We offer a pedagogical application of the capital structure decision-making process. The application consists of a two-stage interactive spreadsheet model by which the student assumes the role of financial manager. The student first performs construction and analysis of six traditional capital structure scenarios to find the optimal debt level-the level that minimizes weighted average cost of capital (WACC) and maximizes firm value-then applies Monte Carlo simulation to those scenarios. During their investigation of alternative capital structure scenarios, students must deal with the reality that WACC components, thus WACC itself, are stochastic variables. The capital structure model has proven very helpful for students to investigate and better understand the relationship between debt and equity capital components in their relative effects on WACC and firm value, and also to appreciate the impact on estimated WACC of uncertainty and variability in its components.
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Understanding Weighted Average Cost of
Capital: A Pedagogical Application
Sam G. Berry, Carl E. Betterton and Iordanis Karagiannidis1
The Citadel
We offer a pedagogical application of the capital structure decision-making
process. The application consists of a two-stage interactive spreadsheet
model by which the student assumes the role of financial manager. The
student first performs construction and analysis of six traditional capital
structure scenarios to find the optimal debt level - the level that minimizes
weighted average cost of capital (WACC) and maximizes firm value - then
applies Monte Carlo simulation to those scenarios. During their
investigation of alternative capital structure scenarios, students must deal
with the reality that WACC components, thus WACC itself, are stochastic
variables. The capital structure model has proven very helpful for students
to investigate and better understand the relationship between debt and
equity capital components in their relative effects on WACC and firm value,
and also to appreciate the impact on estimated WACC of uncertainty and
variability in its components.
INTRODUCTION
In truth, not even the chairman of the Federal Reserve Board knows how to
identify a firm's precise optimal capital structure or how to measure the effects
of capital structure changes on stock prices and the cost of capital. In practice,
capital structure decisions must be made using a combination of judgment and
numerical analysis. (Brigham and Houston, 2010. p.486).
The weighted average cost of capital (WACC) is an invaluable tool for use by
financial managers in capital budgeting and business valuation analyses, and
consequently, is a key topic in financial management courses. A continuing need
exists for improved methods of teaching and learning this important topic. In a
survey of 392 CFOs Graham and Harvey (2001) find that financial executives
readily use business school techniques like net present value (NPV) and the capital
asset pricing model (CAPM), but are much less likely to follow capital structure
guidance from academia. Graham and Harvey (2001) suggest an explanation for this
behavior might be that business schools are better at teaching capital budgeting and
the cost of capital than at teaching capital structure. Citing this need for better
Spring/Summer 2014 11
capital structure teaching methods, Hull (2008) offers a pedagogical spreadsheet
application of the capital structure decision-making process for a firm issuing debt
to retire equity. Continuing the effort to produce improved teaching methods for
capital structure, our purpose in this paper is to describe pedagogy that includes an
experiential process for students to explore alternative mixes of debt and equity in
the firm's capital structure and to observe the impact of their choices upon WACC
and common stock price.
The traditional approach to estimating the cost of invested capital is to compute
a WACC using point estimates of each input (Keown, Martin, and Petty, 2011; Van
Horne and Wachowicz, 2001; and Welch, 2010). In reality however, there is
uncertainty associated with these inputs. Some of the parameters in the WACC, such
as the unlevered beta and market risk premium, are not known with certainty due to
their stochastic nature or because they are not under the firm's control. These
variable inputs can add to the variability of WACC results. An approach to
estimating WACC that explicitly addresses this uncertainty is to identify and
quantify the uncertainty in individual WACC parameter estimates, then describe the
uncertainty around the expected WACC via Monte Carlo simulation. This paper
describes use of both the traditional and Monte Carlo approaches as a means for
students to (a) investigate and better understand the relationship between debt and
equity in the capital structure, WACC, and firm value and (b) appreciate the impact
on estimated WACC of uncertainty and variability in its components.
The remainder of this paper is organized as follows: The next section describes
the basic spreadsheet model as used by students. Input and output variables are
defined, terminology is given, and key relationships among variables are explained.
The following section describes the use of Monte Carlo simulation to help students
understand the effects of uncertainty on the calculated WACC and how the effect
is influenced by the degree of leverage used. The penultimate section discusses
student learning objectives and assessment, and the final section offers some
concluding remarks.
THE WACC SPREADSHEET MODEL
In this section we present a student-friendly spreadsheet model based on
relatively simple scenario analysis. The spreadsheet can be used in class to introduce
students to the calculation of weighted average cost of capital, and to help them
better understand how changes in the mix of debt and equity affect the firm's cost
of capital and overall corporate valuation. Scenarios are descriptions of different
future states of an organization's environment (Brauers and Weber, 1988). Scenario
analysis has long been used in the business world (Bradfield, Wright, Burt, Cairns
and Van Der Heijden, 2005) and by 1980 the technique was being applied by half
of Fortune 1000 companies (Linneman and Klein, 1983). Its use has continued to
grow with the increased uncertainty, globalization, and complexity in the business
environment (Schoemaker, 1993).
