CAPITAL STRUCTURE AND THE COST OF CAPITAL External ...

CAPITAL STRUCTURE AND THE COST OF CAPITAL
Direct all comments, remarks, questions to:
Calin Valsan
Williams School of Business
Bishop's University
cvalsan-at-ubishops-dot-ca
External financing involves raising capital to finance the assets of the firm. The most important decision to make is whether
to raise debt or equity. This decision impacts the relative proportions of debt and equity. In usual finance vernacular this is
referred to as capital structure. To tackle this problem we need to set out the relevant criteria on which to base our choice.
The traditional decision criterion has been the long-term wealth of shareholders, which is contingent on the fair market
value of the firm. Choosing between external equity and debt is thus a question of maximizing the present value of firm's
cash flows.
The present value of firm's cash flow depends in turn on the absolute magnitude of annual cash flows and on their volatility.
Riskiness is the ultimate factor in deciding the cost of procuring the capital needed to produce those cash flows.
The riskier the cash flow, the more expensive the cost of obtaining outside financing. It stands to reason that in order to
maximize the market value of the firm, the best possible capital structure has to maximize expected cash flows and
minimize the cost of procuring external financing. This cost is simply called the cost of capital, and has at least two
components: the cost of equity and the cost of debt (for companies that issue preferred shares, one has to account for the
cost of preferred shares as well).
One has to be careful not to confuse the cost of capital with the cost of issuing capital. The cost of capital is simply a fair
financial compensation owed to the providers of capital and is proportional to the riskiness of their respective financial
claims. The cost of issuing capital is made of all direct and indirect expenses incurred by the firm in order to bring the bonds
and shares in the hands of claimholders: creditors and shareholders. The cost of issuing capital is also referred to as flotation
cost and is at its very heart an intermediation cost: commission, fees, spreads, money left on the table, etc. These costs are
paid to underwriters, regulators, lawyers, accountants, etc.
The cost of external equity is larger than the cost of debt because equity is riskier than debt. The riskiness of both claims,
however, is contingent on the overall riskiness of the firm. The overall riskiness of the firm is an aggregate of business risk
and financial risk. Business risk is an unavoidable risk faced by any enterprise in the course of conducting its operations. Its
magnitude is given by the specificity of firm's assets. An airline has a different business risk than that of a grocery store. A
pharmaceutical company has a different business risk than that of a bank. Besides the nature of assets, other factors, such as
regulation, exchange rates, morality etc., play an important role in shaping the environment, and hence the risk to which the
firm is exposed. In addition to business risk, firms face an additional type of risk - financial risk- given by the manner in
which they finance their operations. The more debt, the higher the financial risk. Debt adds more risk, because interests
payments represent a contractual, firm commitment to pay predetermined amounts at predetermined time periods. Failure to
fulfill these contractual commitments results in financial distress and failure.
It is therefore customary to treat capital structure as a case of debt financing. We start by assuming an all-equity firm and we
ask what happens to its market value if we substitute some of its equity with debt. Or, we start with a leveraged firm and we
ask what happens to its market value if we substitute its outstanding debt with equity. In order to answer these pseudopractical
questions, we need to understand, as already explained, two things: how cash flow change, and how the cost of
capital change. While determining the change in cash flow appears predictable to a certain extent, estimating the cost of
capital is a daunting task. Of the two main types of capital, the cost of debt is easier to estimate. We simply observe the
interest a firm pays on its loans or the coupon it pays on its bonds. Banks and creditors usually do a fair job at estimating
the riskiness of corporate borrowing. Of course, they all can be wrong at times, but in general the cash flow generated by
debt is reasonably predictable because it is made of fixed payments at fixed intervals. Firms have no choice but to pay their
financial obligations as they come due. The hard part is to estimate the probability the firm will default; firms with solid
solvency ratios borrow at low rates, firms with acceptable solvency ratios borrow at higher rates, and firms on the verge of
financial distress usually do not have access to debt financing. In general, the higher the level of financial leverage, the
higher the marginal interest rate at which the firm can acquire new debt. This follows from the fact that more debt means
more financial risk.
