Lesson-7

Chapter 11: Cash Flow Estimation and Risk Analysis

1. Answer Questions 11-1 thru 11-11 on pp. 456-457.

2. Submit Problems 11-1 thru 11-6 on pp. 458-459.

Discussion Questions (DQs)

11.1- Solution:

Here given,

a)      Cost of equipment                                   = $9 million

Investment in net operating working capital = $3million

Company’s tax rate (t)                                   =40% =0.40

 Initial investment outlay (NCO)                   =?

We know that,

NCO = cost of equipment + Investment in net working capital

          =$9m + $3m

          =$12m

Therefore, the initial cash outflow of Talbot Industries is $12 million.

b). Last year's  expenses of $50,000 is a sunk cost and it  mainly focuses on incremental investment and operating cash flows rather than focusing on an incremental cash flows. Therefore, it does not change our answer.

c). The sales of the building is an opportunity cost for conducting the project in that building. Therefore, the possible after-tax sale price must be charged against the project as a cost. Hence, it will affect our answer and it will also add $1 million to Initial investment outlay.

………………………………………………………………………………………………………

11.2-Solution:

Here given,

Projected sales                                                = $10 million

Operating costs (not including depreciation) =$7million

Depreciation                                                   =$2million

Interest expenses                                            =$2million

Tax rate (t)                                                     =40%

Now,

First year operating cash flow is calculated as follows:

Particular	Amount
Projected sales	$10m
Less: Operating Costs	$7
Earnings before depreciation and Tax(EBDT)	$3m
Less: Depreciation	$2m
Earnings Before Tax (EBT)	$1m
Less: Tax@40%	$0.4m
Earnings After Tax (EAT)	$0.6m
Add: Depreciation	$2m
Operating Cash Flow	$2.6m

Therefore, from the above calculation, the project's cash flow for the first year is $2.6 million ($2,600,000).

………………………………………………………………………………………………………

11.3-Solution:

Here given

Cost of equipment      =$20million

Depreciation                =80% of the cost of equipment

                                    =0.8 x $20m

                                    =$16m

Sales of equipment      =$5m

Company’s tax rate (t) =40%

Now,

Book value = Cost - Depreciation

                   =$20m -$16m

                    =$4m

Gain on sale of equipment=Salvage value-Book value

                                          =$5-$4

                                          =$1m

Tax liability=Profit × Tax rate

                                    = $1m × 0.40

                                    = $0.4m

Equipment after tax net salvage value= Sales- Tax liability

                                                                        = $5m-$0.4m

                                                                        =$4.6m

Therefore, after tax net salvage value of Allen Air Lines equipment is $4.6 million ($4,600,000).

………………………………………………………………………………………………………

11.4-Solution:

Here given,

Cost of new machine                                     =$40000

After-tax cash flows (CFAT)                         = $9000 per year

Estimated economic life (n)                           = 10 years

Weighted average cost of capital (WACC)   =10%

Marginal tax rate (t)                                       =35%

For Existing Machine,

Net cash outlay (NCO) = Cost of machine

                                      =$40000

Regular CFAT             =$9000 per year

Final year CFAT          = $9000

Now,

Year	Cash Flow	PVIFA@10%	PV
0	-$40000	1	-$40000
1-10	$9000	6.14456	$55301.103
NPV			$15301.10

Therefore, the NPV of Chen Company is $15301.10. And the NPV of new machine is positive. So, it would be better option for the Chen Company to buy and install the new machine.

……………………………………………………………………………………………………..

 11.5-Solution:

Here given,

Life of project (n)                                           = 4 years

 Cost of equipment                                         =$800000

Weighted average cost of capital,WACC (k) = 10%

Tax rate (t)                                                      = 40%

a). Depreciation under MACRS method:

Year	Cost of Equipment	Depreciation rate	Depreciation
1	$800000	33%=0.33	$264000
2	$800000	45%=045	$360000
3	$800000	15%=0.15	$120000
4	$800000	7%=0.07	$56000

Again,

By using straight line method, we have,

Depreciation = Cost -BSV/n

                      = $800000-0/4

                      =$200000 per year

Therefore, the depreciation expense of Wendy under straight line method is $200000 per year.

b). Calculation of Present Value

Year	SLM	MACRS	Differential	Differential Tax @40%	PVIF@10%	PV
1	$200000	$264000	64000	$25600	0.9091	$23272.96
2	$200000	$360000	160000	64000	0.8264	52889.6
3	$200000	$120000	-80000	-32000	0.7513	-24041.6
4	$200000	$56000	-144000	-57600	0.6830	-39340.8
NPV						$12780.16

Therefore, the MACRS depreciation method would produce the higher net present value and it would be $12780.16.

