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Case 8: (PNC) Operating
Leverage, Financial
Leverage, and Optimal
Capital Structure
2015
PREPARED BY: JORDAN HUUS
FIN 475 FALL 2015
PREPARED FOR: JAMES HASKINS, PHD
DECEMBER 15, 2015
P a g e | 1 Jordan Huus
Table of Contents
Executive Summary ..............................................................................2
Introduction ..........................................................................................3
Background...........................................................................................3
Statement of Purpose and Rationale ......................................................3
Methodology .........................................................................................4
Body .....................................................................................................4
Recommendation ..................................................................................7
Citations ...............................................................................................7
Appendix 1 ...........................................................................................8
Appendix 2 ...........................................................................................9
Appendix 3 ...........................................................................................10
Appendix 4 ...........................................................................................11
Appendix 5 ...........................................................................................12
Appendix 6 ...........................................................................................13-14
Appendix 7 ...........................................................................................14
Appendix 8 ...........................................................................................15-16
P a g e | 2 Jordan Huus
Executive Summary
Case 8 revolves around further capital structure analysis such as operating leverage,
financial leverage, and optimal capital structure. Throughout the case, many topics are covered to
represent the process used to find the best capital structure. Fortunately, PNC is facing a decision
with great relevance in its efforts to spin off its wholly owned subsidiary, PNC Router. PNC
Router will be spun off in the near future resultant of pressure from PNC Routers president,
Frank Garcia. We will use this opportunity as an example to explain how to locate a firm’s best
capital structure.
PNC Router is faced with two strategic plans for its business to operate in after it spun
off. Plan L and Plan H. Both will be presented and then analyzed to find the best option with the
greatest value. Under Plan L, the company will continue to outsource most parts and use
assembly equipment with a lower initial cost, but higher cost for labor. Under Plan H, Router
would handle all manufacturing in-house, using highly automated equipment. Plan H would have
much higher fixed costs but lower variable costs per unit. Refer to Appendix 1, Table 2a, for
additional information on both cases.
After some analysis as seen in Appendix 3, Table 3, Plan H has substantially more risk
compared to Plan L. Plan H has a higher operating leverage than Plan L. This is because Plan H
has very high fixed costs and low variable costs compared to Plan L. High fixed cost and low
variable cost means that with each additional unit of output, sales figures increase greater than
variable costs. (2015, December 14). Information retrieved from Investopedia.com. Furthermore,
when analyzing both plans’ unlevered and levered operations Plan H has inappropriate risk and
return levels. As seen in Table 3, Plan H has expected ROIC of 12.1% compared to Plan L of
12.7%. Now those figures are seem immaterially close, but let’s factor in a more insightful
measurement, standard deviation. Plan H has an ROE standard deviation of 54.0% compared to
Plan L of 24.2%. Plan H’s high risk is not justified by lower returns of ROIC and ROE when
compared to Plan L.
Based on ROE, riskiness, and WACC, Router should choose to pursue Plan L. The
following assumptions are based on a debt level of 40%. Plan L has a higher expected ROE of
21.23% compared to Plan H of 20.16%. Furthermore, Plan L has much lower risk compared to
Plan H. Standard deviation of ROE for Plan L is 24.20% versus 54.0% for Plan H. So far, Plan L
has lower risk and higher return. As a final point, Plan L has a lower capital requirements as well
as a lower WACC. Capital requirements for Plan L are $1.5 million, roughly two and a half
times smaller than capital requirements for Plan H. This is attractive because Router can operate
with less long-term liabilities on its books. Finally, WACC of 9.56% for Plan L is almost 100
basis points lower than Plan H of 10.40%.
P a g e | 3 Jordan Huus
Introduction
Case 8 presents further concepts to capital structure, introducing tools used to find the
optimal capital structure. Optimizing capital structure is a particularly important subject for PNC
due to its current plan to spin off a wholly owned subsidiary called PNC Router Inc. PNC is
required to develop a capital structure for the subsidiary before they spin it off. As noted in
previous cases, optimal capital structure is connected to weighted average cost of capital or
WACC, and is the focus of this case. By optimizing capital structure, WACC will be minimized.
Background
Some years ago, PNC decided to build specialized routers for its customers. PNC Router
Inc. was formed and the president of Router is Frank Garcia, who has been recently pushing for a
spin-off. Frank believes that a spin-off will allow it to grow and increase chances of success.