The cost of equity is a whole different story. The most accurate thing we can say about the cost of equity (the required rate
1

of return on equity) is that it must be larger than the marginal (i.e., highest) interest rate at which the firm is able to borrow.
By how much? One is at a loss to quantify this premium for lack of a reliable return generating model, that is, a functional
model measuring how return varies with risk. The most notable attempt to produce a return generating model is the Capital
Asset Pricing Model (CAPM). At the beginning, the CAPM was hailed as a breakthrough in modern finance. As it stands
now, the model has been adopted as the default approach to estimating required return by scores of academics and
practitioners alike, in spite of its many apparent flaws. The CAPM is a very elegant and seducing mathematical model, yet
its validity is more a question of metaphysics than of reality. As a practical tool for estimating required returns, the CAPM is
quite unhelpful.
A possible contender for calculating the cost of equity is the dividend growth model. The dividend growth model relies on
estimating the stream of future dividend payments., and comparing it to the current market price of the stock. As a practical
tool, it too, has many debilitating flaws. For one, it provides no mechanism for accounting for risk. In addition, it forces us
to assume the stock is already correctly priced, which in many instances is a no starter. Since capital structure is an exercise
in valuation, this assumption defeats the purpose of the entire process of searching for a fair market value.
The only one left standing is the initial heuristic approach of adding a risk premium to the highest observed interest rate paid
by the firm in order to come up with a rudimentary estimation for the cost of equity. It is indeed a very crude approach,
relying on guesswork and subjective approximation, but at least it does not have the pretense of being accurate and
scientific. In spite of its disheveled appearance, this ad-hoc method is in fact less arbitrary than the more mathematically
sophisticated methods, which are metaphysically enticing, yet seriously lacking in practical relevance.
When we allow the cost of equity to follow the cost of debt, we end up with a complex relationship between financial
leverage and market value. When markets are optimistic and tolerate high risk - either because of misperception or
overconfidence - the relationship between leverage and total market value is approximately flat, edging up slightly as the
total debt ratio approaches 100%. When markets are paranoid and hardly tolerate any credit risk, the relation become
humpback-shaped, increasing for very low levels of debt, and then dropping vertiginously as total debt ratio approaches
100%.
Implicit in this valuation approach is an average cost of capital that can be used to estimate the fair total market value of the
firm by discounting its total cash flows. The calculation of this average cost, however, is contingent on estimating the fair
market weights of equity and debt in the fair total market value of the firm.
The complex valuation profile described earlier owes to the fact that - contrary to what the neo-classical theory contends 1 -
there is no true separation between the investment and the financing decision of the firm. The behavior of, and the options
available to the financial manager are partially contingent on his financing choices. The neo-classical theory sees the world
as a giant clockwork, with well defined and delineated parts and functions, in which various outcomes are observed to flow
linearly from cause A to effect B, while the rest is of the world is graciously suspended in limbo.
The holistic interpretation offered here as a counterweight to the neo-classical model, views the various variables populating
the system as deeply interconnected and banding together in complex, simultaneous interactions, subject to measurement
indeterminacy. Any attempt at measuring a variable in isolation is either doomed or seriously distorted. The price to pay for
this more realistic stance is significant: while one can provide a credible, although approximate description of what might be
going on, one is at a loss to generate normative judgments. One has to rely more on the business savvy, the instinct and the
acumen of the entrepreneur than on the sophistication of mathematical models. This contention has far reaching
implications as far as market regulation goes: if we cannot formulate operational models of financing choices, in which
causal relationships are well specified, then we cannot formulate regulation that is fair and effective. The most effective type
of regulation is probably limited to the one attempting to establish and reinforce trust among market participants and
decision makers.
1 Fisher, Irving (1930) The Theory of Interest: As determined by impatience to spend income and opportunity to invest it. 1954 reprint, New York: Kelley
and Millman.
2

Debt financing : The case of Toy Inc.