12 Journal of Financial Education
Terminology
WACC is determined by the following equation:
WACC = wd rd (1 - T) + wps rps + ws rs (1)
Where,
ws = the proportion of total capital represented by common equity.
rs = rate on common equity.
wps = the proportion of total capital represented by preferred stock.
rps = D ps / P ps = rate on preferred stock.
wd = the proportion of total capital represented by debt.
rd = interest rate on new debt (before tax)
rd (1-T) = r L = after-tax interest rate on new debt, where T = firm's marginal tax
rate.
Model Inputs and Assumptions
The base spreadsheet model2 appears in Figure 1. This model is one that
assumes addition of debt occurs within a context of company recapitalization, that
is, the exchange of one form of financing for another. An example would be
removing common shares from the company's capital structure and replacing them
with bonds. A reverse example would be when a company issues stock in order to
buy back debt securities, thus increasing its proportion of equity capital compared
to its debt capital. The model maintains total initial capital (book value) constant -
additional debt is taken on through several alternative scenarios in which common
equity is proportionally decreased. This approach isolates and emphasizes the
risk/return tradeoffs inherent in placing additional debt in the capital structure.
Students begin in Scenario 1 (column C) by creating a capital structure of their
choosing. They enter values for the amount of debt, the amount of preferred stock
equity, the firm's unlevered beta, and other inputs. Since total capital remains
constant, the amount of common stock equity (book value) is calculated as TOTAL
CAPITAL less the sum of Long Term Debt and Preferred Stock. Of course the
market value of equity will be different in each scenario and will depend on the
WACC and the Firm Value. Upon entering values for debt a student can
immediately see the effect on the WACC and firm's stock price. Students can create
up to six capital structure combinations (scenarios). In Scenarios 2 through 6
students test each of those alternatives with increasingly larger amounts of debt, and
investigate the effect of that increased leverage on WACC and firm value. The firm
value is measured by the present value of future Free Cash Flows to the Firm
(FCFF).
Spring/Summer 2014 13
14 Journal of Financial Education
Cells having shadded background are user inputs. More specifically, students
can enter their estimates for:
1. The applicable effective tax rate - cell C3.
2. The real Risk-Free interest rate – cell C4.
3. The inflation premium - cell C5.
4. The dollar amount of debt the company takes on – cells C9-H9.
5. The dividend paid by the preferred stock – cell C13.
6. The dollar amount financed by the use of preferred stock – cell C15.
7. The market risk-premium – cell C19.
8. The unlevered company beta – cell C21.
9. The Free Cash Flow to the Firm – cell C29.
Most inputs are common for all scenarios (1-6). Only the amounts financed by
debt are allowed to vary by scenario since the purpose of this exercise is for students
to see how different capital structure combinations can affect WACC. The rest of
the numbers that appear on the spreadsheet are calculated results, based on user
inputs. The large number of inputs provides the student with considerable
flexibilities and adds increased realism to the learning experience.
The Cost of debt (row 8) is calculated in a way that reflects the fact that higher
financial leverage leads to an increased probability of default, higher bond interest
rates and multiple symptoms of financial distress. The issue of financial distress cost
as related to WACC is summarized well by Almeida and Philippon (2008):
The risk of bankruptcy for highly-levered companies will rise precisely when it
is most disadvantageous: when it is harder to liquidate assets and more costly
to raise new capital. Bond investors seem to be aware of these risks, and have
usually demanded significant risk premia to hold debt securities issued by
highly-levered firms. But since standard valuations of bankruptcy costs ignore
these economy-wide risks, corporate managers who follow this practice will
underestimate the actual expected costs of debt and may end up with excessive
leverage in their capital structure. (p. 110)
The formulas in cells C8:H8 calculate the cost of debt as the risk free rate of
interest plus the model's built-in yield spread. The spread depends on the company's
bond rating (AAA, BB, etc.), and reflects the higher risk associated with higher debt
levels. Table 1 shows the bond rating criteria of Standard &Poor's Rating Services.
The Cost of Debt and Financial Distress
A company's bond rating depends on its business and financial risk. For a
given level of business risk, bond ratings vary depending on financial risk - and one
of the measures of financial risk is the debt ratio.
Spring/Summer 2014 15
Table 1. Risk Profile for Bond Ratings
Business Risk
Profile Financial Risk Profile
Minimal Modest Intermediat
eAggressive Highly
Leveraged
Excellent AAA AA A BBB BB
Strong AA A A- BBB- BB-
Satisfactory A- BBB+ BBB BB+ B+
Weak BBB BBB- BB+ BB- B
Vulnerable BB B+ B+ B B-
Financial Risk Indicative Ratios (Corporates)
Minimal Modest Intermediat
eAggressive Highly
Leveraged
Funds From
Operations/Debt (%) over 60 45-60 30-45 15-30 below 15
Debt/Capital (%) below 25 25-35 35-45 45-55 over 55
Debt/EBITDA (x) less than
1.4 1.4-2.0 2.0-3.0 3.0-4.5 over 4.5
Table 2. Leverage, Ratings, and Yield Spreads for a
Firm with Satisfactory Risk Profile
Debt/Capital (%) below 25 25-35 35-45 45-55 over 55
Bond Rating A- BBB+ BBB BB+ B+
Yield Spread 0.89% 1.04% 1.22% 2.10% 3.35%
In the model, it is assumed that the company is one with a satisfactory business
risk profile and it is assigned a debt rating based on its leverage ratio (debt to total
capital, cells C11 to H11 in the spreadsheet).3
For each debt level there is assigned a corresponding yield spread to be added
to the Risk-Free Rate (Real Risk-Free rate plus Inflation Premium). Yield spreads
may be obtained for industrial firms from www.bondsonline.com and typical values
appear in table 2. For purposes of this student exercise, the values in Table 2 are
used, with the step function implicit there converted and extended into a best-fit
continuous function that permits representative yield spreads to be identified at any
level of debt up to a maximum of 80% debt to capital. The resulting curve for Yield
Spread as a function of Debt/Capital Ratio appears in Figure 2.
