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## Answer:

### Introduction

The corporate financial management entails various business decisions including investments, financing and the return on the investment and thus, become crucial to take action on commercial wellness. The current study is based on a case of a machinery replacement where the report comprises of the projection of the initial investment, required for the new machinery installation, operating cash flow calculation and the evaluation of the viability of the same. In addition, the investment appraisal techniques have been implemented followed by the sensitivity analysis to deliver the information whether the project could be undertaken. The key purpose of this study is to recommend on the project selection along with the justification, using valid investment appraisal mechanism.

### Incremental initial investment

Initial incremental capital | Amount ($) |

Acquisition cost of new machine | 1000000 |

Sale proceeds of old machine | 100000 |

Tax adjustments on sales of old machine | 60000 |

Additional working capital | 491520 |

Total Initial incremental capital | 1651520 |

The calculation for the initial investment involves the initial cost for the acquisition of new machine, sales proceeds of old machine and the tax adjustments for sale of old machine. The initial incremental investment also involves the calculation for the working capital adjusted with the discounting rate at 10% for 10 years (refer to appendix). Therefore, at the year 0 that is the beginning year, the total initial incremental capital stands at $1651520. In the words of Chemmanur and He (2016, p.72), the total initial incremental capital for an investment is used in the calculation of the net present value, internal rate of return etc for the investments. This further helps in the making the investment decision pertaining to the investments.

### Incremental after tax operating cash flow

Annual incremental operating cash flow | |||

Yearly incremental operating expenses ($) | Discounting factor | Discounted incremental operating expenses ($) | |

year 1 | 78000 | 0.909 | 70902 |

year 2 | 78000 | 0.826 | 64428 |

year 3 | 78000 | 0.751 | 58578 |

year 4 | 78000 | 0.683 | 53274 |

year 5 | 78000 | 0.621 | 48438 |

year 6 | 78000 | 0.564 | 43992 |

year 7 | 78000 | 0.513 | 40014 |

year 8 | 78000 | 0.467 | 36426 |

year 9 | 78000 | 0.424 | 33072 |

year 10 | 78000 | 0.386 | 30108 |

Total Annual incremental operating cash flow | 479232 |

The annual incremental operating expenses involves calculations for the increase in the sales, increase in operating expenses and depreciation. In the opinion of Gao and Zhang (2015, p.110), the calculation for the annual incremental operating cash flow helps in the calculation of net present value as it reduced the net cash inflow making the net present value more realistic. In the present context, the annual incremental operating cash flow has been calculated using the following formula:

Annual incremental operating cash flow = (increased sales - increased operating expenses - increased depreciation) * (1 - tax rate) + increased depreciation.

### Incremental terminal cash flow

Particulars | Amount ($) | Discounting factor (10%, 10) | Amount ($) |

Incremental salvage value | 100000 | 0.386 | 38600 |

tax on incremental salvage value | 30000 | 0.386 | 11580 |

Total incremental salvage value | 70000 | 0.386 | 27020 |

The incremental terminal cash flow involves calculation for the incremental salvage value after making the adjustments for the prevailing tax rate.

### NPV, IRR and Profitability Index for the replacement proposal

Net present value

Incremental Sales ($) | Discounting factor | Discounted incremental sales ($) |

450000 | 0.909 | 409050 |

450000 | 0.826 | 371700 |

450000 | 0.751 | 337950 |

450000 | 0.683 | 307350 |

450000 | 0.621 | 279450 |

450000 | 0.564 | 253800 |

450000 | 0.513 | 230850 |

450000 | 0.467 | 210150 |

450000 | 0.424 | 190800 |

450000 | 0.386 | 173700 |

Total Incremental sales | 2764800 |

Net present value ($) | 661068 |

The net present value in the present case has been calculated by adding up the cash inflows for the new machines and then subtracting the cash outflows. Therefore, in the present case, the cash flows are assumed the total incremental sales and the net salvage value of the new machine at the end to 10th year at 10% discounting rate. While on the other hand, the cash outflows for the new machine involves the total initial incremental expenses and the increased operating cash outflows. In the words of Brealey et al. (2015, p.17), the investment decisions pertaining to the new investments must be taken based on the net present value. The net present value calculation takes into consideration time value of money while also calculating the future cash inflow. Based on the net present value the company has been recommended to invest in the new machine, as it would prove to be beneficial for the company.

