10-3 Explain why the NPV of a relatively long-term project, define as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in the cost of capital than is the NPV of a short-term project.

Answer: NPV assumes that project’s cash flows are discounted in companies cost of capital. Long-term projects are more sensitive to change in cost of capital than short-term projects. It is because higher the term to maturity lesser the discounted cash flow of the project. For example, Project X has maturity period 5 years and Project Y has maturity period of 10 years, both have 10% of cost of capital, and both have $500 cash flow every year. Then,

Cash flow for Project X = (454.54 + 413.22 + 375.65)

Cash flow for Project Y = (454.54 + 413.22 + 375.65 + 341.53 + 310.37)

Now, when cost of capital increase from 10% to 12%

Cash flow for Project X = (446.42 + 398.72 + 355.87)

Cash flow for Project Y = (446.42 + 398.72 + 355.87+ 318.97 + 284.09)

As it can be seen in the example, the value of cash flow of $500 is getting lower and lower year after year. Again when cost of capital increases from 10% to 12% the value of discounted cash flow of $500 is lower more. As it can be noticed, when cost of capital rises from 10% to 12% the discounted cash flow for the short term project also reduce but not as lower as for long term project and since they have short-term maturity the effect will be lower. Therefore, long-term projects higher percentages of cash flows are expected and more sensitive to change in interest rate.

10- 4 Explain why, if two mutually exclusive projects are being compared, the short-term project might have the higher ranking under the NPV criterion if the cost of capital is high, but the long-term project might be deemed better if the cost of capital is low. Would changes in the capital ever cause a change in the IRR ranking of two such projects?

Answer: Mutually exclusive projects are those on which it is necessary to choose either project one or project two, or reject both project, but both project cannot be accepted at a time. Long-term projects are more sensitive to changes in the cost of capital than short- term project. Therefore short-term project might have higher rank under the NPV criterion if the cost of capital is high. While if cost of capital is lower, a project with long term maturity will be ranked better as total sum of cash flows of long term project will be higher than short term project.

Yes the change in the capital does cause a change in the IRR ranking of two such projects. For that capital should be change for two of those projects. If capital change for only short term or only long term project then IRR ranking may not change.

10- 5. In what sense is a reinvestment rate assumption embodied in the NPV, IRR, and MIRR methods? What is the assumed reinvestment rate of each method?

Answer: NPV, IRR, and MIRR are rate of return that enables firm or project to identify whether or not to accept project or not. All of those techniques have different assumption but their objective is the same. Out of all these three, NPV is the best. NPV is based on discounted cash flow technique. Firm’s cost of capital is assumed reinvestment rate of NPV. IRR is the discount rate that makes NPV equal to zero. IRR assumed the cash flows are reinvested at project’s rate of return. Modified Internal Rate of Return assumed that firm’s inflows are compounded at firm’s cost of capital and then determine the discounted rate that makes present value of the terminal value equal to the present value of outflows.

10- 6. Suppose a firm is considering two mutually exclusive projects. One has a life of 6 years and the other a life of 10 years. Would the failure to employ some type of replacement chain analysis bias an NPV analysis against one of the projects? Explain.

Answer: Yes, bias exists in NPV analysis against one of the projects, if firm is considering two mutually exclusive projects and a firm fails to employ replacement chain analysis. Suppose a project that has life of 15 years has more cash flows coming in later years and the project which has a life of 10 years has more cash flow coming in early years than NPV analysis favor the project with maturity period of 10 years but in reality a project that has maturity period of 15 years could be better. Therefore, if firm is analyzing two mutually exclusive projects with different maturity period then they have to employ replacement chain analysis to see the true picture of NPV of both the project. For that a firm could use another project that has maturity period of 5 years and firm can compare first two projects with 10 year maturity and after that 5 year of longer term project with new project.

11-2 Operating cash flows, rather than accounting profits, are listed in Table 12-1. What is the basis for this emphasis on cash flows as opposed to net income?

Answer: Net income basically shows the income which the project or company get after deducting cost of goods sold, selling and general expenses, depreciation, amortizations, interest (if any), and tax from Revenue. In fact net profit is unable to show the real picture of cash available. Operating Cash flows shows the real picture of cash available because in cash flows non cash expenses items such as depreciation and amortization are add back. Further, interest expense is not operating activity; it is financing activity which is not included on operating cash flow. Therefore, company emphasis on cash flows as opposed to net income.