We start by trying to estimate the impact of debt financing on the cash flows of the firm. The following simplified example
should give us a good idea of what is going on. Consider the case of Toy Inc., partially financed with debt. Let us assume
that there are two possible outcomes next year: sales can go up by 20%, or sales can go down by 20%. Each scenario has an
equal chance of occurring. Furthermore, let us assume that costs grow (decreases) only half as fast as sales. The pro-forma
income statement shows what happens in each case. When sales slump, Toy Inc. incurs a loss. EBIT and net income turn
negative. Fortunately, the firm still has enough liquidity to pay its obligations and to dampen the drop. For now, the
company is able to survive with minor bruises; its assets, however, will drop, reflecting the loss. If sales increase, the
bulging profits will be associated with an increase in total assets.
Toy Inc.: Pro-forma income statement
Today Next year: sales up 20%, costs up 10% Next year: sales down 20%, costs down 10%
Sales $5,000.00 $6,000.00 $4,000.00
(Costs) $3,500.00 $3,850.00 $3,150.00
(Depreciation) $1,000.00 $1,000.00 $1,000.00
EBIT $500.00 $1,150.00 -$150.00
(Interest) $80.75 $80.75 $80.75
EBT $419.25 $1,069.25 -$230.75
(Tax) $142.55 $363.55 $0.00
Net income $276.71 $705.71 -$230.75
Addition to RE $179.86 $458.71 -$230.75
Dividend $96.85 $247.00 $0.00
Toy Inc.: Pro-forma balance sheet
Today
Next year:
sales up 20%,
costs up 10%
Next year:
sales down 20%,
costs down 10%
Today
Next year:
sales up 20%,
costs up 10%
Next year:
sales down 20%,
costs down 10%
Cash $100.00 $1,468.71 $869.25 Accounts payable $300.00 $300.00 $300.00
Inventory $500.00 $550.00 $500.00 Notes payable $400.00 $400.00 $400.00
A/R $400.00 $440.00 $400.00 Total current liabilities $700.00 $700.00 $700.00
Current assets $1,000.00 $2,458.71 $1,769.25
Long-term debt $1,500.00 $1,500.00 $1,500.00
Gross fixed assets $3,000.00 $3,000.00 $3,000.00 Other long-term $0.00 $0.00 $0.00
Depreciation $1,000.00 $2,000.00 $2,000.00 Outstanding shares $1,120.14 $1,120.14 $1,120.14
Net fixed assets $2,000.00 $1,000.00 $1,000.00 Retained earnings $179.86 $638.57 -$50.89
Other assets $500.00 $500.00 $500.00 Owner's equity $1,300.00 $1,758.71 $1,069.25
Total assets $3,500.00 $3,958.71 $3,269.25 Total liabilities and equity $3,500.00 $3,958.71 $3,269.25
3

Financial ratios reflect the fortunes of the company. When sales are up, all solvency and profitability ratios are up as well.
Earnings per share, dividend per share, and book value of equity are all up. It is not possible to estimate the dividend yield,
simply because we don't know how the stock price will change if earnings increase. It will probably go up as well, but by
how much, it is anyone's guess.
When sales are down, solvency and profitability ratios are down as well. In fact, profitability ratios turn negative, due to the
loss. It is likely that the stock price will decrease too, but since Toy Inc. will pay no dividend, we can obviously ascertain a
zero dividend yield.
Toy Inc.: Selected ratios
Today Next year: sales up 20%, costs up 10% Next year: sales down 20%, costs down 10%
TAT 1.43 3.51 1.22
FAT 2.50 2.73 4.00
D/E 1.69 1.25 2.06
Total debt ratio 0.63 0.56 0.67
LT debt ratio 0.43 0.38 0.46
TIE 6.19 14.24 -1.86
Cash coverage 18.58 26.63 10.53
Profit margin 5.53% 11.76% -5.77%
ROA 7.91% 17.83% -7.06%
ROE 21.29% 40.13% -21.58%
Dividend per share $0.97 $2.47 $0.00
EPS $2.77 $7.06 -$2.31
Book value per share $13.00 $17.59 $10.69
Dividend yield 3.87% ? 0.00%
Cash flows follow the fortunes of earnings as well. When earnings are up, we see a significant increase in total cash flows,
due to a larger dividend payment. When earnings are down, cash flows retreat to the bare minimum represented by interest
payments.