………………………………………………………………………………………………………

11.6-Solution:

Here given

Machine's base price                           =$108000

 Another modification cost                 =$12500

Life of machine (n)                             =4 years under MACRS 3-years class

Salvage value (SV)                             =$65000

Increase in working capital (WC)       =$5500

Operating savings                               =$44000 per year

We know that,

a). NCO= Cost of machine+ Modification cost+ Increase in working capital

            =-($108000 +$12500+$5500)

            =-$126000

Therefore, the net cash outflow for the Campbell Company for capital budgeting purposes is -$ 126000.

b). Calculation of 3 years operating cash flows

Cost of machine = Base price +Modification cost

                            =$10800+$12500

                            =$120500

Depreciation Schedule under MACRS depreciation method is as follows:

Year	Cost	Depreciation Rate	Depreciation
1	$120500	33%	$39765
2	120500	45	54225
3	120500	15	18075

Calculation of Operating Cash Flows is shown in the following table:

Particular	Year 1	Year 2	Year 3
Incremental Savings	$44000	$44000	$44000
Less: Depreciation	39765	54225	18075
Earnings Before Tax(EBT)	4235	=10225	25925
Less: Tax@35%	1482.75	-3578.75	9073.75
Earnings After Tax(EAT)	2752.75	-6646.25	16851.25
Add: Depreciation	39765	54225	18075
Operating Cash Flow	$42517.75	$47578.75	$34926.25

C). Calculation of year 3 CFAT

Sales of Equipment	$65000
Tax Liability( $65000-$8435) X 0.35	-$19797.75
Working Capital Released	$5500
Final Year CFAT	$50702.25

Therefore, the final year CFAT of the Campbell Company is $50702.25.

Working Note:

For calculating accumulated depreciation:

Accumulated depreciation = (45%+33%+15%) × cost of equipment

                                            =93% × $120500

                                            =$112065

And, Book value =Cost-Accumulated depreciation

                            =$120500-$112065

                             =$8435

D). Project's cost of capital (k)     =12%

Calculation of NPV is shown in the following table:

Year	Cash Flow	PVIF@12%	PV
0	-$126000	1	-$126000
1	$42517.25	0.8929	$37963.65
2	$47578.75	0.7972	$37929.78
3	(50702.25+34926.25)=$85628.5	0.7118	$60950.37
NPV			$10843.8

From the above, it is known that NPV of the Campbell Company is positive i.e. $10843.8. So, the company should purchase the machine.

………………………………………………………………………………………………………

References

C. Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi: New Age International Publishers.

Brigham, Eugene F.; Ehrhardt, Michael C. (2014). Financial Management: Theory and Practice (14 ed.). Delhi, India: Cengage Learning.

11-1. Answer:

a.      Project Cash Flow; Accounting Income

 Projected Cash Flow: Cash flow, which is the relevant financial variable, represents the actual flow of cash. Projected cash flow gives an insight regarding the future cash needs as it grows its business activities.

Accounting income: It reports accounting data as defined by Generally Accepted Accounting Principles (GAAP).  It measures the accounting performance from past data to show present status of a company.

b.      Incremental Cash Flow; Sunk Cost; Opportunity Cost; Externality; Cannibalization; Expansion Project; Replacement Project

Incremental Cash Flow: Incremental cash flows are those cash flows that arise solely from the asset that is being evaluated. On other words, it can be defined as additional cash flow that organization receives by operating new projects. A positive incremental cash flow indicates a better sign for an organization so that investing in these projects are beneficial for the company. For example, assume an existing machine generates revenues of $1,000 per year and expenses of $600 per year. A machine being considered as a replacement would generate revenues of $1,000 per year and expenses of $400 per year. On an incremental basis, the new machine would not increase revenues at all, but would decrease expenses by $200 per year. Thus, the annual incremental cash flow is a before-tax savings of $200.

Sunk Cost: A sunk cost is one that has already occurred and it is not affected by the capital project decision. Sunk costs are not relevant to capital budgeting decisions.