### Internal rate of return

Incremental initial investment ($) | -1651520 |

Annual incremental operating expenses ($) year 1 | 372000 |

year 2 | 372000 |

year 3 | 372000 |

year 4 | 372000 |

year 5 | 372000 |

year 6 | 372000 |

year 7 | 372000 |

year 8 | 372000 |

year 9 | 372000 |

year 10 | 372000 |

Total incremental salvage value ($) | 100000 |

IRR | 19% |

The calculation for the internal rate of return involves annual incremental cash inflow at subtracting the cash inflow from sales by the annual incremental operating expenses. In the given case scenario, the cash flow from the sales is $450000 per annum and the annual incremental operating expenses is $78000 (refer to appendix). The total incremental salvage value of $100000 at the end of the 10th year has also been considered for internal rate of return calculation. The internal rate of return for the new machine is 19%, which is greater than the required rate of return of 10%. Therefore, the company has been recommended to invest in the new machine, as it would help the company to increase its profit potential.

Profitability index

Profitability index | 1.40 |

The profitability index for the new machine is 1.40. This means that the net cash flow from the investment is 1.4 times greater than the initial investment in the machine. The profitability index for the new machine has been made on the below stated formula:

Profitability index = present value of future cash flows / initial investment

In the present case scenario, the present value of the cash inflow involves net present value of sales plus total incremental salvage value subtracted by annual incremental operating expenses.

### Sensitivity analysis of NPV

As mentioned by Huang and Petkevich (2016, p.73), the sensitivity analysis of the net present value helps in evaluating the exact internal rate of return which in turn helps in investment decision making.

At 10%

At 10% | |

Total Initial incremental capital | 1651520 |

Total incremental salvage value | 27020 |

Total Incremental inflow | 2285568 |

At 30%

At 30% | |

Total Initial incremental capital | 1407280 |

Total incremental salvage value | 15890 |

Total Incremental inflow | 1149852 |

At 10% discounting factor the initial incremental capital is $1651520 and the total incremental salvage value is $27020. While on the other hand, at 30% discounting factor the initial incremental capital is $1407280 and the total incremental salvage value is $15890.

At 10% | |

NPV | 661068 |

At 30% | |

NPV | -241538 |

Based on the net present value at different rate of return it can be concluded that when the rate of return increases the net present value starts decreasing. This net present value at different discounting rate helps in the evaluation of the internal rate of return.

Sensitivity analysis of NPV | ||

Discount rate | 10% | 30% |

NPV ($) | 661068 | -241538 |

10 - IRR / 10 - 30 | (661068 - 0) / (661068 - (-241538)) | |

10 - IRR/ - 20 | 661068 / 902606 | |

10 - IRR / - 20 | 0.7323992971 | |

10 - IRR | - 14.64798594 | |

- IRR | - 24.64798594 | |

IRR | 24.65% |

The sensitivity analysis involves the discounting of the initial investments and cash flow on at various rate of return. This helps in evaluating the net present value at different discounting rate. The calculation for the internal rate of return involves use of one positive and one negative NPV. These are then applied to the sensitivity analysis for NPV formula to generate the IRR of the investment. In the present case scenario, the discounting ate for the positive net present value has been assumed 10%. While on the other hand, the discounting are for the negative NPV has been calculated at 30% after using the trial and error method. The trial and error method involves calculation for negative NPV based on the discounting rate of 16% and 20% respectively (refer to appendix). At 10% and 30% discounting rate for the present case scenario, the IRR is 24.65%. Therefore, meaning that the investment in the new machine would be profitable for the company.

### Theoretical background of the three investment decision methodologies

In the current case of investment decision making, the evaluation for the investments decision have been made based on the results of the net present value, internal rate of return and profitability index. As mentioned by Ross et al. (2015, p.66), the net present value is considered as the most effective and efficient investment appraisal tool. The reason behind this is that the calculation for the net present value involves calculation for the time value of money. In this context, Brooks et al. (2016, p.217) stated that the net present value calculation also taken into consideration the future cash inflows while discounting them to present rate. This discounting at the present rate makes the investment decision making much more easier and relevant. However, Huang and Petkevich (2016, p.72) argued stating that the net present value calculation are ineffective in case of two different project of two different sizes. The reason behind this is that the NPV calculation results are highly influenced by the inputs thus making it ineffective in case of two different sizes projects.

The internal rate of return is simpler to use as compared to other investment appraisal techniques. Like the net present value, the internal rate of return also takes into consideration the time value of money while helping in mitigating the hurdle rate. However, Goldstein and Hackbarth (2014, p.534) argued that the calculation for the internal rate of return do not take into consideration the economies of scale thus, making the calculation not dependable. Moreover, the internal rate of return cannot be taken into consideration while deciding two mutually exclusive projects. The reason behind this is that the internal rate of return calculations taken into accounts the rate of return while ignoring the return on investments. In this context, Ross et al. (2015, p.65) stated that the internal rate of return calculations shows the return on the total money invested.

