Capital Budgeting

Capital Budgeting PaperOverviewFor this week’s assignment, review the attached articles and any outside research (at least 3 outside references) you have done related to how the evaluation process and selection of capital projects are affected by mutually exclusive projects, project sequencing, and capital rationing. Pay particular attention to Burns and Walker’s 2009 article, “Capital Budgeting Surveys: The Future is Now,” which is attached .InstructionsWrite a 5-page paper (References and cover pages not included) that summarizes your conclusions about capital budgeting. Include the following:Analyze the major components of capital budgeting process evaluation and selection of capital projects.Explain the rationale and the effect of mutually exclusive projects.Examine some of the foundations and key issues of capital budgeting decision making, including how companies can determine the success of their portfolio of investment projects and decisions on capital rationing. Assess ethical considerations that may arise in capital budgeting.Compare and contrast project sequencing and capital rationing.Explain the calculation and interpretation of net present value (NPV), internal rate of return (IRR), payback period, and profitability index (PI) of a capital project.Explain the calculation and interpretation of the weighted average cost of capital (WACC), including how taxes affect the cost of capital from different capital sources.Based on the article, briefly evaluate the current development on capital budgeting and benefits discussed by Burns and Walker (2009).Be sure your assignment meets the following guidelines. Refer to the attached scoring guide for specific information about how your paper will be evaluated.Written communication: Written communication is free of errors that detract from the overall message.Scholarship: Use at least 5 outside sources to support your main points and analysis.APA formatting: All resources and citations should be formatted according to current APA style and formatting guidelines.Length: 5 typed, double-spaced pages (Introduction and conclusion required)Font and font size: Times New Roman, 12 point.Please pay close attention to the paper scoring guide and ensure that you covered all elements.Any questions or concerns, please let me know
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Capital Budgeting Surveys: The Future is Now
Burns, Richard M;Walker, Joe
Journal of Applied Finance; 2009; 19, 1/2; ProQuest Central
pg. 78
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Capital Budgeting Simulation
Using Excel: Enhancing the
Discussion of Risk in Managerial
Accounting Classes
By Sylwia Gornik-Tomaszewski, DBA, CMA, CFM
EXECUTIVE SUMMARY
An Excel-based capital budgeting
simulation model that contains a
degree of randomness and uncertainty
can be used to expand classroom
any leading managerial accounting textbooks
provide only limited coverage of risk in the
context of capital budgeting, often referred
to as capital investment analysis. Capital
budgeting chapters usually focus on widely
used decision models, such as net present value (NPV), internal rate of return (IRR), accounting rate of return (ARR),
profitability index (PI), and the payback period (PB), and are
often enhanced with analyzing tax implications in capital budgeting decisions.1 But only the deterministic versions of these
models, in which no randomness is involved, are covered.
Cash flows are forecasted as single figures, and their uncertainty is ignored. The risk associated with an investment project is expressed in the selected discount rate (required rate of
return). The lesson being told, therefore, is that the greater
the risk that is associated with an investment, the greater the
return that is required.
In practice, however, several different techniques are used
to deal with the uncertainty of investment projects. Firms
might combine NPV with PB when analyzing the total risk of
a project. They also might use sensitivity analysis, scenario
analysis, risk-adjusted discount-rate approach, or simulation.
M
discussions of risk in the context of
capital investment analysis. This adds
a level of detail that is often overlooked by most managerial accounting
textbooks.
M A N A G E M E N T A C C O U N T I N G Q U A R T E R LY
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SUMMER 2014, VOL. 15, NO. 4
These techniques are applied following the assumption
that it is relevant to consider a projectâ??s total risk when
evaluating the project and when the returns from the
project are positively correlated with the returns from
the firm as a whole.2
Although the leading textbooks do not delve into
these methods for dealing with uncertainty in investments, the techniques can be explained easily in the
classroom, especially when supplemented with spreadsheet applications. An educational model developed in
Excel can provide a simple simulation of the NPV of an
investment project whose outcome is uncertain. The
model is easy to use, requiring only a basic Excel package and not the @Risk add-in.
rate. Also needed is the firmâ??s required rate of return to
discount the after-tax net cash flow to present value.
Rows 5 to 15 of the spreadsheet contain assumed data
on price per unit (p), number of units sold (q), unit production cost (c), unit selling cost (s), annual depreciation
(D), the firmâ??s marginal tax rate (T), and the firmâ??s required rate of return (k).
To build uncertainty into the model, assume that the
first three variablesâ??p, q, and câ??are random (stochastic) in nature. This requires an estimation of the probability distribution for each of these random variables.