16 Journal of Financial Education
Figure 2. Yield Spread as a Function of Debt Ratio
The yield spread corresponding to a given debt level is applied automatically,
based upon the amount of debt the student enters. For example, in Scenario 2 the
company's debt to capital ratio is 32%, falling in the upper portion of the BBB+
bond rating range in Table 2. Based on the relationship shown in Figure 2, the yield
spread corresponding to that specific debt level is 1.0214%. Thus, we assign the
company a total cost of debt equal to a risk-free rate of 5% plus a yield spread of
1.0214% for a total of 6.0214%. Similarly, in Scenario 3 where the debt ratio is
equal to 48% the company has a cost of debt equal to 5% plus 1.90% for a total of
6.90%. Students can readily see that choosing a higher leverage ratio will lead to a
higher cost of debt.
The Cost of Equity
For the cost of equity a similar process was developed that reflects the additional
risk of leverage. The students enter the unlevered company beta. Levered betas are
calculated based on the company capital structure using the Hamada equation.
(2)
bb T
D
E
s Lvered b Unlevered
11 ()
Spring/Summer 2014 17
In equation (2) D is the amount of debt, E the total equity, T the tax rate, bs_Levered the
levered beta, and bs_Unlevered the unlevered beta.
Higher degrees of leverage commensurately lead to higher levered betas and
thus a higher cost of equity. Using the levered betas we calculate the cost of equity
using the Capital Asset Pricing Model (CAPM) equation:
rs = r RF + b s Levered (r M - r RF )(3)
In equation (3) rs is the cost of equity, rRF the risk-free rate, rM the required market
rate of return, and bs_Levered the levered beta.
The Cost of Preferred Stock
Finally, the required return on preferred stock is calculated as the average of
cost of debt and cost of common equity. Preferred shares have risk due to price
fluctuations; preferred stock is a perpetuity and as such is sensitive to changes in
interest rates. If interest rates rise, the price of the preferred falls, and although
dividends may continue, an investor could be stuck with lower-valued stock that
could be sold only at a substantial loss. With the cost of preferred stock and the
preferred stock dividend, the price of preferred stock is calculated as:
(4)
PD
r
ps ps
ps
From equation (1) and the cost of debt, preferred stock, and common stock
calculations WACC is calculated in row 25 of the spreadsheet. Then, the user's
input for the Free Cash Flow to the Firm (FCFF) is used to estimate the present
value of all future free cash flows to the firm, i.e., the firm's market value. FCFF is
the cash flow generated by the business after deducting investments in new capital
so, FCFF = NOPAT - Net Investment4 . WACC is the return that investors expect to
make from investing in the enterprise and therefore is the appropriate discount rate
for FCFF. The growth rate (g) of the FCFF is assumed to be zero without loss of
generality. Hence, the Value of the firm is calculated from Equation (5).
Firm Value = FCFF/WACC (5)
Firm value does not show anywhere in the model but instead is used to estimate
the number of shares. When the firm moves from the base capital structure to any
of the higher debt scenarios a new bond is issued and the proceeds are used to buy
back stock. This will reduce the number of shares. We assume that the number of
shares in the base case scenario is 180,000. The new number of shares following
recapitalization is calculated from Equation (6).
18 Journal of Financial Education
Figure 3. Charts Illustrating WACC, Stock Price,
and Component Weights of WACC
(6)
Shares Shares FirmValue Debt eferred
FirmValue Debt eferred
new old new new
old old
(Pr
(Pr)
)
Based on Equation (6), the new number of shares is calculated in row 30 of the
model. Finally, the common stock price is calculated in row 31 from Equation (7).
(7)
CommonStock ice FirmValue Debt eferred
Shares
FCFF WACC Debt eferred
Shares
Pr Pr
/Pr
Model Outputs
Once they complete the entries shown in Figure 1, students can see the WACC
and the stock price for each of the six scenarios. In a second worksheet of the model,
a graph (Figure 3) is generated to give the students a visual overview of all six
Spring/Summer 2014 19
scenarios. Students can observe the relative benefits of leverage in Scenarios 1
through 6. The more debt the company takes on, the lower the WACC, and the
higher the company's stock price. But when debt is raised even further (Scenarios
5 and 6) the increased financial risk overcomes the benefits of increased leverage
and students see that WACC goes up and firm value (as measured by the stock
price) goes down. Students can easily confirm that when the WACC is minimized
the company's value is maximized.