Opportunity Cost: An opportunity cost is a cash flow that a firm must forgo to accept a project. For example, if the project requires the use of a building that could otherwise be sold, the market value of the building is an opportunity cost of the project.

Externality:  It refers to the cost or benefits of a transaction to parties who do not directly participate in it. Externality can be either positive or negative. For example, a merger can lead to higher share prices and bonuses for employees, benefiting shareholders and employees at the two companies merging, this can create wealth and positively impact a community.

Cannibalization: Cannibalization is a phenomenon that results when a firm develops a new product or service that steals business or market share from one or more of its existing products and services. Thus one product may take sales from another offering in a product line. Although the idea of cannibalization may seem primarily negative, it also has some positive implications.

Expansion Project: A new expansion project is defined as one where subtracting the firm invests in new assets to increase sales. Here the incremental cash flows are simply the cash inflows and outflows. In effect, the company is comparing what its value looks like with and without the proposed project.

Replacement Project: It occurs when the firm replaces an existing asset with a new one in order to reduce operating costs, to increase output, or to improve product quality. In this case, the incremental cash flows are the additional inflows and outflows that result from replacing the old asset. In a replacement analysis, the company is comparing its value if it makes the replacement versus its value if it continues to use the existing asset.

c.       Net Operating Working Capital Changes; Salvage Value

Net Operating Working Capital Changes: Net operating working capital changes are the increases in current operating assets resulting from accepting a project less the resulting increases in current operating liabilities, or accruals and accounts payable. A net operating working capital change must be financed just as a firm must finance its increases in fixed assets. Salvage Value: Salvage value is the market value of an asset after its useful life. Salvage values and their tax effects must be included in project cash flow estimation.

d.      Stand-alone Risk; Corporate (within-firm) Risk; Market (beta) Risk

Stand-alone Risk:  Stand-alone risk is the project’s total risk if it were operated independently.

Stand-alone risk ignores both the firm’s diversification among projects and investors’ diversification among firms. Stand-alone risk is measured either by the project’s standard deviation of NPV (σNPV) or its coefficient of variation of NPV (CVNPV). Note that other profitability measures, such as IRR and MIRR, can also be used to obtain stand-alone risk estimates.

Corporate (within-firm) Risk: Within-firm risk is the total riskiness of the project giving consideration to the firm’s other projects, that is, to diversification within the firm. It is the contribution of the project to the firm’s total risk, and it is a function of (a) the project’s standard deviation of NPV and (b) the correlation of the projects’ returns with those of the rest of the firm. Within-firm risk is often called corporate risk, and it is measured by the project’s corporate beta, which is the slope of the regression line formed by plotting returns on the project versus returns on the firm.

Market (beta) Risk: Market risk is the riskiness of the project to a well-diversified investor; hence it considers the diversification inherent in stockholders’ portfolios. It is measured by the project’s market beta, which is the slope of the regression line formed by plotting returns on the project versus returns on the market.

e.       Sensitivity Analysis; Scenario Analysis; Monte Carlo Simulation Analysis

 Sensitivity analysis: It indicates exactly how much NPV will change in response to a given change in an input variable, other things held constant. Sensitivity analysis is sometimes called “what if “analysis because it answers this type of question.

Scenario analysis: It is a shorter version of simulation analysis that uses only a few outcomes. Often the outcomes considered are optimistic, pessimistic and most likely.

Monte Carlo simulation analysis: It is a risk analysis technique in which a computer is used to simulate probable future events and thus to estimate the profitability and risk of a project.

f.       Risk-adjusted Discount Rate; Project Cost of Capital

Risk-adjusted Discount Rate: A risk-adjusted discount rate incorporates the riskiness of the project’s cash flows. The cost of capital to the firm reflects the average risk of the firm’s existing projects. Thus, new projects that are riskier than existing projects should have a higher risk-adjusted discount rate. Conversely, projects with less risk should have a lower risk-adjusted discount rate. This adjustment process also applies to a firm’s divisions. Risk differences are difficult to quantify, thus risk adjustments are often subjective in nature.

Project Cost of Capital: A project’s cost of capital is its risk-adjusted discount rate for that project. In other words, it is a minimum acceptable expected rate of return on a project given its risk. It is used to evaluate a particular project based on the corporate WACC.

g.      Decision Tree; staged Decision-tree Analysis; Decision Node; Branch

Decision Tree: A schematic tree-shaped diagram used to determine a course of action or show a statistical probability. Each branch of the decision tree represents a possible decision or occurrence. The tree structure shows how one choice leads to the next, and the use of branches indicates that each option is mutually exclusive.

