Question 1: Annual sales revenue and costs (other than depreciation)

 Year 1 Year 2 Year 3 Year 4 Units 1350 1350 1350 1350 Unit price \$200 \$206 \$212.18 \$218.55 Unit cost \$100 \$103 \$106.09 \$109.27 Sales \$270000 \$278100 \$286443 \$295036.3 Cost \$135000 \$139050 \$143221.5 \$147518.1

The market interest rate, which is the cost of capital, has a premium for inflation. Without the premium for inflation, the real interest rate will be less than the nominal interest rate. This will result in a nominal cash flow, which is greater than real cash flow since nominal cash flow incorporates inflation. Discounting the real cash flow at the nominal interest rate will result in a low net present value.  Thus, it is realistic to discount the real cash flow at the real interest rate and nominal cash flow at the nominal interest rate (Baker & English, 2011). It is much more realistic to calculate the nominal cash flow than to reduce the nominal interest rate to real interest rate.

Question 2: Annual incremental operating cash flow statements

 Year 1 Year 2 Year 3 Year 4 Units 1,350 1,350 1,350 1,350 Unit price \$200.00 \$206.00 \$212.18 \$218.55 Unit cost \$100.00 \$103.00 \$106.09 \$109.27 Sales \$270,000 \$278,100 \$286,443 \$295,036 Costs 135,000 139,050 143,222 147,518 Depreciation 99,990 133,350 44,430 22,230 Operating income before taxes (EBIT) \$35,010 \$5,700 \$98,792 \$125,288 Taxes (40%) 14,004 2,280 39,517 50,115 EBIT (1 – T) \$21,006 \$3,420 \$59,275 \$75,173 Depreciation 99,990 133,350 44,430 22,230 Net operating CF \$120,996 \$136,770 \$103,705 \$97,403

Annual Cash Flows due to Investments in Net Working Capital

 Year 0 Year 1 Year 2 Year 3 Year 4 Sales \$270,000 \$278,100 \$286,443 \$295,036 NWC ( 40% of sales) 40,500 41,715 42,966 44,255 CF due to investment in NWC) (40,500) (1,215) (1,251) (1,289) 44,255

After-tax salvage cash flow

 Salvage value \$25,000 Book value 0 Gain or loss \$25,000 Tax on salvage value (@ 40%) 10,000 Net terminal cash flow \$15,000

Question 3: projected Net cash flows

 Year 0 Year 1 Year 2 Year 3 Year 4 Long Term Assets (\$300,000) 0 0 0 0 Operating Cash Flows 0 \$120,996 \$136,770 \$103,705 \$97,403 CF due to investment in NWC (40,500) (1,215) (1,251) (1,289) 44,255 Salvage Cash Flows 0 0 0 0 15,000 Net Cash Flows (\$340,500) \$119,781 \$135,519 \$102,416 \$156,658

NPV = ∑ {Net Period Cash Flow/ (1+R)^T} – Initial Investment

=  (\$119,781/(1+0.12)1 )+(\$135,519/(1+0.12)2 )+(\$102416/(1+0.12)3)+(\$156,658/(1+0.12)4)-\$340,500

= \$46,939

IRR

IRR is the interest rate at which the net present value is equal to zero

IRR = 18.2%.

MIRR = (FVCF(c) / PVCF (fc)) ^ (1 / n) -1

= 15.7 %

Payback Period

 Years 0 1 2 3 4 Cash Flow (\$340,500) \$119,781 \$135,519 \$102,416 \$156,658 Cumulative Cash Flow for Payback (\$340,500) (\$220,719) (\$85,200) \$17,216 \$173,874

Payback Period= 2.8 Years

The net present value rule indicates that a project is acceptable if the NPV is positive. In this case, the NPV is positive. The IRR rule, on the other hand, considers the value of IRR and the WAC. If IRR exceeds the WAC, then the project should be undertaken. IRR in this scenario is 18.2%, and WAC is 12%. Thus, the IRR exceeds WAC, and the project is fit to be undertaken. The MIRR rule is similar to that of IRR. Since MIRR is greater than the cost of capital, the project is accepted (Baker & English, 2011).  The payback period is less than the economic life of the machinery. The project will have paid back in 2.8years while the economic life of the machine is four years. This indicates that the project is profitable and thus acceptable. All the rules of capital budgeting indicate that this project should be accepted.

Question 4: Risk

In the context of capital budgeting, a risk is a possibility of an investments actual returns being lower than the expected return. Risk involves losing some of the investment or the entire investment.  The standard deviation measures the risk of specific investment or the average returns of the historical returns (Rüschendorf, 2013).  A high standard deviation is a sign of a high degree of risk. Risk quantification occurs through attaching some probabilities to the happenings of negative events. If it is certain that, an event cannot occur, it gets a probability of zero, and if certain it will occur, it gets a probability of one. The probabilities of 0 and 1 only occur when the risk is certain. When the risk is uncertain, the probability assigned is between zero and one. Maximum risk occurs when there is maximum uncertainty at the probability of 0.5.

Some types of project, historical data is very significant in assessing risk. The use of historical data is common when the investment involves an expansion. A company looking to expand can use its historical data to assess the risk involved.  For a new business, a company can look at the historical data of other companies in the same line of business and assess risk. In some instances, historical data may not be available. In such a case, a company will have to depend on the judgment of the executives. Besides, some of the statistics used in analyzing historical data have its basis on subjective judgment. The availability of data determines the method used to quantify risk.