MONTE CARLO SIMULATION
While scenario analysis is a powerful and useful tool, one serious limitation is
that it does not explicitly consider probability and uncertainty (Markham and
Palocsay, 2006). Several of the inputs to the model discussed in the previous section
have uncertain values. An approach to estimating expected WACC that explicitly
addresses this uncertainty is to apply Monte Carlo simulation5 . Use of this tool is
growing in the finance arena. For example, Rozycki (2011) describes the use of
Monte Carlo Simulation in making capital budget decisions, and Chang and
Dasgupta (2011) show how Monte Carlo Simulation can be used in capital structure
research.
In this section, we describe how students use Monte Carlo simulation to
understand how and to what extent the uncertain variables affect their estimates of
the WACC, and how important the effect of uncertainty is for various debt-equity
combinations. In a nutshell, students first identify the sources of uncertainty in
estimating WACC parameters, then quantify the uncertainty around the estimation
of each WACC parameter, and finally aggregate and quantify the uncertainty around
the expected WACC via Monte Carlo simulation.
Monte Carlo simulation is a numerical approach used to solve problems or
reveal more information about a situation by repeated random sampling. It can be
thought of as artificially creating a chance event or series of related events (for
example, a process) many independent times, and observing a summary or
distribution of results. The estimated parameters of that distribution will be in error
by some amount. One can never know the exact size of this error because the true
value of the quantity estimated is unknown. One can show however, that the
parameter estimate obtained from a simulated process or calculation is a consistent
estimator of the true parameter. For example, as the number of random sample trials
is increased, the half-width interval and corresponding standard error related to the
estimated mean become smaller such that one has an asymptotically valid
confidence interval for the mean (Barreto and Howland, 2006).
Typically, a model is prepared in which selected inputs are designated as having
a distribution of values rather than point (single) values. This is done with those
inputs which are not known with certainty. With tools available today almost any
probability distribution can be assigned to an input of the model. When the
distribution is unknown, the one that represents the best fit to the available data can
20 Journal of Financial Education
Figure 4. Distributions for Real Risk-Free Rate,
Market Risk Premium, and Unlevered Beta
be used. In a given trial, a random value from each input variable's distribution is
selected and calculation of outputs is performed with those random values. After
thousands of trials, the model outputs can be plotted as a frequency distribution that
shows not only the most likely outcome, but also a range of possible outcomes, and
the probability of those outcomes. The simulation results remain estimates whose
accuracy is defined by user inputs, but assuming the model is reasonably correct, the
results can be more informative than alternative single-point estimates, or even
scenario sets, that may be otherwise produced. If input variables exhibit correlation,
this can also be modeled. The Monte Carlo simulation models were constructed
using the Crystal Ball® software package (Crystal Ball® is spreadsheet-based
application suite for predictive modeling, and is a registered trademark of Oracle
Corporation). Students have access to this software in our school's financial lab.
Uncertain Input Variables
In the calculations of the base model all variables were specified by the user as
single-point values. However, in reality several key inputs are not known with
certainty. Beta is one of these uncertain variables. Students can use historical data
Spring/Summer 2014 21
to calculate the firm's beta and plug it into the base model as a single number. They
can do the same with a second uncertain variable - market risk premium. Using their
(single-point) estimate for the market risk premium, students can calculate the cost
of equity using the CAPM equation. These two variables can never be predicted
with certainty. Predictions also vary significantly for the real risk-free rate, which
constitutes the third uncertain variable considered here. We now describe these key
uncertain model inputs and characterize their variability. With students, these
variables would typically be investigated using a combination of lecture and
assigned research by the students to uncover the type and extent of variability
involved. Depending upon the number of students involved, this can be a useful
team exercise, with each team reporting to the class, proposing and defending a
distribution for each variable. Figure 4 shows the distributions we have used for
Real Risk-Free Rate, Market Risk Premium, and Unlevered Beta.
Real Risk-Free Rate
In general, the nominal or quoted rate on a security is composed of the risk-free
rate plus compensation for risk. The Real Risk-Free Rate, denoted here as rRF* , is the
interest rate that would exist on a security that had no risk, including no inflation
risk. This may be thought of as a US Treasury security in a world without inflation.
The nominal rate, denoted here as rRF , is equal to the risk-free component plus an
inflation premium, i.e., rRF = rRF* + IP. Brigham & Houston (2010) cite the difficulty
of measuring the Real Risk-Free rate but say most experts think that rRF* has
fluctuated in the range of 2 to 4 percent in recent years. Accordingly, we adopted
that range and elected to use a triangular distribution with minimum of 2 percent and
a maximum of 4 percent to represent the Real Risk-Free rate.
Market Risk Premium
The market risk premium is the premium investors require to hold an average
stock compared to the least risky or risk-free investment, typically taken as a US
Treasury bond. The size of the premium is a function both of the investor's risk
aversion and how risky the investor perceives the market to be.
