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You may solve the following problems algebraically, or you may use a financial calculator or Excel spreadsheet. If you choose to solve the problems algebraically, be sure to show your computations. If you use a financial calculator, show your input values. If you use an Excel spreadsheet, show your input values and formulas.

Question 1:
oProficient-level: Describe the Net Present Value (NPV) method for determining a capital budgeting project's desirability. What is the acceptance benchmark when using NPV?
oDistinguished-level: Identify the NPV method's strengths and weaknesses.
Question 2:
oProficient-level: What is the payback period statistic? What is the acceptance benchmark when using the payback period statistic?
oDistinguished-level: Identify what problem of the Payback Period method is corrected by using the Discounted Payback Period method.
Question 3:
oProficient-level: Describe the Internal Rate of Return (IRR) method for determining a capital budgeting project's desirability. What is the acceptance benchmark when using IRR?
oDistinguished-level: Explain how the NPV and IRR methods are similar and how they are different.
Question 4:
oProficient-level: Describe the Modified Internal Rate of Return (MIRR) method for determining a capital budgeting project's desirability. What are MIRR's strengths and weaknesses?
oDistinguished-level: Explain the differences in the reinvestment rate assumption that distinguishes MIRR from IRR.
Question 5:
oProficient-level: Compute the NPV statistic for Project Y and tell [advise] whether the firm should accept or reject the project with the cash flows shown in the chart if the appropriate cost of capital is 10 percent.
Distinguished-level: Explain how decreases in the cost of capital lead to an increase in the number of approved projects.

## The Net Present Value Method

The net present value (NPV) method for calculating the capital budget of a particular project is the ideal procedure. The business owners should use this process while evaluating whether to invest or not in a particular business or not. It gives the most accurate form of mathematical point of view and time value for money point of view solution (Roise et al., 2016). The NVP method gives more correct than the profitability index and internal rate of return process of capital budget evaluation.

The net present value method is generally used when the capital investment project are large in terms of scope and money. In Net Present Value analysis, the discounted cash flows are used. It considers both risk and time variables. The cash flows are forecasted are delivered by a project discounting them back to the present value with the use of time span of the project and the weighted average cost of capital of the firm.

The benchmark to determine the acceptance of the project is when the result is positive then the firm should invest in the project and if it is negative, the firm should rethink.

The main advantage of NPV is that it considers the idea that the future value is less than the present value (Gabriel Filho et al., 2016). Therefore, the cash flows are discounted by the capital cost of another period. The NVP also helps to understand whether an investment will be beneficial for a company or not .It also takes the amount by which the business decision will increase the firm’s value. The final advantage of NPV is that it takes into account both the cost and the risk in the project.

The biggest limitation of using the Net Present Value method requires a lot of assumptions and guesswork about the firms cost of capital.id the cost of capital taken in hand is too low then the result of investment may not me optimal whereas if the assumed cost of capital is too high the result in investment is good (Schmidt, 2015). Moreover, the NPV is not a useful method to compare the two projects with different size as the unit id the NPV result is in terms of money and size of the input cannot be determined.

The payback period statistic helps in decision-making process of the firms and the accuracy of the rate of return on the investment. The payback period refers to the amount of time required to recover the investment cost (Roise et al., 2016). The payback period helps go determine the decision whether or not a firm should undertake a project or not (Ross et al., 2014). The payback period of capital budgeting ignores the time value for money unlike other methods like internal rate of return discounted cash flow and net present value.  In the process of payback period the number years covered to recover the investment of fund is considered.

The benchmark to understand the desirability of a business is the length of the payback period. The longer the payback period the lesser desirable is the project (Schmidt, 2015).

The problem, which is faced in the method of pay back period, is that, it does not take into account the time value for money. The discounted payback method sums up the present values of the cash flows until zero is reached.

The internal rate of return is similar to decision-making process of that of NPV. While calculating the NPV, the present value of the cash flow is summed up at particular interest rate (Gabriel Filho et al., 2016). The IRR refers to that interest rate. The NPV equals the main cause to zero. It determines the profitability and potentiality of the investments.