Although a discrete distribution could be used with a
finite, relatively small number of possible values with
known probabilities, it is more convenient to use continuous distributions in a simulation. The RAND function in Excel generates various continuous distributions
commonly used in applications. Assume that the three
random variablesâ??p, q, and câ??are normally distributed.
Cells C14:E15 contain the mean (␮) and standard deviation (␴) for each of the three random variables. As you
can see in Figure 1, the price per unit (p) is normally
distributed with ␮ = $10 and ␴ = $2; the number of
units sold (q) is normally distributed with ␮ = 2,000 and
␴ = 300; and the unit production cost (c) is normally distributed with ␮ = $2 and ␴ = $0.25. These small numbers are selected on purpose to make the model easy to
understand. Users of the model can use their own
prices, costs, quantities, and determine distributions of
these numbers. It is suggested, however, that certain
basic rules should apply, such as assuming p>c and
␴<␮, to avoid complications that obscure the purpose and focus of this exercise. With those assumptions, applying the Excel function =NORMINV(RAND(),␮,␴) will generate random values for p, q, and c based on normal distribution. For example, the formula =NORMINV(RAND(),C14,C15) in cell C5 generates the random price per unit (p) from a normal distribution. The values for q and c are generated in a similar manner from their respective means and standard deviations. Now that the data inputs are defined, the next step is to build the NPV model, seen in cells A17:E26 of Figure 1. The model assumes that (1) the initial investment necessary to introduce the new product is $10,000 (cell C20), (2) the new product will have a life of five Basic Simulation Model A simulation model is a computer model that imitates a real-life situation. When applicable in capital budgeting, the simulation approach generally is more feasible for analyzing large projects because the technique requires estimates to be made of the probability distribution of each cash flow element. Simulation uses random numbers to drive the modeling process. All spreadsheet packages are capable of generating random numbers between 0 and 1. In Excel, random numbers are generated by entering the formula =RAND() in a cell. The random numbers are uniformly distributedâ??that is, any number between 0 and 1 has the same chance of occurrence. Also, different random numbers generated in one spreadsheet are probabilistically independent, meaning the random value in one cell does not affect random values in other cells.3 It is critical to understand that flux is an important characteristic of simulation. We will have to get accustomed to constantly changing numbers because all the cells containing the RAND function will change each time we press the recalculate key (F9) or do anything to affect calculation. Figure 1 presents a simple capital budgeting model involving the introduction of a new product. We will need to determine annual after-tax cash flows generated by the new product. Therefore, the first step in developing the model is to enter the relevant data needed to compute these cash flows. This includes data to determine revenues, costs, depreciation, and marginal tax M A N A G E M E N T A C C O U N T I N G Q U A R T E R LY 13 SUMMER 2014, VOL. 15, NO. 4 Figure 1: Capital Budgeting with Simulation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 131 132 133 134 A B C D E NCF p q c s D T k Mean: StDev: 10.16 2,292 2.04 1 2,000 40% 10% H p 10 2 price per unit number of units sold unit production cost (excluding depreciation) unit selling cost annual depreciation the firm's marginal tax rate required rate of return q 2,000 300 The NPV Determination: NPV G CAPITAL BUDGETING WITH SIMULATION Data: Item Investment F Year (t) now 1 2 3 4 5 Amount (10,000) 14,311 14,311 14,311 14,311 14,311 T ax E ffec t 1 60% 60% 60% 60% 60% c 2 0.25 A f e r - ta x NCF t (10,000) 10,587 10,587 10,587 10,587 10,587 $30,132 Simulation: Iteration 1 2 3 4 5 6 7 8 9 10 100 Mean StDev Min NPV $30,132.07 $30,450.64 $20,031.96 $33,898.81 $14,301.81 $34,231.82 $19,130.41 $31,494.15 $28,536.55 $38,796.87 $30,653.14 $15,188.38 $24,329.62 $10,808.35 $1,537.28 Frequency table for 100 iterations N PV Frequency 0 0 10,000 8 20,000 30 30,000 30 40,000 27 50,000 4 >50,000
1
100
years (rows 21-25), and (3) no additional investments
will be required during the product lifespan. These assumptions make the annual after-tax cash flows generated from the sale of the new product identical. They
are computed using the formula NCFt = [q(p) â?? q(c) â??
D](1â??T) D; where NCFt is the net cash flow in period
t. Unless a company is a tax-exempt organization, only
the after-tax amount (column E) should be used when
M A N A G E M E N T A C C O U N T I N G Q U A R T E R LY
determining the desirability of an investment proposal.
