inflow of benefits while the negative refers to negative amounts directed at the projects. That is,

NPV = PV (added value/benefits) PV (costs) (I)

PV (benefits) = P (P/B, 10%, n) (salvage) and

PV (Cost) = P (P/O, 10%, n) (operating cost) + P (investment cost),

(Where P refers to investment cost, B refers to benefit value, n refers to the project horizon, and O refers to the annual operating costs).

Therefore, the calculation of NPV includes:

NPV = B (P/B, 10%, n) (salvage) (O (P/O, 10%, n) (operating cost) + P (investment cost)) (II)

Scenario 1: The current production and Constant Fixed Operating Cost

Table 1. NPV (contribution) Calculation for the upgrading of the present machine

planning horizon year 0 1 2 3 4

B (Contribution) \$0.00 \$50,000.00 \$50,000.00 \$50,000.00 \$50,000.00

O (Operating Cost) \$0.00 \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00

P/B per year (Added Value) \$0.00 \$45,454.55 \$86,776.86 \$124,342.60 \$158,493.27

P/O per year (Operating Cost) \$0.00 \$9,090.91 \$8,264.46 \$7,513.15 \$6,830.13

P(Investment) \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00

NPV (PV of Contribution less PV of Costs) (10,000.00) 26,363.64 68,512.40 106,829.45 141,663.14

Table 2: NPV (Contribution) Calculation for the new machine

planning horizon year 0 1 2 3 4

B (Contribution) \$0.00 \$80,000.00 \$80,000.00 \$80,000.00 \$80,000.00

O (Operating Cost) \$0.00 \$30,000.00 \$30,000.00 \$30,000.00 \$30,000.00

P/B per year (Added Value) \$0.00 \$72,727.27 \$138,842.98 \$198,948.16 \$253,589.24

P/O per year (Operating Cost) \$0.00 \$27,272.73 \$24,793.39 \$22,539.44 \$20,490.40

P(Investment) \$50,000.00 \$50,000.00 \$50,000.00 \$50,000.00 \$50,000.00

NPV (PV of Contribution less PV of Costs) (50,000.00) (4,545.45) 64,049.59 126,408.72 183,098.83

Table 3: The comparisons of the two alternatives of the machines

Planning Horizon Year 0 1 2 3 4

NPV (Old Machine) (10,000.00) 26,363.64 68,512.40 106,829.45 141,663.14

NPV (New Machine) (50,000.00) (4,545.45) 64,049.59 126,408.72 183,098.83

Notably, the values of NPV gradually increase marking the impact of the contribution of the either machines production. The new machine gains value from a negative NPV and eventually breaks even and continues to depict a higher NPV than the upgrade of the old machine. Although the new machine arguably cost more in acquiring and the fixed annual operating expenses the superior quality of the products ensure that the contribution is enough to cater for the cost and the initial investment. In this case, the acquiring a new machine is a more feasible option in anticipation of an increase in demand for the product.

Figure 1. NPV vs. Planning Horizon for the old machine upgrade and the new machine

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Scenario 2: Increase in Output of the Machines and decrease in fixed operating cost (Assume Constant growth of 2% and 4% decline in fixed operating cost)

Table 4: NPV (contribution) Calculation for the upgrading of the present machine considering increase of production

Planning Horizon Year 0 1 2 3 4

B (Contribution) \$0.00 \$50,800.00 \$61,816.00 \$73,052.32 \$84,513.37

O (Operating Cost) \$0.00 \$9,600.00 \$9,600.00 \$9,600.00 \$9,600.00

P/B per year (Added Value) \$0.00 \$46,181.82 \$97,269.42 \$152,154.71 \$209,878.48

P/O per year (Operating Cost) \$0.00 \$8,727.27 \$7,933.88 \$7,212.62 \$6,556.93

P(Investment) \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00 \$10,000.00

NPV (PV of Contribution less PV of Costs) (10,000.00) 27,454.55 79,335.54 134,942.09 193,321.55

Table 5: NPV (Contribution) Calculation for the new machine considering increase of production

planning horizon year 0 1 2 3 4

B (Contribution) \$0.00 \$81,600.00 \$83,232.00 \$84,896.64 \$86,594.57

O (Operating Cost) \$0.00 \$30,000.00 \$30,000.00 \$30,000.00 \$30,000.00

P/B per year (Added Value) \$0.00 \$74,181.82 \$142,968.60 \$206,752.70 \$265,897.96

P/O per year (Operating Cost) \$0.00 \$27,272.73 \$24,793.39 \$22,539.44 \$20,490.40

P(Investment) \$50,000.00 \$50,000.00 \$50,000.00 \$50,000.00 \$50,000.00

NPV (PV of Contribution less PV of Costs) (50,000.00) (3,090.91) 68,175.21 134,213.25 195,407.55

