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Non-discounted payback period

Discuss about the Uncertainty Management In Simulation-Optimization Of Complex.

Booli Electronics is the electronics manufacturer that carries on its business from Carlton, Victoria, Australia. Owing to the technological changes the company wants to make new model for their existing product SSHA. The focus of this report will be evaluating the acceptability of new SSHA project through various measures. These measures will include the calculation of net present value, Profitability index, Payback period and internal rate of return (McAuliffe 2015). Another objective of the report is to perform the sensitivity analysis of NPV with regard to changes in the selling prices and changes in the selling quantity.

Payback period is used to calculate the time in which the initial investment of the project will be recovered. The main issue with payback period is that it does not consider the time value of money which is an important aspect to consider (Leung et al. 2014). Further, it is concerned about the time in which the initial investment is recovered but ignores the cash flows after that Period.

 Year Cash inflow Cumulative cash flow 0 \$   (47,025,000.00) 1 \$       9,158,160.00 \$          9,158,160.00 2 \$     34,307,097.60 \$        43,465,257.60 3 \$     25,842,344.45 \$        69,307,602.05 4 \$     16,194,120.97 \$        85,501,723.02 5 \$     23,547,757.33 \$      109,049,480.35

Non-discounted payback period = 2 + (47,025,000 – 43.465,257.60) / (69,307,602.05 – 43,465,257.60) = 2.14 years.

It recognizes the cost and benefit correlation of the project. The profitability index of new SSHA model is calculated as follows –

PI = PV of future cash flows / Initial investment

PI = \$ 77,573,881.43 / 47,025,000 = 1.65

IRR is the point at which the cash inflows and cash outflows of the project are equal (Leyman and Vanhoucke 2016). As per the Excel calculation the IRR of new SSHA model is 19.77%.

It is the difference among the present value of cash inflows and cash outflows. Generally, the acceptability of the project is evaluated through calculating the NPV (Gallo 2014). If the NPV is positive then the project is accepted and if the NPV is negative the project is not accepted. The NPV of new SSHA model project is \$ 30,548,881.43 (Pasqual, Padilla and Jadotte 2013).

It is the technique of evaluating the impact of changes in the variables of the project and the variables selected are those variables which can be expected most. While the sensitivity analysis is performed generally the unfavourable situations are taken into consideration. The variables taken into consideration are taken based on the most likely expected factors like changes in the selling price or the selling quantity in the given case (Brooks 2015). However, the impact of the changes of these variables shall be analysed to evaluate the changes in the net present value and its acceptability. Main factors leading to sensitivity analysis are as follows –

• It helps to analyse the main variables that may have an impact on the NPV if there is a change in that variable
• It reveals the likely impact and the ways to eliminate or minimize the impact on the NPV
• It helps to analyse whether the impact on the NPV will have an effect of the decision making procedure.

## Profitability index

Further, the sensitivity analysis is conducted through following approaches –

• The base case output like NPV is identified 1stand then the base case input like changes in selling price is measured for analysing the sensitivity. Al other variables like discounting rate, selling quantities are kept constant.
• Value of the output with new input value is found out
• The percentage change or amount change in the output is found out with the change in the input percentage or amount.
• Thereafter the sensitivity is found out through dividing the percentage change in output by the percentage change in the input (Yuniningsih, Widodo and Wajdi 2017).
 Price NPV Changes changes \$                              - 500 \$            (15,635,004.70) 515 \$            (11,930,414.90) 15 \$      3,704,589.80 530 \$              (8,225,825.11) 15 \$      3,704,589.80 545 \$              (4,521,235.31) 15 \$      3,704,589.80 560 \$                (816,645.51) 15 \$      3,704,589.80 575 \$               2,887,944.28 15 \$      3,704,589.80 590 \$               6,592,534.08 15 \$      3,704,589.80 605 \$             10,297,123.88 15 \$      3,704,589.80 620 \$             14,001,713.67 15 \$      3,704,589.80 635 \$             17,706,303.47 15 \$      3,704,589.80 650 \$             21,410,893.27 15 \$      3,704,589.80 665 \$             25,115,483.06 15 \$      3,704,589.80 680 \$             28,820,072.86 15 \$      3,704,589.80 695 \$             32,524,662.66 15 \$      3,704,589.80 710 \$             36,229,252.46 15 \$      3,704,589.80 725 \$             39,933,842.25 15 \$      3,704,589.80 740 \$             43,638,432.05 15 \$      3,704,589.80 755 \$             47,343,021.85 15 \$      3,704,589.80 770 \$             51,047,611.64 15 \$      3,704,589.80 785 \$             54,752,201.44 15 \$      3,704,589.80 800 \$             58,456,791.24 15 \$      3,704,589.80 815 \$             62,161,381.03 15 \$      3,704,589.80 830 \$             65,865,970.83 15 \$      3,704,589.80 845 \$             69,570,560.63 15 \$      3,704,589.80 860 \$             73,275,150.43 15 \$      3,704,589.80 875 \$             76,979,740.22 15 \$      3,704,589.80 890 \$             80,684,330.02 15 \$      3,704,589.80 905 \$             84,388,919.82 15 \$      3,704,589.80
 Changes in price 2% Changes in NPV 12% Sensitivity 555.41%

From the above it can be identified that the output that is the NPV increases with the increase in the input that is selling price. As per the above table and graph with the selling price ranged from \$ 500 to \$ 905 the NPV is increased from -\$15,635004.70 to \$ 84,388,919.82. Thus, there is a change of \$ 37,04,589.80 in the NPV with every \$ 15 increase in the selling price. In other words, for every 2% changes in the selling price there is 12% changes in the NPV. Therefore the resultant sensitivity is 555.41%. Therefore, there is positive correlation between the input and output. To be more specific, with the increase in input that is selling price there is an increase of output that is NPV. Thus, the NPV is highly sensitive with regard to changes in the selling price (Arrow et al. 2013).