Currently, PNC owns all of Router’s stock, but the plan is for Router to finalize its operating
plan and capital structure and then sell shares to the public via IPO.
Finalizing PNC’s plan choice is going to be the overarching theme in Case 8. Two
strategic plans will be presented and then analyzed to find the best option. Under Plan L, the
company will continue to outsource most parts and use assembly equipment with a lower initial
cost, but higher cost for labor. Under Plan H, Router would handle all manufacturing in-house,
using highly automated equipment. Plan H would have much higher fixed costs but lower
variable costs per unit. Refer to Appendix 1, Table 2a, for additional information on both cases.
Statement of Purpose and Rationale
The issues in finding the correct strategic option, Plan L or H, lies within finding the
correct capital structure. Comparing optimal capital structure of both plans is essential because of
the widespread differences between the two. Differences such as variable costs, fixed costs, units
demanded, debt levels, equity levels, and many more greatly affect value of the firm. All of the
previously mentioned variables affect the way a capital structure should be formed. Fixed and
variable costs effect operating leverage. Operating leverage is a measurement of the degree to
which a firm or project incurs a combination of fixed and variable costs. (2015, December 14).
Information retrieved from Investopedia.com. Higher operating leverage levels produce higher
gross margins. As the volume of sales in a business increases, each new sale contributes less
to fixed costs and more to profitability.
Furthermore, variables such as the required amount of capital affect financial leverage.
Router will need to raise a certain amount of capital during its IPO and potential debt issuance.
Therefore, each plan must be analyzed to determine optimal debt levels to determine the best
capital structure. Financial leverage is the amount of debt a company takes on in their capital
structure. This debt is a type of fixed income security such as bonds and preferred equity, which
are used to finance business operations. (2015, December 14). Information retrieved from
Investopedia.com. Higher financial leverage can help reduce tax expenses but can become a
detriment if used too much.
Looking at Appendix 6, Table 7, we can see the effects of financial leverage on return on
equity, or ROE. ROE measures a corporation’s profitability by revealing how much profit a
company generates with the money shareholders have invested. ROE is an important ratio to
P a g e | 4 Jordan Huus
investors, in that it is calculated by taking net income divided by total equity. With this
calculation in mind, ROE should be positively affected by higher financial leverage because
returns less equity is needed to meet the capital requirements. Simply put, by adding debt to the
capital structure, less equity will be needed causing the denominator of the ROE calculation to be
lower. This theory is exemplified by looking at Plan L before and after leverage is used. Equity
used before financial leverage is $1,500,000 and falls to $900,000 after financial leverage is
used.
Methodology
As seen in many of the appendices, many different techniques and methodologies are
used in our analysis of Plan L and H. A continuous theme throughout our analysis consisted of
side-by-side comparison of the two, allowing the direct evaluation of both outcomes. Many
different analysis tools such as Hamada equation, scenario analysis, and CAPM were used. The
Hama equation, used in Appendix 7, Table 8, is a method of analyzing a firm’s cost of capital as
it uses additional financial leverage, and how that relates to the overall riskiness of the firm.
Scenario analysis, used in Appendix 4, Table 4, is a way of testing results when changing one
variable at a time. This is helpful in that it shows how reactive important figures such as ROIC
and break-even units are affected from changes in different input variables.
Body
Operating leverage is a measurement of the degree to which a firm or project incurs a
combination of fixed and variable costs. Higher operating leverage levels produce higher gross
margins. As the volume of sales in a business increases, each new sale contributes less to fixed
costs and more to profitability. Higher allocation to fixed costs and lower allocation to lower
costs is a sign of using operating leverage. (2015, December 14). Information retrieved from
Investopedia.com.
Financial leverage is the amount of debt a company takes on in their capital structure.
This debt is a type of fixed income security such as bonds and preferred equity, which are used
to finance business operations. Higher financial leverage can help reduce tax expenses but can
become a detriment if used too much. (2015, December 14). Information retrieved from
Investopedia.com.
Business risk is a type of risk caused by potential problems that may arise attributable to
that company. Potential problems such as the market conditions for sales figures, legislation
regulating a company’s products, or the competition that company faces are all examples of
business risk. Companies with higher business risk should have lower debt ratios to help avoid
chances of bankruptcy. (2015, December 14). Information retrieved from Investopedia.com.