The benchmark of IRR is that if the Cost of Capital is more or equal to the project, the project with high IRR is approved. If the IRR is lower than the cost of capital, the project with lower IRR is approved (Schmidt, 2015).

The similarity between NPV and IRR is that both of them consider the time value for money. For independent investment proposals, where there is no competition with each other, the result of both NPV and IRR is same (Gabriel Filho et al., 2016). Similarly, in investment proposals that involve cash outflows in the initial period followed by series of inflow, the result under both methods is the same.

The dissimilarities between the two are shown in the following table:

 NET PRESENT VALUE METHOD INTERNAL RATE OF RETURN METHOD · The determination of the discount rate is by discounting of the future cash flows of a project. · It gives importance to the market rate of interest. · Cash inflows are reinvested at the cost of capital or cut off rate. · The discount rate is not determined beforehand under this process. It is calculated on trial and error basis. · It does not consider any market rate of interest but invests at maximum rate of interest (Gabriel Filho et al., 2016). · Cash inflows are reinvested at internal rate of return.

The modified internal rate of return is a process to rank the investment projects of unequal size. It assumes that positive cash flows are reinvested at the cost of capital of the firm and the initial outflows of cash are financed at the cost of the firm. The MIRR is the most accurate form of calculating the cost and profitability of any investment project (Gabriel Filho et al., 2016).

The advantage of the MIRR is that it is a better and improved method for evaluating a project. It takes care of all the shortcomings of the IRR and NPV method of calculation. Moreover, it is easily understandable as it takes into account the possible reinvestment rate.

The disadvantage of MIRR is that it asks for both financing rate and cost of capital. It involves two additional decisions that may lead to confusion. The managers may hesitate in involving two different estimates (Gabriel Filho et al., 2016).

MIRR does not assume that all cash flows will be re-invested in projects with the same rate of return that IRR does. This is the point of difference between the two. The MIRR would help in comparison to other projects in a better way.

Computation of NPV of project Y:

NPV = C x {(1 - (1 + R)-T/ R} − Initial Investment, where C is the expected cash flow per period, R is the required rate of return, and T is the number of periods over which the project is expected to generate the income.

 year PV of 10% (1 - (1 + R)-T) / R) Cash flow (in \$) PV of Cash flow 0 1 -6000 -6000 1 .9090 3350 3045.15 2 0.82640 4180 3454.352 3 0.7513 1520 1141.976 4 0.6830 300 204.9 NPV= 9692.756

The NPV calculated in project Y is positive, therefore, the firm could undertake the project as the market value of the firm would enhance by the amount of the NPV.

If the firm encounters a decrease in the cost of capital, it would invest more in long-term projects. This would allow the companies enhance its debt to equity.

Payback Period = years full recovery + unrecovered cost at beginning of last year
cash flow in following year

computation of payback period:

 year Cash flow(in \$) Cumulative cash flow( in \$) 0 -1450 1 250 -1200 2 380 -820 3 620 -200 4 1000 800 5 100 900

The payback period lies between year 3 and year 4, which can be taken as 3.2 years. There is a \$200 of investment yet to be made and there is a projection of \$1000 at the end of year 4.It can be hereby assumed that there is similar monthly amount of flow of cash in year. That implies that the business has a payback of 3.5 years. Therefore, the project is desirable.

If the discounted payback period is calculated it would always be greater than the non discounted payback period if the cash flow is positive.

References

Gabriel Filho, L. A., Cremasco, C. P., Putti, F. F., Goes, B. C., & Magalhaes, M. M. (2016). Geometric Analysis of Net Present Value and Internal Rate of Return. Journal of Applied Mathematics & Informatics, 34, 75-84.

Roise, J. P., Harnish, K., Mohan, M., Scolforo, H., Chung, J., Kanieski, B., ... & Shen, T. (2016). Valuation and production possibilities on a working forest using multi-objective programming, Woodstock, timber NPV, and carbon storage and sequestration. Scandinavian Journal of Forest Research, 31(7), 674-680.

Ross, S. A., Westerfield, R., & Jaffe, J. F. (1990). Corporate finance (Vol. 2). Homewood: Irwin.

Schmidt, R. (2015). How to Use the Modified Internal Rate of Return (MIRR), PropertyMetrics.

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