Staged decision-tree analysis: The tools we use depend on the nature of the problem we are trying to solve. Often when we are choosing between competing alternatives, we turn toward decision trees. When we simply wish to quantify the risk or the uncertainty, the tool of choice is Monte Carlo simulation.

Decision node: A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute e.g. whether a coin flip comes up heads or tails each branch represents the outcome of the test and each leaf node represents a class label decision taken after computing all attributes.

Branch: Decision trees have three kinds of nodes and two kinds of branches. A decision node is a point where a choice must be made; it is shown as a square. The branches extending from a decision node are decision branches, each branch representing one of the possible alternatives or courses of action available at that point. The set of alternatives must be mutually exclusive.

h.      Real Options; Managerial Options, Strategic Options; Embedded Options

Real Options: Real options occur when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life. They are referred to as real options because they deal with real as opposed to financial assets.

Managerial Options: Managerial options are those options which give opportunities to managers to respond to changing market conditions.

Strategic Options:  Strategic options are those options which often deal with strategic issues rather than dealing with small routine issues.

Embedded Option: Embedded options give an option that is a part of another project.

i.        Investment Timing Option; Growth Option; Abandonment Option; Flexibility Option

Investment Timing Option: Investment timing options give companies the option to delay a project rather than implement it immediately. This option to wait allows a company to reduce the uncertainty of market conditions before it decides to implement the project.

Growth Option: It refers to the ability of a project to provide long-term growth despite negative values. For example, a new research program may appear negative, but it might lead to new product innovations and market growth. We need to consider the growth options of projects. This includes the opportunity to expand into different geographic markets and the opportunity to introduce complementary or second-generation products. It also includes the option to abandon a project if market conditions deteriorate too much.

Abandonment Option: It refers to the ability to abandon or get out of a project that has gone bad. An abandonment option is a clause in a contract that permits either party to leave the contract before obligations have been fulfilled.

Flexibility Option:  Flexibility option must be added at the time of booking. Amendments to date and  route or time may incur an increase in fare, all amendments to date, route and time are subject to availability, all amendments and cancellations must be made before the original departure date are the important of flexibility option.

………………………………………………………………………………………………………

11.2- Answer:

Only cash can be spent or reinvested, and since accounting profits do not represent cash, they are of less fundamental importance than cash flows for investment analysis. Dividends and free cash flows represent cash flows, rather than on earnings per share, which represent accounting profits. Operating cash flows, rather than accounting profits, are used in project analysis. This is because operating cash flows exclude non-cash revenues and includes non-cash charges whereas accounting income includes the revenues and expenses listed on the income statement which were not even received or paid during the accounting period (Brigham, Eugene F.; Ehrhardt, Michael C., 2014).

………………………………………………………………………………………………………

11.3-Answer:

Since the cost of capital includes a premium for expected inflation, failure to adjust cash flows means that the denominator, but not the numerator, rises with inflation, and this lowers the calculated NPV.

............................................................................................................................................................

11.4-Answer:

Capital budgeting analysis should only include those cash flows which will be affected by the decision. Sunk costs are unrecoverable and cannot be changed, so they have no bearing on the capital budgeting decision. Opportunity costs represent the cash flows the firm gives up by investing in this project rather than its next best alternative, and externalities are the cash flows (both positive and negative) to other projects that result from the firm taking on this project. These cash flows occur only because the firm took on the capital budgeting project; therefore, they must be included in the analysis.

…………………………………………………………………………………………………….

11.5- Answer:

When a firm takes on a new capital budgeting project, it typically must increase its investment in receivables and inventories, over and above the increase in payables and accruals, thus increasing its net operating working capital. Since this increase must be financed, it is included as an outflow in Year 0 of the analysis. At the end of the project’s life, inventories are depleted and receivables are collected. Thus, there is a decrease in NOWC, which is treated as an inflow.