Financial risk stems from the possibility that shareholders may lose money due to a
business’s inability to pay financial obligations. Financial risk is heightened when a company has
large liabilities on their balance sheet. This means that the company has many creditors
expecting to be paid. If that company is unable to make enough EBIT, than they have a high
chance of defaulting on current liabilities. (2015, December 14). Information retrieved from
Investopedia.com.
P a g e | 5 Jordan Huus
Plan H has substantially more risk compared to Plan L. Plan H has a higher operating
leverage than Plan L. This is because Plan H has very high fixed costs and low variable costs
compared to Plan L. High fixed cost and low variable cost means that with each additional unit
of output, sales figures increase greater than variable costs. Furthermore, when analyzing both
plans’ unlevered and levered operations Plan H has inappropriate risk and return levels. As seen
in Appendix 6, Table 7, Plan H has expected ROIC of 12.1% compared to Plan L of 12.7%. Now
those figures are seem immaterially close, but let’s factor in a more insightful measurement,
standard deviation. Plan H has an ROE standard deviation of 54.0% compared to Plan L of
24.2%. Plan H’s high risk is not justified by lower returns of ROIC and ROE when compared to
Plan L.
Optimal capital structure occurs when firms minimize their Weighted Average Cost of
Capital, or WACC. Equity and debt both come at a price to the borrowing company and are what
make up WACC. Equity financing has cost associated with the dividends paid and stock price
appreciation that shareholders expect to receive. Additionally, companies who use bond
financing must pay out interest payments to bond holders. These are the two main types off cost
that make up the composition of WACC. Other forms of cost include preferred stock which are
treated very similarly to bonds.
Firms seeking to minimize WACC are in turn adding value to their company. As noted in
previous cases, the proportions allocated to debt and equity determine a company’s capital
structure. Higher allocations of debt cause a company to have higher financial leverage as well as
higher risk and return. Different mixtures of debt and equity weighting can lower WACC by
using interest payment on debt as tax deductible expenses. Thus, higher use of debt, instead of
equity, leads to lower taxes and higher income. This effect only helps a company to a certain
point, before interest payments become too high and start to negatively affect a company’s
bottom line.
The first step a company must take in determining their own optimal capital structure is
to find the different debt financing options available to them and the relative cost. Higher
weights of debt in capital structure can lead to higher cost on that debt. As seen in Appendix 5,
Table 6, different weights, starting with 0% and ending at 60%, can be seen and thus used in
subsequent analysis. The aforementioned table was created through discussions with investment
bankers according to Router’s financial statements and overall health. Investment bankers are
paid to have their finger on the pulse of capital markets. Accuracy of cost figures associated with
weights of debt should be used as reliable information and perhaps updated if too much time
expires or a material change in market trends occurs.
When looking at Table 6, in Appendix 5, directors may observe that potential savings
could be made if debt were taken out at 20% the first round of financing and another 20% during
a second round. The thought is that it would lower cost of debt by separately financing the two,
causing the average cost of debt to be at 7.6% instead of 12.0%. Unfortunately, things aren’t that
simple. The cost figures presented in Table 6 are ongoing interest payments and are not inclusive
of one-time fixed payments during issuance. Each time debt financing is made, there is a fixed
cost passed on to the borrower for fees such as administrative costs. These fixed costs offset
potential savings made from issuing multiple rounds of financing.
To determine the effects of financial leverage, analysis was performed in Table 7
Appendix 6. The tables show the different effects of financial leverage on Plans L and H. 0%
leverage and 40% leverage were used as scenarios to observe ROIC. The goal is to define if
P a g e | 6 Jordan Huus
financial leverage appropriately effects of risk return trade-off. When looking at the outcomes of
0% financial leverage, Plan L and Plan H have ROIC of 14.8% and 14.2%, respectively. These
returns are calculated by taking expected “Net income” and dividing it by “Total assets under
Plan …” ROIC is a calculation used to assess a company’s efficiency at allocating capital and
gives a sense of how well a company is using capital to generate returns. Unfortunately, higher
financial leverage, at 40%, causes ROIC to fall under both plans. After financial leverage of 40%
is implemented, ROIC for plans L and H fall to 12.7% and 12.1%, respectively.