The market risk premium is not known with certainty, and so it must be
estimated (Brigham and Houston, 2007). Of course, estimates vary depending upon
the source. For example, Fernandez (2010) has reviewed more than 150 textbooks
and finds that recommendations for the market risk premium range from three
percent to ten percent. In a second paper, Fernandez, Aguirreanalloa and Corres
(2011) find that professors, analysts and company managers use different estimates
for the market risk premium (professors use 5.7%, analysts 5.0%, and managers
5.6%.). For the market risk premium distribution we elected to use a truncated
lognormal distribution having a mean of 5.50 percent and a standard deviation of
1.70%, with lower and upper truncation values of 1.50% and 15% respectively.
22 Journal of Financial Education
Unlevered Beta
The beta coefficient for an asset is a relative measure of correlated volatility
(risk) that compares the return on that asset with the return on a benchmark market
portfolio. The beta of the benchmark market volatility (market beta) is usually taken
to be unity. The "true" current beta of an asset is not known, and must be estimated
using historical and other data. For example, in order to obtain a regression estimate
of beta one must make at least three important data choices (Damodaran, 2011)
which can have a major effect on the beta estimate (Armitage, 2005). One must
choose a market index, decide how many years the data period will include, and also
select a time interval for the return data (e.g., daily, weekly, monthly). For any such
estimate there is an associated standard error – a reminder that the beta value
obtained is not known with certainty.
To model beta for Monte Carlo sampling here, a skewed distribution of beta
values was used that follows the shape and range found by Ang, Lui, and Schwarz
(2010). They developed OLS regression estimates of beta for 29,096 firms in non-
overlapping five year samples from 1960-2005 for all industries and found the
distribution of beta values to be, as expected, centered around one. The distribution
had a mean of 1.093 and a standard deviation of 0.765. The distribution of beta was
positively skewed, at 0.783 and fat-tailed with a kurtosis of 6.412. The beta for a
specific industry or specific firm would be expected to have somewhat less
variability than all industries together. Because we are modeling a firm that is
hypothetical, we elected to use a skewed distribution having a modal value of 1.000
with lower and upper extremes at 0.500 and 3.000 respectively. However, within the
range of empirical reasonability, we would encourage students to experiment with
different distributions for representing the unlevered beta.
Simulation Results
Once the distributions are assigned to all input variables, the model is
recalculated repeatedly and automatically by starting the simulation. With each
recalculation random values are drawn from the input distributions for use in the
model, and WACC values are obtained for the six scenarios. We set the number of
trials at 100,000 and thus obtained for each scenario 100,000 values of WACC. The
software automatically tabulates statistics, produces frequency histograms, and
provides related information about the outputs. Figure 5 shows frequency
histograms for resulting WACC in the six scenarios. All six scenarios have output
distributions of similar shape – skewness is consistent at a range of 1.03 to 1.09.
Mean WACC values and standard deviations do differ somewhat as shown in Table
3, which gives summary statistics for 100,000 trials. Recall that in the single-value
base model the minimum WACC occurred at Scenario 4 (see Figure 1); for the
simulation here the minimum average WACC does not occur at Scenario 4, rather
Spring/Summer 2014 23
Figure 5. WACC Frequency Diagrams for Six Scenarios
it is at Scenario 5.
It is of interest that the standard deviation becomes progressively smaller from
Scenario 1 to Scenario 6. Even though (mean) WACC goes down and then up as
expected (although not as markedly as in the single-value model) the uncertainty in
WACC - as measured by the standard deviation of the resulting distribution - is a
decreasing function of leverage. The higher the leverage the more certain we are of
our estimate of WACC. This can be counter intuitive to students, and a rich source
of discussion. Students are reminded that as leverage increases, the firm by
definition is relying more on debt as a source of capital, and less on equity. With
greater leverage, the contribution of equity to the WACC is reduced accordingly. By
use of sensitivity analysis (standard outputs of the simulation), students can trace the
24 Journal of Financial Education
Table 3. WACC Values for Six Scenarios from Simulation
and from the Base Model
Scenario 123456
Std. Dev. WACC
from Simulation 3.39% 2.93% 2.36% 2.03% 1.66% 1.28%
Mean WACC from
Simulation 11.28
%10.31
%9.34% 9.01% 8.91% 9.15%
WACC from Base
Model 8.99% 8.33% 7.75% 7.65% 7.80% 8.31%
WACC Difference
between Simulation
and Base Model 2.29% 1.98% 1.59% 1.36% 1.11% 0.84%
Figure 6. Mean WACC Values from Simulation and from the Base Model
sources of variance in WACC as well as the relative contributions of those sources.
In doing so, students see that the most important source of variability (risk) is the
unlevered beta (see Figure 9). While the unlevered beta has the greatest relative
contribution to variance in WACC, the overall impact of beta is progressively
Spring/Summer 2014 25
Figure 7. Probability of Scenario 4 WACC being 7.652% or Lower
Figure 8. Probability of Scenario 5 WACC being 7.799% or Lower
26 Journal of Financial Education
Figure 9. Contribution to Variance by the Three Input Variables – Scenario 1
diminished as leverage increases. Thus, while the mean value of WACC rises, its
variance decreases.