……………………………………………………………………………………………………

11.6- Answer:

a)      Simulation analysis: It involves working with continuous probability distributions, and the output of a simulation analysis is a distribution of net present values or rates of return. It is basically a risk analysis technique which uses the computer to simulate future events and to estimates the probabilities and riskiness of projects.

b)       Scenario analysis: It involves picking several points on the various probability distributions and determining cash flows or rates of return for these points. Basically, scenario analysis uses probabilities of changes in the dependent variables with the given change in more than one independent variable at a time.

c)       Sensitivity analysis: It involves determining the extent to which cash flows change, given a change in one particular input variable. 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.

……………………………………………………………………………………………….

11.7-Answer:

The cost of capital used in the capital budgeting is weighted average of debt, preferred stock and common equity which are used as capital by the firm. It helps to adjust the risk of project. WACC act as the rate of return which is important to satisfy all of the firm's investors. Interest expenses or interest payment should not be deducted when a project's cash flows are calculated for use in capital budgeting analysis because the cost of debt is already included in WACC. Thus, deducting interest expenses from the project's cash flows might result in double counting or repeat counting of same interest costs twice.

............................................................................................................................................................

11.8- Answer:

It is important that the firm should take care about the timing of cash flows. It is very difficult to estimate cash flow as number of variables and many individuals and departments are involved in capital budgeting which is very essential. Because of time value of money, capital budgeting cash flows should in theory be analyzed exactly as they occur (Brigham, Eugene F.; Ehrhardt, Michael C., 2014). There might be little compromise between accuracy and feasibility. The daily cash flows would in theory be most accurate but daily cash flows would result costly, complex to use and probably would not give accurate result than yearly cash flow estimates. It is because the firm cannot predict or forecast to identify such degree of detail information. Therefore in most cases, we assume three rules to assign cash flows to time period which are as follows:

·         Capital expenditures occur at beginning of the periods

·         Capital inflows occur at the end of periods

·         Operating cash flow both revenues and expenses are netted out and reported at the end of the product in which they are generated.

But these are conservative assumptions, so the projects that pass NPV hurdle with them in place are almost certain to pass under more favorable assumptions. However for the projects with highly predictable cash flows, it is best to assume that cash flows occur at mid-year, or even quarterly or monthly to avoid imparting a downward bias to the NPV.

………………………………………………………………………………………………………

11.9- Answer:

The basic purpose of a replacement project is to improve efficiency or to maintain or increase revenues by replacing deteriorated or obsolete fixed assets such as equipment or facilities. On the other hand, the primary purpose of an expansion project is to enhance revenues by increasing operating capacity in existing products or markets or by focusing on operations to expand into completely new products or markets. These two types of projects differ in that an expansion project focuses on the firm’s revenues whereas a replacement project focuses on creating efficiencies within the firm.

………………………………………………………………………………………………………

11.10-Answer:

Like anything, projects do have risks. There are three types of project risks associated with capital budgeting projects that being considered for inclusion in a firm’s capital budget.

1.      Beta (Market) Risk:
This looks at the risk of a project through the eyes of the stockholder. It looks at the project not only from a company's perspective, but from the stockholder's overall portfolio. It is measured by the effect the project may have on the company's beta.

2.      Within-firm (Corporate) Risk:
This risk assumes the project a company intends to pursue is not a single asset but incorporated with a company's other assets. As such, the risk of a project could be diversified away by the company's other assets. It is measured by the potential impact a project may have on the company's earnings.

3.       Stand-Alone Risk:
This risk assumes the project a company intends to pursue is a single asset that is separate from the company's other assets. It is measured by the variability of the single project alone. Stand-alone risk does not take into account how the risk of a single asset will affect the overall corporate risk.

………………………………………………………………………………………………………

11.11. Answer:

Market risks are that part of risks which cannot be eliminated, and it stems from factors that systematically affect most firms such as war, inflation, recession, and high interest rates. It can be measured by a stand-alone risk which tends to move up or down with markets risks. In addition, it is also true that stand-alone risk measures the dangers associated with a single facet of a company’s operations or holding a specific asset or project. Stand-alone risk allows firms to determine a project market’s risk as if it were operating as an independent entity.  Therefore, having said this, while market risk should be the only “relevant” risk, companies are likely to emphasize as much stand-alone risk as on market risk because it helps to determine market risk as it is a tool for making subjective and judgmental modifications.

………………………………………………………………………………………………………

References:

C. Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi: New Age International Publishers.

Brigham, Eugene F.; Ehrhardt, Michael C. (2014). Financial Management: Theory and Practice (14 ed.). Delhi, India: Cengage Learning.