Looking at Appendix 6, Table 7, we can see the effects of financial leverage on return on
equity, or ROE. ROE measures a corporation’s profitability by revealing how much profit a
company generates with the money shareholders have invested. ROE is an important ratio to
investors, in that it is calculated by taking net income divided by total equity. With this
calculation in mind, ROE should be positively affected by higher financial leverage because
returns less equity is needed to meet the capital requirements. Simply put, by adding debt to the
capital structure, less equity will be needed causing the denominator of the ROE calculation to be
lower. This theory is exemplified by looking at Plan L before and after leverage is used. Equity
used before financial leverage is $1,500,000 and falls to $900,000 after financial leverage is
used.
Minimizing WACC is widely accepted as the best way to optimize firm value. Typically,
by minimizing the cost of capital that a firm uses, it is able to increase profitability and
efficiency. This is not always the case for companies in unique financial positions. Startup
companies that have very high business risk may forgo issuing debt. One reason that stem from
this decision may be to limit financial risk. Startup companies are inherently risky and they may
not want to add to further financial risk. Secondly, issuing debt may be too costly and may be
better off just issuing equity. Debt issuance such as bonds require periodic interest payments.
Negative net income figures may not be able to pay these payments off as they come due.
The Hamada Equation analyzes a firm’s costs of capital as it uses additional financial
leverage, and how that relates to the overall riskiness of the firm. Hamada’s equation can depict
how much additional risk a firm will take on by using financial leverage. (2015, December 14).
Information retrieved from Investopedia.com. It does this by separating out the beta, or risk, of a
company’s business risk total risk. Once a firm’s unlevered beta is found it can be compared to
the levered beta. This provides a representation of the increase in riskiness the firm receives
when financial leverage is used.
The aforementioned concept behind the Hamada’s equation is exemplified in Appendix
8, Tables 8. Table 8 shows unlevered betas for Plan H and L where debt is 0%. Unlevered beta
for Plan L is 1.1 and 1.3 for Plan H. As allocation of capital structure increases it’s percentage of
debt, beta begins to increase. At 40% weight of debt, beta has increased to 1.54 and 1.82 for Plan
L and H respectively. That is an increase of risk of 40% for each project, a substantial change to
the riskiness of the entire firm. Furthermore, Hamada’s equation can be used to determine cost of
equity by entering the levered beta in to the CAPM model of Modigliani Miller.
Alternative ways to work around M&M theories and confirm the cost of equity is to
speak with investment bankers about the estimated rate at which prospective buyers would
require a return. Investment bankers know the demand for a company from speaking with
investors in the primary market. This perhaps could provide them with additional data to
estimate cost of equity for Router.
P a g e | 7 Jordan Huus
Optimal Capital structure is found by pinpointing minimum WACC. Minimum WACC
locates optimal capital structure because it simply finds the lowest cost for the firms required
capital. By lowering the cost of capital, firms stand to pay less in taxes, interest, and dividends to
shareholders. Router’s minimum WACC for Plans L and H can be seen in Appendix 8, Tables 9,
10, and Graph 1. At 40% financed with debt, both plans L and H are the lowest at 9.56% and
10.40%.
Recommendation
Based on ROE, riskiness, and WACC, Router should choose to pursue Plan L. The
following assumptions are based on a debt level of 40%. Plan L has a higher expected ROE of
21.23% compared to Plan H of 20.16%. Furthermore, Plan L has much lower risk compared to
Plan H. Standard deviation of ROE for Plan L is 24.20% versus 54.0% for Plan H. So far, Plan L
has lower risk and higher return. As a final point, Plan L has a lower capital requirements as well
as a lower WACC. Capital requirements for Plan L are $1.5 million, roughly two and a half
times smaller than capital requirements for Plan H. This is attractive because Router can operate
with less long-term liabilities on its books. Finally, WACC of 9.56% for Plan L is almost 100
basis points lower than Plan H of 10.40%.
Citations
http://www.investopedia.com/terms/r/returnoninvestmentcapital.asp?header_alt=c
http://www.investopedia.com/terms/r/returnonequity.asp?header_alt=c
http://www.investopedia.com/terms/n/nopat.asp?header_alt=c
http://www.investopedia.com/terms/o/operatingleverage.asp?header_alt=c
http://www.investopedia.com/walkthrough/corporate-finance/5/capital-structure/financial-
leverage.aspx?header_alt=c
http://www.investopedia.com/terms/c/capitalstructure.asp?header_alt=c
http://www.investopedia.com/terms/f/financialrisk.asp?header_alt=c
http://www.investopedia.com/terms/b/businessrisk.asp?header_alt=c
P a g e | 8 Jordan Huus
Appendix
Appendix 1
Table 1
Above is original data provided by for the strategic options available for Router. Under
Plan L, the company will continue to outsource most parts and use assembly equipment with a
lower initial cost, but higher cost for labor. Plan L has higher variable costs of $329 and lower
fixed costs of $400,000 compared to Plan H of $150 and $2,800,000, respectively. Under Plan H,
Router would handle all manufacturing in-house, using highly automated equipment. Plan H
would have much higher fixed costs but lower variable costs per unit. Furthermore, the capital
required for Plan L is much lower than Plan H. This is because under Plan H, Router will need to
spend large amounts of capital to buy automated machinery.