Depreciation is not a cash flow. Because it affects the
taxes that must be paid, however, it has an indirect effect on the companyâ??s cash flows. The depreciation deduction shields the revenues from taxation and thereby
reduces the amount of taxes that the company must
pay. The reduction in tax payments made possible by
the depreciation tax shield is equal to D â?? T.
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SUMMER 2014, VOL. 15, NO. 4
In the Excel model, the after-tax net cash flows are
computed in three steps:
(1) The formula in cell C21 is =$C$6*$C$5$C$6*($C$7$C$8)-$C$9.
(2) Cell D21 contains =1-$C$10, which is the tax
effect.
(3) Cell E21 finishes the calculation by multiplying
the annual cash flows by the tax effect and then
adding depreciation. The formula is
=(C21*D21)$C$9.
The formulas used in C21:E21 are copied in rows
22-25. The NPV amount is computed in cell E26 using
=NPV(C11,E21:E25)?. Net cash flows are discounted at the 10% required rate of return (C11) except
for the initial investment (E20), which is incurred now,
at t=0.
mate of an expected NPV of the project, as well as its
risk. With this information, it is possible to compute the
probability of achieving an NPV that is greater or less
than any particular value. The calculation is z = (x â??
Expected NPV)/Standard Deviation, where z is the
number of standard deviations and x is the particular
value we want to check.
For example, if we wanted to compute the probability
of achieving an NPV less than or equal to $0 using the
results in Figure 1, the calculation would be z = ($0 â??
$24,329.62)/$10,808.35. The result is -2.25 standard deviations. By referring to a normal distribution table, we
can determine that the probability of a value less than 2.25 standard deviations from the mean is 1.22%. Thus,
there is a 1.22% chance that the actual NPV will be
negative for this project.
Replications of Simulation
Frequency Table and Histogram
The calculations to this point show only one possible
scenario for the five-year horizon. The $30,132 NPV in
cell E26 indicates that this independent project is
acceptableâ??the NPV represents a $30,000 gain (the return from the project is greater than the cost of capital,
that is the return available by investing the capital elsewhere). The project is expected to add value to the
firm, and it should improve shareholdersâ?? wealth, but
this might be a result of a lucky set of random numbers.
The next step is to check this by replicating the basic
simulation 100 times.
To do this, a data table is created in the range
A30:B131. Column A (A32:A131) labels each iteration,
1 through 100. To begin with the existing NPV calculation, the formula =E26 is entered into cell B31. Next,
highlight cells A31:B131. From the Data tab in the
Excel ribbon, click on the What-If Analysis dropdown
menu and select Data Table. This will bring up the
Data Table dialog box. Leave the Row Input Cell field
blank. For the Column Input Cell, select any blank cell
in the worksheet (such as C32). Click OK. This operation tricks Excel into repeating the NPV model calculations 100 times, each time using new random numbers.
Below the data table, formulas have been added to
show the mean, standard deviation, and the minimum
and maximum values of the 100 iterations (cells
A132:B135). These simulation results provide an esti-
A histogram, a graphical representation of the data distribution, can help us visualize the results from the
model and facilitate further analysis. A histogram is a
summary graph showing a count of the data points
falling in various ranges. Consequently, it is a rough approximation of the frequency distribution of the data.
Users of the model may then examine the histogram for
the general shape of the frequency distribution and its
symmetry. This may give them a better understanding
of the data and help them form expectations regarding
the probability of various outcomes. For instance, in our
example, the users may gain a better understanding of
how probable it is that the project would yield a negative NPV and, therefore, should not be accepted.
Although a histogram option is available in the
Analysis Tools (Data Analysis) in Excel that provides a
one-step method for generating a histogram, that option
does not retain a link to the data that was used to generate it. That is, the histogram will remain static and
will not change anytime the spreadsheet recalculates.
The following method does not have this drawback.
Create a frequency table of the data. This will provide data ranges for our histogram and retain a link to
the data. In Excel, this can be done using the FREQUENCY formula, which calculates how often certain
values occur within a specified range and then returns a
vertical array of numbers. The syntax for the formula is
M A N A G E M E N T A C C O U N T I N G Q U A R T E R LY
15
SUMMER 2014, VOL. 15, NO. 4
Figure 2: Histogram of NPV After 100 Replications
Histogram of NPV
40
35
30
Frequency
25
20
Frequency
15
10
5
0
0
10,000
20,000
30,000
NPV
=FREQUENCY(data_array,bins_array), where data_
array is the data set that contains the values for which
we want to count frequencies and bins_array is an array
containing the intervals we want to use to group the
values.