There are substantial differences between the calculated WACC values in the
base model and the mean values of WACC resulting from the simulation. For the
students, this is food for thought! These differences are summarized in Table 3 and
shown graphically in Figure 6. The difference diminishes progressively as the debt
leverage grows. This is consistent with the earlier observation that uncertainty in
mean WACC decreases with increasing debt leverage.
For Scenario 4 the most likely WACC value is about 8%, and the mean value
is 9.01%, but the calculated value for that scenario from the base model is 7.652%.
The simulation results indicate, as shown in Figure 7, that there is only about a 28%
probability of WACC being 7.652% or less.
Taking Scenario 5 as a similar example, the most likely value of WACC is about
8% while the mean value is 8.91%. In the single-value base model, the WACC value
for Scenario 5 was 7.799%. The simulation results indicate again, as shown in
Spring/Summer 2014 27
Figure 8, there is only about a 28% probability of a WACC being 7.799% or better
(less).
Figure 9 shows Scenario 1's contribution to variance by the three input
variables. This is representative of all scenarios; contribution of Unlevered Beta
ranged from 74.8% to 71.0% across the six scenarios. Corresponding ranges for
Market Risk Premium and Real Risk-Free Rate were 23.7% to 22.7% and 1.6% to
6.3% respectively. Thus the relative impact of the three variables is fairly stable.
From a review of the sensitivity charts, students readily conclude that the most
important variable is Unlevered Beta, followed by Market Risk Premium - even for
highly leveraged situations where most of the financing comes from debt.
LEARNING OBJECTIVES AND EVALUATION
The initial motivation for this work was a summary report from the Assurance
of Learning (AOL) Committee where the authors teach. The capstone course for
both graduate and undergraduate business majors includes a business simulation
along with a related test that is available to all schools using the business simulation.
Mean student performance at the authors' school on several discipline-specific test
questions was significantly lower than peer group overall mean. In several other
areas the same students were at par or higher than their peers. One of the finance-
related topics on which performance was lower than desired was "Leverage and the
Value of The Firm."
The mission of The Citadel School of Business Administration (CSBA) is to
educate and develop leaders of principle to serve a global community. CSBA
learning goals support the intent to build ethical leaders, but also reflect the belief
that for its graduates to be successful, a necessary condition is that they be proficient
in the traditional disciplines of business: Accounting, Economics, Finance,
Management, Marketing, Operations, and Information Systems.
Three years ago, the first listed author learned of the perceived learning deficit
related to leverage and firm value, a key idea in the finance discipline. To address
this discipline-specific need, he developed the six-scenario, spreadsheet-based
WACC model described here. He envisioned the model as a learning tool to help
address the discipline-specific deficit. Using the WACC model in several classes he
gathered anecdotal evidence and continued to make improvements based on student
response and comments. During 2012 the other two authors joined the effort to
further enrich the tool as a source of student learning by extending the interactive
model with student-performed Monte Carlo simulation.
The spreadsheet model of capital structure appears to be very helpful to
students. Evidence thus far is localized rather than program wide, and partly based
on student self-reported data. Based on this preliminary evidence, the authors are
optimistic about student use of the WACC model. The pedagogical value of having
students use interactive spreadsheet models has been well summarized by Leon, Seal
and Przasnyski (2006). As students create various capital structure scenarios for
28 Journal of Financial Education
their hypothetical firm they can interact and receive immediate feedback via the
calculated WACC and firm value. Students generally find this simple scenario
analysis both challenging and easy to understand - it stimulates analytical thinking
and facilitates the consideration of multiple interacting variables in an easy,
accessible format. The model promotes critical thinking and questioning about firm
capital structure. For example, after practicing with the model students:
1. Gain experience in setting different debt levels and immediately see the
results and trade-offs of leverage.
2. See the effect of different values of the firm's Beta, via its relation with risk
premium, on the cost of common equity.
3. Are able to better explain WACC and its importance within a firm.
4. Can articulate the importance of working toward minimum WACC, having
observed memorably that minimum WACC occurs at the point where the firm's
stock price is maximized.
In accord with evidence-based processes promoted by accrediting bodies, the
Citadel School of Business is in the process of replacing course-specific objectives
with measurable major learning outcomes. These outcomes or objectives will be
shared across all sections of the same course. For the finance discipline, all faculty
teaching the same course have agreed to include specific, measurable objectives, in
this case, related to WACC and capital structure of the firm. The model and
approaches presented here can be used within a class context in which student
learning outcomes could include:
1. Explain the capital structure decision within an organization.
A. Define WACC and explain its scope and importance within a firm.
B. Identify the major interactions between components that make up WACC
(e.g., greater debt increases risk, which increases both cost of debt and
cost of equity).
C. Recognize the effect of leverage on the price and yield of preferred stock.
D. Describe the relationship between firm value and WACC.
2. Recognize and evaluate uncertainty in key components of WACC.
A. Describe the impact of variability and uncertainty.
B. Distinguish between traditional practice and risk modeling in developing
WACC.