Input Data, Both Plans
Price $384
Unit Demand, Expected 16,000
Tax Rate 40%
Data for Plan L
Variable cost/unit $329
Total fixed op. costs $400,000
Non-cash component of FC $200,000
Maximum units of capacity 20,000
Required Capital (or assets) $1,500,000
Data for Plan H
Variable cost/unit $150
Total fixed op. costs $2,800,000
Non-cash component of FC $1,400,000
Maximum units of capacity 35,000Required Capital (or assets) $4,000,000
P a g e | 9 Jordan Huus
Appendix 2
Table 2
Units demanded may be very different conditional to economic market conditions. As
seen above in Table 2, five different market conditions have been stated with relative probability
levels. These probability levels are then used to estimate a reasonable level of units sold and
subsequent revenue generated. After calculating each economic impact on units sold and
revenue, expected value figures and standard deviation from the mean can be calculated. These
figures are important for painting a picture of riskiness and variability between the two plans.
Plan L has a lower standard deviation compared to Plan H, depicting Plan H as the higher risk
project. Finally, risk reward trade-off is consistent with this model. Plan H has higher expected
return relative to Plan L.
Sales Revenue and Probability Dist
Awful (Exp. x 0) 0.10 0.000 0 $0 0 $0
Poor (Exp x .5) 0.20 0.500 8,000 $3,072,000 8,000 $3,072,000
Expected Units 0.40 1.000 16,000 $6,144,000 16,000 $6,144,000
Good (exp. x 1.5) 0.20 1.500 20,000 $7,680,000 24,000 $9,216,000
Great (exp. X 2) 0.10 2.000 20,000 $7,680,000 32,000 $12,288,000
Expected Values: 14,000 5,376,000$ 16,000 6,144,000$
Standard Deviation (SD): 6,261 2,404,220$ 8,764 3,365,207$
Coefficient of Variation (CV): 0.45 0.45 0.55 0.55
Revenue
(Thousands)
Revenue
(Thousands)
Factor: Multiply
it by expected
units from
above to find
units produced
Units Sold:
Factor times
expected sales,
constrained to
max level
(Thousands)
Sales Data Applicable to HSales Data Applicable to L
Probability of
this market
condition
Units Sold:
Factor times
expected sales,
constrained to
max level
(Thousands) Market conditions
P a g e | 10 Jordan Huus
Appendix 3
Table 3
Operating profitability is calculated by sales minus total operating costs. Operating costs
consist of variable costs and fixed costs. The importance of operating profitability is the
company’s ability to sell products at a profitable rate. Return on invested capital, ROIC, is an
additional measurement to rate the profitability of operating capital based on the amount of
outstanding capital. ROIC is calculated by taking net operating profit after taxes, NOPAT, and
then dividing it by the total capital. More simply, ROIC measures the profitability of debt and
equity capital raised.