Toy Inc.: Cash flows to claimholders
Today Next year: sales up 20%, costs up 10% Next year: sales down 20%, costs down 10%
CF to creditors $80.75 $80.75 $80.75
CF to shareholders $96.85 $247.00 $0.00
CF from assets $177.60 $327.75 $80.75
4

Debt financing and Toy Inc. in a parallel universe
Let us now imagine a parallel universe in which everything is the same as in ours, except that we have magically substituted
all the debt of Toy Inc. with equity. In this parallel universe, Toy Inc. is entirely equity financed, and we will henceforth call
it all-equity Toy Inc. The pro-forma financial statements of all-equity Toy Inc. are very similar to those of Toy Inc. As in the
previous case, a drop in sales results in a loss and entails a decrease in total assets.
All-equity Toy Inc.: Pro-forma income statement
Today Next year: sales up 20%, costs up 10% Next year: sales down 20%, costs down 10%
Sales $5,000.00 $6,000.00 $4,000.00
(Costs) $3,500.00 $3,850.00 $3,150.00
(Depreciation) $1,000.00 $1,000.00 $1,000.00
EBIT $500.00 $1,150.00 -$150.00
(Interest) $0.00 $0.00 $0.00
EBT $500.00 $1,150.00 -$150.00
(Tax) $170.00 $391.00 $0.00
Net income $330.00 $759.00 -$150.00
Addition to RE $214.50 $493.35 -$150.00
Dividend $115.50 $265.65 $0.00
All-equity Toy Inc.: Pro-forma balance sheet
Today
Next year:
sales up 20%,
costs up 10%
Next year:
sales down 20%,
costs down 10%
Today
Next year:
sales up 20%,
costs up 10%
Next year:
sales down 20%,
costs down 10%
Cash $100.00 $1,503.35 $950.00 A/P $0.00 $0.00 $0.00
Inventory $500.00 $550.00 $500.00 N/P $0.00 $0.00 $0.00
A/R $400.00 $440.00 $400.00 Current liabilities $0.00 $0.00 $0.00
Current assets $1,000.00 $2,493.35 $1,850.00
Long-term debt $0.00 $0.00 $0.00
Gross fixed assets $3,000.00 $3,000.00 $3,000.00 Other long-term $0.00 $0.00 $0.00
Depreciation $1,000.00 $2,000.00 $2,000.00 Outstanding shares $3,285.50 $3,285.50 $3,285.50
Net fixed assets $2,000.00 $1,000.00 $1,000.00 Retained earnings $214.50 $707.85 $64.50
Other assets $500.00 $500.00 $500.00 Owner's equity $3,500.00 $3,993.35 $3,350.00
Total assets $3,500.00 $3,993.35 $3,350.00 Total L&E $3,500.00 $3,993.35 $3,350.00
5

Financial ratios follow the trajectory of sales and earnings. When sales are up, all ratios are improving and cash flow grows
larger. When sales are down, all ratios get weaker and cash flow drops to zero, as there is no money left for dividend
payment. Unlike Toy Inc., the cash flow of all-equity Toy Inc. is only made of dividend payments. When earnings are
growing, so does the cash flow. When incurring a loss, all-equity Toy's Inc.'s cash flow dries up.
All-equity Toy Inc.: Selected ratios
Today Next year: sales up 20%, costs up 10%
Next year: sales down 20%, costs
down 10%
TAT 1.43 1.50 1.19
FAT 2.50 6.00 4.00
D/E 0.00 0.00 0.00
Total debt ratio 0.00 0.00 0.00
LT debt ratio 0.00 0.00 0.00
TIE 0.00 0.00 0.00
Cash coverage 0.00 0.00 0.00
Profit margin 6.60% 12.65% -3.75%
ROA 9.43% 19.01% -4.48%
ROE 9.43% 19.01% -4.48%
Dividend per share $1.16 $2.66 $0.00
EPS $3.30 $7.59 -$1.50
Book value per share $35.00 $39.93 $33.50
Dividend yield ? ? 0%
All-equity Toy Inc.: Cash flows to claimholders
Today Next year: sales up 20%, costs up 10% Next year: sales down 20%, costs down 10%
CF to creditors $0.00 $0.00 $0.00
CF to shareholders $115.50 $265.65 $0.00
CF from assets $115.50 $265.65 $0.00
6

Debt financing in parallel universes: Toy Inc. and all-equity Toy Inc. side by side
A cursory inspection of Toy Inc. and all-equity Toy Inc. shows very similar tendencies in financial ratios and cash flows. To
get a more revealing picture we need to analyze them side by side. We start with their current standing and we see that most
differences are rather subtle (except for the differences due to the lack of leverage, that is). All-equity Toy Inc. has a slightly
higher profit margin and return on assets (no interest payments to reduce earnings), yet it boasts a lower return on equity.