The profitability index calculations like the NPV and IRR takes into account the time value of money thus, making the investment decision more meaningful. Moreover, the calculation of the profitability index takes into account all the cash flows for the entire life while ascertaining the exact rate of return for the investments. In this context, Prezas and Simonyan (2015, p.105) added that the profitability index calculations are more relevant as the calculations involve different amount cash flows for different projects. While on the other hand, Hanousek et al. (2015, p.27) stated that in case of profitability index, it is difficult to understand the discounting rate as the cash flow and initial investments are shown at cumulative value. Huang and Petkevich (2016, p.71) agreed to this and further added that the calculation for the profitability index are difficult in case there are useful life of the projects differ from one another.

### Reason behind these being superior to ARR and payback period

The calculations for the investment decision making in the present case scenario are based on the calculations of net present value, internal rate of return and profitability index. The reason behind choosing these tools of investment decision making is that they take into consideration the time value of money. Moreover, in the present case the investment decision making is based on identical project that is machines. This justifies the inclusion of the internal rate of return in the investment decision making. Moreover, both the machines in the present case have identical useful life, which makes the profitability index outcome more relevant. Furthermore, the net present value takes into consideration the risks pertaining to future cash flows, which helps in evaluating the exact amount by which the value of the company would be increased.

The accounting rate of return has been excluded from the investment decision-making calculation because the ARR calculations ignore time value of money. In this context, Brooks et al. (2016, p.218) stated that the accounting rate of return ignores the cash flow from the investments, which makes the outcomes irrelevant. In the present case, the calculation for the investment decision making have taken into consideration the terminal value of the project. However, the accounting rate of return ignores the terminal value of the project thus, leading to exclusion of the investment appraisal tool in the present case. In this context, Goldstein and Hackbarth (2014, p.535) stated that the accounting rate of return calculation are simple and are based on the accounting profit. This calculation on the accounting profit helps in measuring the profit potential that the company might expect from the investment. The fact that the accounting rate of return does not involve time value of money therefore, the accounting results cannot be considered while decision making.

As mentioned by Brealey et al. (2015, p.77), the payback period provide a crude measure about the liquidity of the project assisting in decision-making. The payback period determines the period within which the initial investment in the project can be recovered. The outcome of the payback period between two different projects can be used for determining which project would return the initial investment at the earliest. In this context, Gao and Zhang (2015, p.111) cited that the payback period does not involve time value of money therefore, the outcome of this investment decision making tool cannot be considered. Chemmanur and He (2016, p.76) agreed to this and further added that the calculations for the payback period ignores the amount beyond the payback period. Moreover, the payback period does not provide any concrete evidence whether the investment would help in increasing the value of the firm. Therefore, the investment decision making in the present case scenario excludes the payback period calculations.

### Conclusion

From the above calculations and findings, it is quite clear that the investment in the new machine would be profitable for the company. The net present value, internal rate of return and the profitability index are all favourable suggesting that the investment would help the company increase its profit potential. The reason behind the selection of the net present value, internal rate of return and profitability index is that the calculations for these investment tools involve time value of money consideration. Moreover, the project is identical with similar useful life thereby, making the selection of these tools more relevant. However, the accounting rate of return and the payback period have also been excluded because; the methods do not consider time value of money. While on the other hand, the calculations based on these tools do not consider all the cash flows.

### Recommendation

The company has been recommended to consider investing in the new machines as the capital investment decision making tools provide favourable outcomes. This means that the investment in the new machine worth $1000000 would help to increase the profit potential of the company. Moreover, the company has also been recommended to continue evaluation of the investment decision making based on the NPV, IRR and profitability index as because they take into consideration time value of money and entire cash flow.

## Reference list

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Brooks, C., Godfrey, C., Hillenbrand, C. and Money, K. (2016). Do investors care about corporate taxes?. Journal of Corporate Finance, 38, pp.218-248.

Chemmanur, T. and He, S. (2016). Institutional trading, information production, and corporate spin-offs.Journal of Corporate Finance, 38, pp.54-76.

Corporate Finance. (2016). South-Western Pub.

Gao, L. and Zhang, J. (2015). Firms’ earnings smoothing, corporate social responsibility, and valuation.Journal of Corporate Finance, 32, pp.108-127.

Goldstein, I. and Hackbarth, D. (2014). Corporate finance theory: Introduction to special issue. Journal of Corporate Finance, 29, pp.535-541.

Hanousek, J., Ko?Ќenda, E. and Shamshur, A. (2015). Corporate efficiency in Europe. Journal of Corporate Finance, 32, pp.24-40.

Huang, K. and Petkevich, A. (2016). Corporate bond pricing and ownership heterogeneity. Journal of Corporate Finance, 36, pp.54-74.

Prezas, A. and Simonyan, K. (2015). Corporate divestitures: Spin-offs vs. sell-offs. Journal of Corporate Finance, 34, pp.83-107.

Ross, S., Westerfield, R., Jaffe, J., Lim, J., Tan, R. and Wong, H. (2015). Corporate finance. [Singapore?]: McGraw-Hill Education (Asia).