0 $400,000 -$400,000 -$240,000 -16.0% $2,800,000 -$2,800,000 -$1,680,000 -42.0%
8,000 $3,032,000 $40,000 $24,000 1.6% $4,000,000 -$928,000 -$556,800 -13.9%
16,000 $5,664,000 $480,000 $288,000 19.2% $5,200,000 $944,000 $566,400 14.2%
24,000 $6,980,000 $700,000 $420,000 28.0% $6,400,000 $2,816,000 $1,689,600 42.2%
32,000 $6,980,000 $700,000 $420,000 28.0% $7,600,000 $4,688,000 $2,812,800 70.3%
Exp. Value: $5,006,000 $370,000 $222,000 14.80% $5,200,000 $944,000 $566,400 14.16%
Std. Dev.: $2,059,866 $344,354 $206,613 0.14 $1,314,534 $2,050,673 $1,230,404 0.31
CV: 0.41 0.93 0.93 0.93 0.25 2.17 2.17 2.17
Operating Profitability Under Plans L and H
Pre-tax
Operating
Profit (EBIT)
Plan L: Low Fixed, High Variable Costs
Units
Demanded
(not units sold
if con-strained)
Plan H: High Fixed, Low Variable Costs
Return on
Invested Capital
(ROIC)
Net Oper. Profit
After Taxes
(NOPAT)
Total
Operating
Costs
Total Operating
Costs
Return on
Invested Capital
(ROIC)
Pre-tax
Operating Profit
(EBIT)
Net Oper. Profit
After Taxes
(NOPAT)
P a g e | 11 Jordan Huus
Appendix 4
Table 4
The previous sensitivity analysis depicts the different effects cause by changes in one
variable at a time. By changes units of measurement such as price, average demand, fixed costs
and more, outcomes can be analyzed and then compared to the opposing plan. One great
example in the above table is the ROIC relative to changes in price. ROIC is calculated by taking
net income divided by total capital. Plan L has large variating ROIC when changes in price
occur. Plan H has much more consistent changes in ROIC caused by changes in price. More
consistent returns seen in Plan H stem from a larger amount of required capital. Larger amounts
of total capital in the denominator of the ROIC calculation to become larger, which causes
changes in the numerator to affect ROIC less
Price L H Price L H
$307 -18,349 17,812 $307 -49.9% -7.1%
$384 7,273 11,966 $384 32.0% 23.6%
$461 3,035 9,009 $461 113.9% 54.3%
Average
Demand L H
12,800 20.3% 4.9%
16,000 32.0% 23.6%
19,200 43.7% 42.3%
Variable Variable
Cost Breakeven ROIC Cost Breakeven ROIC
$264 3,333 101.3% $120 10,606 35.6%
$330 7,407 30.9% $150 11,966 23.6%
$396 -33,333 -39.5% $180 13,725 11.6%
Fixed Fixed
Cost Breakeven ROIC Cost Breakeven ROIC
$320,000 5,818 37.3% $2,240,000 9,573 37.6%
$400,000 7,273 32.0% $2,800,000 11,966 23.6%
$480,000 8,727 26.7% $3,360,000 14,359 9.6%
Required Required
Capital ROIC Capital ROIC
$1,200,000 40.0% $3,200,000 29.5%
$1,500,000 32.0% $4,000,000 23.6%
$1,800,000 26.7% $4,800,000 19.7%
Prod. Prod.
Constraint ROIC Constraint ROIC
16,000 32.0% 28,000 93.8%
20,000 46.7% 35,000 134.8%
24,000 51.1% 42,000 146.4%
Breakeven Units
Expected values
Expected values
Expected values
Expected values
ROIC
Plan L Plan H
ROIC
P a g e | 12 Jordan Huus
Appendix 5
Table 5
Table 6
Table ______, above, shows the existing assets that both Plan L and Plan H currently
have on their books. This table is used to establish the amount of additional capital needed to
meet the requirements for each plan. Plan L has capital requirements of $1,500,000, with only
$1,264,320 currently available. The additional capital of $234,680 will need to be raised either
through equity issuance in the form of an IPO, or through issuing bonds. Plan H has higher
capital requirements due to high initial cost of automated machinery. Capital requirements for
Plan H will need to conclude at $4,000,000, with only $1,265,320 currently available. Again,
either through IPO or debt issuance, Router will need to produce the difference of $2,734,680.
Table ______ depicts the different costs of debt available relative to different amounts of
debt. Different weights, starting with 0% and ending at 60%, can be seen and thus used in
subsequent analysis. The aforementioned table was created through discussions with investment
bankers according to Router’s financial statements and overall health. Investment bankers are
paid to have their finger on the pulse of capital markets. Accuracy of cost figures associated with
weights of debt should be used as reliable information and perhaps updated if too much time
expires or a material change in market trends occurs.