Question 5: Sensitivity Analysis

Sensitivity analysis is a technique used to determine how different values of an independent variable impact on a dependent variable under some given assumptions. It is a way of predicting the outcome of a decision made given a range of variables. It shows how a change in one variable affects the outcome. Capital budgeting incorporates sensitivity analysis to unearth the possible relationships between a project and profitability, sales, liquidity and the overall capital management of the entity.

1. A) Primary weaknesses

Among the major weaknesses of sensitivity analysis is that it is irrelative in nature. It only considers the extent of a change and not the probability of that change occurring. In addition, in standalone form, it offers no solution. The information it provides requires further analysis and interpretation to reach a decision (Baker & English, 2011). It also assumes that variables can change independently of other variables.

1. B) Primary usefulness

Sensitivity analysis is very simple and is a source of information to direct the managements’ planning efforts. Through its application, information becomes available to the management in a form that guides professional decision-making. In addition, it identifies areas where the management needs to concentrate in to attain the overall goal of the organization. The technique is significant in checking for quality (Baker & English, 2011). When the management know which variables are crucial to the success of a project, then they can b able to intensify the success of the project.

Sensitivity Analysis Diagram

 Deviation NPV Deviation from Base Case from Units Base Case WACC (r) Sold Salvage -30% \$173,928 \$14,687 \$125,079 -15% 159,237 59,392 126,509 0% 145,337 104,096 127,939 15% 132,172 148,801 129,369 30% 119,693 193,505 130,799 Range \$54,235 \$208,193 \$5,720

A steep sensitivity line shows a greater risk. Along the line, a small change in any variables results to a decline in the net present value. From the graph above, the units sold line is steep than the interest rate and salvage value lines. This shows that a small change in estimated sales leads to a large decline in the net present value. This shows that Sydney Johnson needs to worry more about the accuracy of estimating and forecasting sales.

Question 6:

 Scenario Probability Unit Sales Unit Price NPV Best Case 25% 2,000 \$220 \$278,940 Base Case 50% 1,350 \$200 \$88,010 Worst Case 25% 1,000 \$150 (\$48,527) Expected  NPV = \$ 101,608 σ = \$116,573 CV = σ/Expected NPV =   1.15

Question 7: Scenario Analysis

This is a technique for approximating the expected returns of a project after a specific period. It assumes that a definite change in the key project factors occurs. Commonly, the technique helps in estimating the changes in the value of an investment after unfavorable conditions. The analysis involves determining the expected returns at diverse rates of reinvestment. By using the principles in statistics and mathematics, the technique provides a basis to estimate the changes in the investment value after the occurrence of a different situation rather than the expected situation (Amer, Daim, & Jetter, 2013). Scenario analysis usually considers three outcomes, which are the best case, most likely case, and worst case.

Scenario analysis is significant in that it presents the stakeholders and interested parties with an avenue to discuss critical questions. It also offers a shift from what is certain to what could happen. It makes it possible to establish the foreseeable outcomes and explore them. In addition, it encourages creativity. When defining scenarios, it encourages thinking about possibilities instead of what can happen. This kind of thinking can generate creative ideas and solutions to issues that arise in the future. However, it can oversimplify an issue given that the analysis has to balance with the time and resources available. Again, scenario analysis just generated ideas, which need to be put into practice.

Question 8: Simulation Analysis

Simulation analysis is a technique of financial analysis, which uses spreadsheets or interactive systems. The uncertain cash flow variables are entered as probability distribution parameters continuously rather than point values. Values for the uncertain variables are selected with a random number generator, which is then combined, and the NPV calculated. This result in a distribution of NPV based on the sample of values selected. The computer software can generate graphs and other statistics, which the decision makers can use to make decisions (Lee et al., 2009). Simulation analysis allows investors to convert an investment chance to a choice. Its major advantage is that it can factor in different values for various inputs. In addition, it is also very refined on that computer a computer software cam does not make mistakes. However, its use has a limit by the fact that managers are unable to specify the variables resulting in variables limited values (Zio, 2013). Another disadvantage is that simulation tends to assume the probability of extreme events such as a financial crisis.

Question 9:

This project has a coefficient of variation of 1.15, which is above the average variation range 0.2 to 0.4. This places the project in the high-risk category since it has a high coefficient of variation that the common project. The coefficient of variation measures the stand-alone risk. The stand-alone risks assume that a company’s project is pursuing a single asset separate from other assets. Therefore, it is measured by the variability of the single project. It is a measure of the variability of the expected returns

Question 10

The project has a risk, which is above average. The adjusted cost of capital, in this case, would be 17 percent. At this rate, the NPV is \$89,421whcih is still acceptable. Therefore, the risk-adjusted cost of capital yields an acceptable NPV. Thus, the new line is acceptable.

Question11: Other Subjective Risk Factors

The numerical analysis to determine the risk involved cannot cover all the risk factors involved in a project. A risk such as a costly lawsuit can make the project riskier. In addition, there is the possibility of the project assets can be deployed within the company. Due to these factors, the project can be risky than the analysis indicates.

References

Amer, M., Daim, T. U., & Jetter, A. (2013). A review of scenario planning. Futures, 46, 23-40.

Baker, H. K., & English, P. (2011). Capital budgeting valuation: Financial analysis for today’s investment projects. Hoboken, NJ: Wiley.

Lee, A. C., Lee, J. C., & Lee, C. F. (2009). Financial analysis, planning & forecasting: Theory and application. Singapore: World Scientific.

Rüschendorf, L. (2013). Mathematical risk analysis. Springer Ser. Oper. Res. Financ. Eng. Springer, Heidelberg.

Zio, E. (2013). The Monte Carlo simulation method for system reliability and risk analysis (p. 198p). London: Springer.

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