Because FREQUENCY returns an array, it must be
entered as an array formula. That requires selecting a
range of adjacent cells into which we want the returned
distribution to appear. Furthermore, the number of elements in the returned array will be one greater than the
number of elements in bins_array. The extra element in
the returned array returns the count of any values above
the highest interval.4
The frequency table appears in cells E30:G39 in
Figure 1. For this example, it shows how many NPV
observations are negative, how many are between $0
M A N A G E M E N T A C C O U N T I N G Q U A R T E R LY
40,000
50,000
>50,000
and $10,000, how many are between $10,000 and
$20,000, and so on up to values greater than $50,000.
Cells E32:E37 contain the upper limit for each interval,
so they represent the bins_array. Note that cell E38 lists
>$50,000. This will be the label for the extra element in
the returned array.
Next we need to select the range G32:G38. Type in
=FREQUENCY(B32:B131,E32:E37) and then press
CTRL????, which enters it as an array
formula. If the formula is not entered as an array formula, there will be only one result in cell G32. If
entered correctly, results will appear in each of the cells
selected.
With this frequency table formed, it is now easy to
create a histogram. Select the frequency table cells
(E32:G38) and create a column chart (see Figure 2).
16
SUMMER 2014, VOL. 15, NO. 4
The categories from column E of the frequency table in
Figure 1 serve as the labels for the horizontal axis in
Figure 2. Notice that this method of generating a histogram retains the link to the data. Any changes in the
data will also change the chart. To freeze the results, select and copy the range of cells, then use Paste Values
to replace the formulas with the actual numbers.
tional managerial accounting curriculum.
Use in the Classroom
Additional References
This model was used in several graduate managerial accounting classes. It was usually discussed at the end of
a lecture on capital investment decisions. After a short
introduction that described the model and its purpose,
the model was built in real-time, and simulations were
run. Students also watched the construction of the frequency table and the histogram. They were usually
very interested in the topic and fascinated by the everchanging simulation output. The spreadsheet was later
posted online so students could further explore the intricacies of the model on their own.
To reinforce studentsâ?? learning and their interest in
simulation, a homework project was assigned that required students to develop a different model. Students
should be made aware that when they try to build the
model using their spreadsheets, each result will undoubtedly be different. No two answers will ever be
exactly the same. This fact should stimulate critical
thinking and creativity.
Enterprise Risk Management Initiative Staff, â??Impact
of Risk Management Failures on the Financial
Crisis,� http://erm.ncsu.edu/library/article/financialcrisis-failures#.Us9gbNJDvNk, January 3, 2011.
Michelle M. Harner, â??Ignoring the Writing on the Wall:
The Role of Enterprise Risk Management in the
Economic Crisis,� Journal of Business and Technology
Law, October 15, 2009, p. 45.
Jennifer Saranow Schultz, â??An Education in Risk
Management Can Offer a Leg Up,� The New York
Times, August 20, 2009, p. F2.
Sylwia Gornik-Tomaszewski, DBA, CMA, CFM, is an associate professor in the Department of Accounting and
Taxation of The Peter J. Tobin College of Business at St.
Johnâ??s University in Queens, N.Y. You can contact Sylwia at
(718) 990-2499 or gornikts@stjohns.edu.
Endnotes
1 For example: Charles T. Horngren, Srikant M. Datar, and
Madhav T. Rajan, Cost Accounting, 15th edition, Prentice Hall,
2014; Eric Noreen, Peter C. Brewer, and Ray H Garrison,
Managerial Accounting for Managers, third edition, McGraw-Hill,
2014; Carl S. Warren, James M. Reeve, and Jonathan Duchac,
Managerial Accounting, 12th edition, Cengage Learning, 2014;
and Susan V. Crosson and Belverd E. Needles, Managerial
Accounting, 10th edition, Cengage Learning, 2014.
2 R. Charles Moyer, James R. McGuigan, Ramesh P. Rao, and
William J. Kretlow, Contemporary Financial Management, 12th
edition, Cengage Learning, 2012.
3 Wayne L. Winston and S. Christian Albright, Practical
Management Science: Spreadsheet Modeling and Applications, fourth
edition, Cengage Learning, 2011.
4 Ibid.
5 For example, users may use the RAND function to generate
random numbers from such distributions as: (1) uniform
distribution between a and b (the Excel formula is =a (ba)*RAND(), where the known values are substituted for a and
b); and (2) exponential distribution with mean m (the Excel
function is =-m*LN(Rand()), where the known value is
substituted for m).
Further Uses of the Model
The simple capital budgeting example presented in
Figure 1 can be extended in a variety of ways. For example, more of the input variables could be made random, or the probability distribution for individual variables used in the simulation may assu …
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