Values for Router at Present Time (Book Values): Plan L Plan H
Existing total assets $1,265,320 $1,265,320
Existing Debt $0 $0
Existing net capital $1,265,320 $1,265,320
Total capital required for Plan $1,500,000 $4,000,000
Additional capital needed for Plan $234,680 $2,734,680
Percent Percent Interest
financed financed Rate on
with debt with equity Debt(wd) (we) (kd )
0% 100% 7.3%
10% 90% 7.4%
20% 80% 7.6%
30% 70% 8.1%
40% 60% 8.6%
50% 50% 10.0%
60% 40% 12.0%
Interest Rate Cost Schedule
P a g e | 13 Jordan Huus
Appendix 6
Table 7
Plan L Debt (Book value) 0% $0
Equity after financing $1,500,000
Total assets under Plan L $1,500,000
Interest rate 7.3%
Product Pre-tax Taxes Net
Demand Probability EBIT Interest income (40%) income ROE
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Awful 0.10 (400,000.00)$ -$ (400,000)$ (160,000)$ (240,000)$ -16.00% N/A
Poor 0.20 40,000.00$ -$ 40,000$ 16,000$ 24,000$ 1.60% N/A
Average 0.40 480,000.00$ -$ 480,000$ 192,000$ 288,000$ 19.20% N/A
Good 0.20 700,000.00$ -$ 700,000$ 280,000$ 420,000$ 28.00% N/A
Great 0.10 700,000.00$ -$ 700,000$ 280,000$ 420,000$ 28.00% N/A
Expected value: $370,000 $0 $370,000 $148,000 $222,000 14.80% $0
Standard deviation: 13.77% #VALUE!
Coefficient of variation: 0.93 #VALUE!
ROIC: 14.80%
Plan H Debt (Book value) 0% $0
Equity after financing $4,000,000
Total assets under Plan H $4,000,000
Interest rate 7.3%
Product Pre-tax Taxes Net
Demand Probability EBIT Interest income (40%) income ROE
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Awful 0.10 (2,800,000)$ -$ (2,800,000)$ (1,120,000)$ (1,680,000)$ -42.00% N/A
Poor 0.20 (928,000)$ -$ (928,000)$ (371,200)$ (556,800)$ -13.92% N/A
Average 0.40 944,000$ -$ 944,000$ 377,600$ 566,400$ 14.16% N/A
Good 0.20 2,816,000$ -$ 2,816,000$ 1,126,400$ 1,689,600$ 42.24% N/A
Great 0.10 4,688,000$ -$ 4,688,000$ 1,875,200$ 2,812,800$ 70.32% N/A
Expected value: $944,000 $0 $944,000 $377,600 $566,400 14.16% 0.00
Standard deviation: 30.76% #VALUE!
Coefficient of variation: 2.17 #VALUE!
ROIC: 14.2%
Section II. Leveraged: 40% of Assets Financed with Long-Term Debt
Plan L Debt (Market value) 40% $600,000
Equity after financing $900,000
Total assets under Plan L $1,500,000
Interest rate 8.6%
Product Pre-tax Taxes Net
Demand Probability EBIT Interest income (40%) income ROE TIE Ratio
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Terrible 0.10 -$400,000 $51,600 -$451,600 -$180,640 -$270,960 -30.1% -7.8
Poor 0.20 $40,000 $51,600 -$11,600 -$4,640 -$6,960 -0.8% 0.8
Average 0.40 $480,000 $51,600 $428,400 $171,360 $257,040 28.6% 9.3
Good 0.20 $700,000 $51,600 $648,400 $259,360 $389,040 43.2% 13.6
Great 0.10 $700,000 $51,600 $648,400 $259,360 $389,040 43.2% 13.6
Expected value: $370,000 $51,600 $318,400 $127,360 $191,040 21.23% 7.17
Standard deviation: 24.20% 7.03
Coefficient of variation: #REF! 0.98
ROIC: 12.7%
Plan H Debt (Market value) 40% $1,600,000
Equity after financing $2,400,000
Total assets under Plan H $4,000,000
Interest rate 8.6%
Product Pre-tax Taxes Net
Demand Probability EBIT Interest income (40%) income ROE
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Terrible 0.10 -$2,800,000 $137,600 -$2,937,600 -$1,175,040 -$1,762,560 -73.4% -20.3
Poor 0.20 -$928,000 $137,600 -$1,065,600 -$426,240 -$639,360 -26.6% -6.7
Average 0.40 $944,000 $137,600 $806,400 $322,560 $483,840 20.2% 6.9
Good 0.20 $2,816,000 $137,600 $2,678,400 $1,071,360 $1,607,040 67.0% 20.5
Great 0.10 $4,688,000 $137,600 $4,550,400 $1,820,160 $2,730,240 113.8% 34.1
Expected value: $944,000 $137,600 $806,400 $322,560 $483,840 20.16% 6.86
Standard deviation: 54.0% 1490.3%
Coefficient of variation: 2.68 2.17
ROIC: 12.1%
TIE Ratio
TIE Ratio
TIE Ratio
P a g e | 14 Jordan Huus
Table 7 above shows the effects of using debt on net income and ROE. The first two
tables consist of Plan L and H with zero financial leverage. With zero financial leverage, interest
payments are zero, allowing net income to be higher. In the scope of these two plans, additional
capital is needed both projects. Therefore, we must add financial leverage to the analysis which
can be seen in the lower two tables within Table 7. These two tables depict a financial leverage
level of 40%. Interest payments increase and lower net income for both Plan L and H.