Table 6: NPV comparison of the two alternatives

Planning Horizon Year 0 1 2 3 4

NPV (Old Machine) (10,000.00) 27,454.55 79,335.54 134,942.09 193,321.55

NPV (New Machine) (50,000.00) (3,090.91) 68,175.21 134,213.25 195,407.55

The values of NPV are higher for the second scenario considering the significant decline in the fixed operating cost and the increase in the contribution of the products. Nonetheless, the new machine gains value from a negative NPV and eventually breaks even and continues to depict a higher NPV than the upgrade of the old machine. Although the new machine arguably cost more in acquiring and the fixed annual operating expenses the superior quality of the products ensure that the contribution is enough to cater for the cost and the initial investment. In this case, the acquiring a new machine is a more feasible option in anticipation of an increase in demand for the product.

Figure 2: NPV vs. Planning Horizon for the old machine upgrade and the new machine after increment of productivity

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Conclusion

The best alternative is to upgrade the current machine on the short run since it records a higher NPV compared to the option of replacing the old machine. However, on the long run, the replacement option is more viable since the lifetime of the old machine is limited to a fixed amount of time and also the new machine record as Improved NPV values with an extended product life. The NPV technique provides a mathematical valuation of the project to ascertain the viability of the alternative project. In this case, given an equal product life, the project has little differences although the upgrade of the old machine is more viable considering that fewer costs are incurred while considerable production returns are also high. Nevertheless, the graphical presentation indicates that with a longer product life, the new machine could be a viable project to invest.

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The AHP technique: The Selection of an ERP System

Introduction

The analysis hierarchy process involves the utilization of a technique to provide a solution to complex group decisions. The principal focus of the method is the provision of an authentic solution to multi-components whereby the techniques seeks to resolve congested decision problems. The AHP technique incorporates the utility of pair-wise matrix whereby the decision problems are converted to a hierarchy to facilitate the comprehension of sub-problems. A systematic evaluation of the options is carried out where two items are considered per evaluation.

In this case, the primary decision problem is the selection of the best alternative for an ERP system. There are options of three ERP system available for consideration which are system Q, W and R. the choice of an ERP system is a critical decision since most of a firms decision and processes goes through the ERP system, hence it is crucial to select the best-suited system. An ERP mainly constitutes integrated cross-functioning modules thus facilitating multiple functionalities across the hierarchy of an organization (Miles, 2015). Various features are vital in the evaluation and the choice of the ERP. The different characteristic of the ERP may eventually affect its performance, efficiency and utility thus the conglomerate composition for an authentic and real-time ERP is determined through an AHP.

The choice of the AHP technique in the selection of an ERP is based on the sufficiency to synthesis various kinds of information and subsequently delivering on the best alternative for an ERP system. The firm essentially considers a set of metrics hence involving the availability of some decision problems. Decision problems are best solved using analytical techniques to facilitate the evaluation of the available parameters and subsequently deliberating on the best alternative. The ERP project involves a seven-stage procedure to complete. The procedure includes the selection of a project panel, identification of the ERP features which form the decision problem array and also the development of objectives as the core guideline to constructing the core objective hierarchy. The next step involves deriving the features and metrics of evaluating the ERP structure and then the unqualified vendors will be eliminated. The remaining alternatives of ERP system are then analyzed, and the findings are later discussed to strike a decision.

Approach and Methodology

The AHP technique is a linear programming tool to deliberate on multidimensional decision problem whereby the alternatives are critically evaluated to derive the best-suited decision. The approach entails the establishment of a hierarchy module it is then broken down into attributes through pair matrix. The analysis of the problem matrix with respect to the objective is done to establish the best score for the problems. The AHP approach, in this case, uses a scale of 1-9 to build on the decision problems breakdown. The standard weights for the problem were then synthesized through Software Expert Choice to achieve the AHP score for the systems.

Consistency Ratio

The process of building up a matrix in the evaluation of decision problems involves the establishment of pertinent provisions in the right order. The ranking of preferences of the decision problems in a logical order is referred to transitive property. The consistency ratio represents the sequence of priorities for the decision problems. The consistency ratio alludes to a consistent path of attributes that eventually transition to the achievement of the project object. The consistency index is calculated in digital format to represent the degree of coherence in the transitive property. The consistency ratio and consistency index are crucial in the solution of multiple decision problems.

The decision problem, in this case, is the selection of the best ERP system for the firm to adopt and implement. The features or attributes of the ERP aid in the assessment consistent ratio and index which are essential in the ranking of the decision problems. The best ERP system should incorporate features such as reliability, user- friendliness, implementation time, functioning and the respective total cost. The solution of the multidimensional decision problem, in this case,...

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