In case of changes in the selling quantity and measuring the sensitivity of NPV, selling quantity will be input and NPV will be the output. The changes in the NPV will be measured with regard to the changes in the selling quantity being the other things like selling price and discounting rate at same level (Baucells and Borgonovo 2013). However, the limitations involved in the sensitivity analysis is that it may produce ambiguous result as it depends on the user’s decision regarding what is pessimistic and what is optimistic. Further, underlying variable is considered as independent. However, in reality it may not be the condition. In this section the variable is taken as the selling quantity and its sensitivity will be analysed with regard to the NPV.

 Sales volume Amount Changes Changes \$                      - 25000 \$  22,354,148.82 45000 \$  24,800,337.66 20000 2,446,188.84 65000 \$  27,246,526.50 20000 2,446,188.84 85000 \$  29,692,715.34 20000 2,446,188.84 105000 \$  32,138,904.18 20000 2,446,188.84 125000 \$  34,585,093.02 20000 2,446,188.84 145000 \$  37,031,281.86 20000 2,446,188.84 165000 \$  39,477,470.70 20000 2,446,188.84 185000 \$  41,923,659.54 20000 2,446,188.84 205000 \$  44,369,848.38 20000 2,446,188.84 225000 \$  46,816,037.22 20000 2,446,188.84 245000 \$  49,262,226.06 20000 2,446,188.84 265000 \$  51,708,414.90 20000 2,446,188.84 285000 \$  54,154,603.74 20000 2,446,188.84
 Changes in quantity 22% Changes in NPV 8% Sensitivity 36.83%

From the above it can be identified that the output that is the NPV increases with the increase in the input that is selling quantity. As per the above table and graph with the selling quantity ranged from 25000 to 285,000 the NPV is increased from \$ 22,354,148.82 to \$ 54,154,603.74. Thus, there is a change of \$ 24,46,188.84 in the NPV with every 20000 increase in the selling quantity. In other words, for every 22% changes in the selling quantity there is 8% change in the NPV. Therefore the resultant sensitivity is 36.83%. Therefore, there is positive correlation between the input and output (Iooss and Lemaître 2015). To be more specific, with the increase in input that is selling quantity there is an increase of output that is NPV. However, the NPV is moderately sensitive with regard to changes in the selling price (Butler et al. 2015). Therefore, if the decision is made with regard to the sensitivity of selling quantity with the NPV, the decision maker shall keep in mind that there is positive correlation among the 2 factors that is for earning more NPV the selling quantity is to be increased.

## Internal rate of return

However, the sensitivity analysis gives the appropriate insight with regard to the issues associated with reference model that is to take decision regarding the project.  Moreover, the decision maker gets the idea regarding how the output (NPV in the given case) is sensitive to changes in the input (selling quantity in the given case) and he can analyse the optimum solution based on the sensitivity (Levy 2015).

Conclusion

From the above discussions it can be concluded that Booli Enterprise shall produce New SSHA model. The decision is taken based on the factors that the NPV of the project is positive that is \$ 30,548,881.41. Further, the payback period of the project is 2.14 that is less than 5 years. Moreover, the IRR of the project is 19.77% that is more than the required rate of return that is 12%. Therefore, new SSHA model shall be produced.

If owing to taking up the new SSHA project the company loses sales on other project then the loss shall be included in the cost of initial investment. if including the loss leads to negative NPV then new SSHA project shall not be taken up. However, if even after including the SSHA project the NPV remains positive then the new SSHA shall be produced.

Reference

Arrow, K., Cropper, M., Gollier, C., Groom, B., Heal, G., Newell, R., Nordhaus, W., Pindyck, R., Pizer, W., Portney, P. and Sterner, T., 2013. Determining benefits and costs for future generations. Science, 341(6144), pp.349-350.

Baucells, M. and Borgonovo, E., 2013. Invariant probabilistic sensitivity analysis. Management Science, 59(11), pp.2536-2549.

Brooks, R., 2015. Financial management: core concepts. Pearson.

Butler, M.P., Reed, P.M., Fisher-Vanden, K., Keller, K. and Wagener, T., 2014. Identifying parametric controls and dependencies in integrated assessment models using global sensitivity analysis. Environmental modelling & software, 59, pp.10-29.

Gallo, A., 2014. A refresher on net present value. Harvard Business Review, 19.

Iooss, B. and Lemaître, P., 2015. A review on global sensitivity analysis methods. In Uncertainty management in simulation-optimization of complex systems (pp. 101-122). Springer, Boston, MA.

Leung, B., Springborn, M.R., Turner, J.A. and Brockerhoff, E.G., 2014. Pathway?level risk analysis: the net present value of an invasive species policy in the US. Frontiers in Ecology and the Environment, 12(5), pp.273-279.

Levy, H., 2015. Stochastic dominance: Investment decision making under uncertainty. Springer.

Leyman, P. and Vanhoucke, M., 2016. Payment models and net present value optimization for resource-constrained project scheduling. Computers & Industrial Engineering, 91, pp.139-153.

McAuliffe, R.E., 2015. Net Present Value. Wiley Encyclopedia of Management, pp.1-1.

Pasqual, J., Padilla, E. and Jadotte, E., 2013. Equivalence of different profitability criteria with the net present value. International Journal of Production Economics, 142(1), pp.205-210.

Yuniningsih, Y., Widodo, S. and Wajdi, M.B.N., 2017. An analysis of Decision Making in the Stock Investment. Economic: Journal of Economic and Islamic Law, 8(2), pp.122-128.

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