C. Select and use appropriate distributions for uncertain WACC input
variables.
3. Apply modeling and analytical skills to WACC decision-making.
A. Assess the impact on WACC of a range of debt levels.
B. Interpret simulation results and perform sensitivity analysis by tracing
the effects that inputs have on the distribution of resulting WACC
Spring/Summer 2014 29
values.
C. Choose and justify, from a range of debt levels, the level most
appropriate for a given firm (i.e., the optimal capital structure).
The learning objectives suggested here correspond to several levels of the
cognitive domain in Bloom's taxonomy - knowledge, comprehension, application,
analysis, synthesis, and evaluation. The objectives can be measured by direct
assessment through use of problem solving, embedded-questions in multiple-choice
tests, or short essay questions. In coordination with our Assurance of Learning
Committee cognizant faculty plan on initiating formal use of some or all of the
objectives described here in Fall 2014 finance courses.
SUMMARY AND CONCLUSIONS
This pedagogy was developed and presented in three main stages. In the first
stage, the student uses the experiential spreadsheet model to explore alternative
mixes of bonds, preferred stock and common stock in six capital structure scenarios.
The capital structure model calculates the resulting WACC and stock price for each
student scenario, and displays a WACC and stock price curve. Students can
immediately evaluate the results of their choices and modify them as they wish.
Their optimal debt-to-equity choice will result in a minimum cost of capital and a
maximum market value of the firm. In the second stage of the pedagogy, student
experience is deepened by applying Monte Caro simulation to the same set of
scenarios. The simulation allows the student to appreciate the character and degree
of uncertainty associated with inputs for WACC. The resulting output distributions
challenge the student to understand the impact that such uncertainty can have on the
WACC and value of the firm. In the third stage a rationale is offered for the
development and use of the model by the authors in a context of student learning
needs. Related student learning outcomes are also suggested.
We conclude, along with Schoemaker (1993), that scenario construction and
analysis is a practical way to stretch people's thinking, and we concur with Bunn and
Salo (1993) that by studying even simple scenarios managers (and students) can
become better prepared to make informed decisions. Our experience also mirrors
that of Markham and Palocsay (2006) who found that discussion of scenarios and
what-if analysis leads naturally to other modeling techniques, such as simulation.
Like scenario analysis, spreadsheet-based Monte Carlo simulation can provide
the student with a powerful tool for investigating and understanding financial
models when risk and uncertainty are present. Such simulation enables the student
to (a) check the validity of the assumptions underlying a financial model; (b) explore
the sensitivity of the model results to the input parameters whose values are
uncertain or are subject to random variation; and (c) better understand the inherent
variability of the final results.
The model described here takes a two-layer approach to exploring and
30 Journal of Financial Education
understanding WACC. The first layer is the interactive WACC-Stock Price scenario
analysis and the second layer is the Monte Carlo Simulation. The scenarios depict
the potential range of plausible alternatives; the simulation explores the uncertainty
and random variability associated with those alternatives. The model is highly
interactive and provides many opportunities for student engagement and learning.
These approaches are individually powerful tools for improved financial modeling
and risk assessment. Together, they provide a potent mechanism for students to
better understand the capital structure decision-making process.
ENDNOTES
1 The authors are thankful for helpful suggestions and constructive comments
from an anonymous reviewer and the Editor, as well as earlier encouragement and
critique from attendees at the 2012 joint Annual Conference of the Academy of
Business Education and the Financial Education Association.
2 The base spreadsheet model is available to interested readers upon email
request to the corresponding author at iordanis@citadel.edu.
3We are planning to expand our model so that the student would also select the
type of business risk (using, for example, a combo box) and the spreadsheet will
automatically select the debt rating and yield spreads.
4 Even though NOPAT (Net Operating Profit After Tax) and Net Investment are
both income measures, combined they represent the FCFF due to the depreciation
expense impact being netted out in both income measures.
5Our purpose is not to describe details of Monte Carlo simulation; there are
plentiful references that provide such information. One that gives a good overview
of both Monte Carlo simulation and Crystal Ball is Charnes (2007).
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32 Journal of Financial Education
... In accordance with the mandate of the National Energy Policy [1], which is to minimize the use of the portion of petroleum, optimize the use of natural gas, maximize renewable energy, and convert coal into energy reserves, the Indonesian government is currently committed to accelerating the gasification program on electricity generation. This program is at the same time to reduce carbon emissions and other greenhouse gases according to the Kyoto Protocol [2]. ...
... …………… [2] The value of WACC will be a reference to the calculation of the financial feasibility. The financial feasibility indicator that is shown with the Internal Rate of Return (IRR) value should be higher than this WACC value. ...
... The Weighted Average Cost of Capital is one of the important parameters in finance analysis and it will help several applications like firm valuation, capital budgeting analysis, and EVA (Berry, 2014 andRehman, 2010). The standard formula for WACC is as follows: ...
... The discount rate should reflect the project's risk. The starting point tends to be the firm's own weighted average cost of capital (i.e., WACC), which includes its cost of debt and equity financing (also see Berry et al., 2014), respectively. Given the tax benefit of debt financing, the WACC includes the after-tax cost of debt. ...