Appendix 7
Table 8
Table 8 shows unlevered betas for Plan H and L where debt is 0%. These betas were
found using Hamada’s equation. Unlevered beta for Plan L is 1.1 and 1.3 for Plan H. As
allocation of capital structure increases it’s percentage of debt, beta begins to increase. At 40%
weight of debt, beta has increased to 1.54 and 1.82 for Plan L and H respectively. That is an
increase of risk of 40% for each project, a substantial change to the riskiness of the entire firm.
Tax rate 40%
Plan L Plan H
wd D/S 1.1 1.3
0% 0.00 1.10 1.30
10% 0.11 1.17 1.39
20% 0.25 1.27 1.50
30% 0.43 1.38 1.63
40% 0.67 1.54 1.82
50% 1.00 1.76 2.08
60% 1.50 2.09 2.47
Hamada bU
P a g e | 15 Jordan Huus
Appendix 8
Table 9
Table 10
Plan L, Optimal Capital Structure Analysis Should use per share analysis first then Optimal capital structure
Percent
financed
with debt,wd
(1)
Market Debt/
Equity, D/S
(2)
Before-tax
cost
of debt,
rd (3)
After-tax cost
of debt, (1-
T) rd (4)Beta, b (5)
Cost of Equity, rs
(6) WACC (7)
Value of
Firm:
FCF/WACC
(8)
Expected TIE
Ratio: EBIT/I
(9)
0% 0.00 7.30% 4.38% 1.10 10.3% 10.30% $2,155,340
10% 0.11 7.40% 4.44% 1.17 10.7% 10.04% $2,210,275
20% 0.25 7.60% 4.56% 1.27 11.1% 9.81% $2,262,536
30% 0.43 8.10% 4.86% 1.38 11.7% 9.66% $2,298,613
40% 0.67 8.60% 5.16% 1.54 12.5% 9.56% $2,321,205
50% 1.00 10.00% 6.00% 1.76 13.6% 9.80% $2,265,306
60% 1.50 12.00% 7.20% 2.09 15.3% 10.42% $2,130,518
Plan H, Optimal Capital Structure Analysis
Percent
financed
with debt,wd
(1)
Market Debt/
Equity, D/S
(2)
Before-tax
cost
of debt,
rd (3)
After-tax cost
of debt, (1-
T) rd (4)
Beta, b (5)
Cost of Equity, rs
(6) WACC (7)
Value of
Firm:
FCF/WACC
(8)
Expected TIE
Ratio: EBIT/I
(9)
0% 0.00 7.30% 4.38% 1.30 11.3% 11.30% 5,012,389
10% 0.11 7.40% 4.44% 1.39 11.7% 11.00% 5,147,219
20% 0.25 7.60% 4.56% 1.50 12.3% 10.73% 5,277,674
30% 0.43 8.10% 4.86% 1.63 13.0% 10.54% 5,374,834
40% 0.67 8.60% 5.16% 1.82 13.9% 10.40% 5,444,060
50% 1.00 10.00% 6.00% 2.08 15.2% 10.60% 5,343,396
60% 1.50 12.00% 7.20% 2.47 17.2% 11.18% 5,066,190
P a g e | 16 Jordan Huus
Graph 1
The above tables, Table 9 and 10, begin to wrap-up the final analysis of optimal capital
structure. WACC calculations have been made using different weights of debt, from 0% to 60%.
Next, each WACC figure can be calculated by blending costs of debt and equity together
proportionate to their weights. Optimal capital structure for each plan will consist of a debt and
equity levels that minimize WACC. As seen in the above tables and graphs, minimum WACC
occurs at 40% debt and 60% equity for both Plans L and H. Furthermore, the value of the firm
has been calculated as well, which appropriately corresponds to the minimum WACC.