11-3 Why is it true, in general, that a failure to adjust expected cash flows for expected inflection biases the calculated NPV downward?

Answer: According to NPV assumption, all the cash flows are discounted on company’s cost of capital. If company fails to adjust expected inflection on their cost of capital then the cost of capital which the company is using to discount expected cash flows will be lower than the inflection adjusted cost of capital. As company is using lower cost of capital rate (without adjusting inflection on their cost of capital) to discount their cash flows, the discounted cash flow will be higher and calculated NPV (Sum of discounted cash flows – Project initial cost) will be lower.

11-4 Explain why sunk costs should not be included in a capital budgeting analysis, but opportunity costs and externalities should be included.

Answer: Sunk costs are those expenses which have already occurred. These costs do not really affect the decision whether or not to accept the new project. Further, sunk cost is one time cost so it does not increase as the company implements additional projects. Therefore sunk cost should not be included in a capital budgeting analysis. For example, previous years R&D cost of company is sunk cost. Therefore, if company is going to implement project this year R&D cost should be excluded.

Opportunity costs are those cash flows that company could have generated from assets the company already own. Since company has to give up those cash flows to implement another projects, they have to include those cash flows in capital budgeting. For example, if company has one building and company is using that building for their own purpose. Now company is planning to rent that building for $1,000,000 per year. If company rent that building then they have to rent another small building for their own purpose which cost them 500,000. While analyzing this project, they have to include opportunity cost associated with renting new building as cash cost.

Externalities are effects a project has on other parts of the company as well as on the environment. For example, when company introduces new products it may affect the sales volume of other product offered by same company as well as sales volume of its competitors. This effect is also called cannibalization effect, because the new business or new product eats the company’s existing business or product. The lost cash flow should be adjusted on new projects.

11-5 Explain how net operating working capital is recovered at the end of a project life, and why it is included in a capital budgeting analysis.

Answer: In order to support the new projects additional inventories are required and firm gets its additional inventories from its vendors as a result account payable as well as accruals increases. While because of the expansion of company towards new projects company’s revenue also increase and tie up as additional accounts receivable. Therefore, the difference between increase in operating current assets and the increase in operating current liabilities is the change in net operating working capital. At the end of the project’s life all the additional account receivable are collected where as all additional inventories will be used. As all receivable will be collected, all accruals and payable will be paid by the end of projects. In this way new operating working capital is recovered at the end of a project life.

Capital budgeting is the technique of analyzing potential projects. Capital budgeting helps to identify the various cost associated with project, cash flows of projects and ultimately help to make decision whether or not to acquire that project. Since operating working capital (inventories) is essential element of project it is included on capital budgeting analysis.

11-6 Define (a) simulation analysis, (b) scenario analysis, and (c) sensitivity analysis.

(a) Simulation Analysis: Simulation analysis combined both sensitivities analysis and probability distribution together. It is basically a risk analysis technique which uses the computer to simulate future events and to estimates the probabilities and riskiness of projects. Simulation analysis is more advance techniques to analyze risk than scenario analysis and sensitivity analysis.

(b) Scenario Analysis: Scenario Analysis is technique of risk analysis. Scenario analysis help to identify proportion change in NPV with respect to change in one or more input variables, other things held constant. Basically, scenario analysis uses probabilities of changes in the dependent variables with the given change in more than one independent variable at a time.

In scenario analysis, the financial analyst start with base case or most likely set of input variables and request marketing, engineering and other mangers to specify a worst-case scenario (low sales unit, low sales price, high variable and flexed cost) and best case scenario(high sales unit, high sales price, low variable and flexed cost) (Brigham & Ehrhardt, 2009)

(c) Sensitivity Analysis: Sensitivity analysis is a technique that enable to identify the proportion change in NPV with respect to change in an input variable, other things held constant. For example, cash flows of projects are determined by many variables and if one variable could turn out to be different than the expected values, the overall value of cash flow will be different and hence the NPV. Therefore, sensitivity analysis helps firm to calculated NPV with the given change in one variable other things help constant. The variables which can be change one at a time are sales price, variable cost, fixed cost, growth rate, cost of capital and others.

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