This case is intended to help students on accounting undergraduate and postgraduate courses deepen their understanding of capital budgeting. We introduce a working example and hypothetical case to show that knowing an investment project's net present value (NPV) is important but is not sufficient. Shareholders would also like to know how and when a project pays the excess wealth it generates. In the case we show in monetary amounts, how much each group receives in every time period; how much is received in the form of excess wealth by the existing shareholders; and, when does that excess wealth starts to accrue. The case can be used specifically in the final year undergraduate and postgraduate accounting study programmes.
This paper contains the statistics of the Equity Premium or Market Risk Premium (MRP) used in 2011 for 56 countries. We got answers for 85 countries, but we only report the results for 56 countries with more than 6 answers. Most previous surveys have been interested in the Expected MRP, but this survey asks about the Required MRP. The paper also contains the references used to justify the MRP, comments from persons that do not use MRP, and comments from persons that do use MRP.
- Seth Armitage
This volume provides a thorough exposition of the theory relating to the cost of capital--a core subject in academic finance and also of genuine practical importance. Any serious attempt to value a business requires an estimate of its cost of capital. This book explains models and arguments in a way which does justice to this reasoning, while minimizing the prior knowledge of finance and maths expected of the reader. It is intended primarily for students at advanced undergraduate levels.
Kolb's experiential theory of learning, later modified by McCarthy to develop the 4MAT model, shows that active experimentation is a large part of learning for all types of learners. We use the 4MAT model as the theoretical underpinning to explore and develop some illustrative interactive tutorials to support the teaching of OR/MS spreadsheet modeling. Due to a much shallower learning curve on the new generation of screen capture technology, the design and creation of such spreadsheet support modules can now realistically be done by individual faculty in a reasonable amount of time. Three levels of interactivity are used in the modules to match the learning stages of the 4MAT model. We discuss implementation issues with current screen capture software and the benefits and limitations of this approach for supporting the teaching of spreadsheet modeling in OR/MS.
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![Humberto Barreto]()
- Frank Howland
This highly accessible and innovative text (and accompanying website: Www.wabash.edu/econometrics) uses Excel (R) workbooks powered by Visual Basic macros to teach the core concepts of econometrics without advanced mathematics. It enables students to run monte Carlo simulations in which they repeatedly sample from artificial data sets in order to understand the data generating process and sampling distribution. Coverage includes omitted variables, binary response models, basic time series, and simultaneous equations. The authors teach students how to construct their own real-world data sets drawn from the internet, which they can analyze with Excel (R) or with other econometric software.
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![Robert M. Hull]()
This paper offers a pedagogical application of the capital structure decision-making process for a firm issuing debt to retire equity. The application has proven successful in helping advanced business students understand the impact of the debt choice on firm value. The application introduces a tool that students can use as future financial managers. The tool is a recent gain to leverage (GL) equation given by Hull's Capital Structure Model (CSM). This CSM equation contains cost of capital variables for which managers can reasonably estimate values compared to the difficulty of directly measuring the dollar value of bankruptcy and agency costs. Surprisingly, the cost of capital variables found in the CSM equations are missing from textbook equations and, until the development of the CSM, even missing from the perpetuity GL research. Given estimates for the costs of capital and tax rates, this paper's pedagogical application shows how managers can use the CSM equation to choose an optimal debt level.
- John Rozycki
Monte Carlo simulation is a useful capital budgeting tool that allows the user to reflect the uncertainty associated with various cash now components. The output from the simulation consists of distributions of net cash flows, which can be used for decision-making and risk management. Unfortunately, Monte Carlo simulations are often implemented using specialized software, making them inaccessible to many students. Moreover, in using specialized software, students may perceive Monte Carlo simulation as a "black box." I demonstrate how to implement Monte Carlo simulation for a complex capital budgeting problem using Microsofi Excel (Excel) and three common distributions: normal, lognormal and uniform. No additional software is needed. Since the simulation is built by modifying an already-understood static capital budgeting worksheet, it is more likely that the simulation will be understood and used.
- Robert E. Linneman
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![Harold E Klein]()
Over the past 5 years the authors have been examining the Fortune 1000 U.S. industrials' changes in corporate planning practices with respect to environmental analysis. Results of earlier studies have been reported in the February 1979 and October 1981 issues of Long Range Planning. This article documents the rapid, domestic increase in the use of multiple scenarios between 1977 and 1981. Given the intention for future use by present users and the length of time multiple scenarios have been used by some firms, this is strong evidence that multiple scenarios are a useful conjectural tool which can help corporate management plan in an unstable environment.
- Markham
- Palocsay
"What-if" or sensitivity analysis is one of the most important and valuable concepts in management science MS. To emphasize its practical relevance in a business environment, we teach students in our introductory MS course to analyze "scenarios" with Excel's built-in Scenario tool. This paper demonstrates the application of the Scenario tool with several examples.
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Source: https://www.researchgate.net/publication/289530651_Understanding_Weighted_Average_Cost_of_Capital_A_Pedagogical_Application
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