Cash flow to shareholders is higher for all-equity Toy Inc., yet, total cash flow is higher for Toy Inc. This is so because total
cash flow of all-equity Toy Inc. is made only of dividend payments, while that of Toy Inc. is made of dividend payments
and interest payments.
Parallel universes: Toy Inc. and all-equity Toy Inc.
All equity Toy Inc.
Toy Inc.
Sales $5,000 $5,000
Net income $330 $276.71
Dividend $115.50 $96.85
Total assets $3,500 $3,500
TAT 1.43 1.43
FAT 2.50 2.50
D/E 0.00 1.69
Total debt ratio 0.00 0.63
LT debt ratio 0.00 0.43
TIE 0.00 6.19
Cash coverage 0.00 18.58
Profit margin 6.60% 5.53%
ROA 9.43% 7.91%
ROE 9.43% 21.29%
Dividend per share $1.16 $0.97
EPS $3.30 $2.77
Book value per share $35.00 $13.00
Dividend yield ? 3.87%
CF to creditors $0.00 $80.75
CF to shareholders $115.50 $96.85
CF from assets $115.50 $177.60
7

The differences between the two parallel universes appear more manifest when analyzed dynamically. The main points can
be summarized as follows:
• Average profit margin is lower, but profit margin volatility is higher for Toy Inc.
• Average ROA is lower, but ROA volatility is higher for Toy Inc.
• Average ROE is higher and ROE volatility is higher for Toy Inc.
• Total cash flows are larger for Toy Inc. (the lower volatility here is somewhat misleading, as we have considered
Toy Inc. is able to make interests payments regardless of the growth outcome)
Parallel universes: Toy Inc. and all-equity Toy Inc. under two growth scenarios
All equity Toy Inc.
Next year:
sales up 20%,
costs up 10%
All equity Toy Inc.
Next year:
sales down 20%,
costs down 10%
Average
Standard
deviation
Toy Inc.
Next year:
sales up 20%,
costs up 10%
Toy Inc.
Next year:
sales down 20%,
costs down 10%
Average
Standard
deviation
Sales $6,000.00 $4,000.00 $5,000.00 $1,414.21 $6,000.00 $4,000.00 $5,000.00 $1,414.21
Net income $759.00 -$150.00 $304.50 $642.76 $705.71 -$230.75 $237.48 $662.18
Dividend $265.65 $0.00 $132.83 $187.84 $247.00 $0.00 $123.50 $174.66
Total assets $3,993.35 $3,350.00 $3,671.68 $454.92 $3,958.71 $3,269.25 $3,613.98 $487.52
TAT 1.50 1.19 1.35 0.22 3.51 1.22 2.37 1.62
FAT 6.00 4.00 5 1.41 2.73 4.00 3.37 0.9
D/E 0.00 0.00 0 0 1.25 2.06 1.66 0.57
Total debt ratio 0.00 0.00 0 0 0.56 0.67 0.62 0.08
LT debt ratio 0.00 0.00 0 0 0.38 0.46 0.42 0.06
TIE 0.00 0.00 0 0 14.24 -1.86 6.19 11.38
Cash coverage 0.00 0.00 0 0 26.63 10.53 18.58 11.38
Profit margin 12.65% -3.75% 4.45% 11.60% 11.76% -5.77% 3.00% 12.40%
ROA 19.01% -4.48% 7.27% 16.61% 17.83% -7.06% 5.39% 17.60%
ROE 19.01% -4.48% 7.27% 16.61% 40.13% -21.58% 9.28% 43.64%
Dividend per share $2.66 $0.00 $1.33 $1.88 $2.47 $0.00 $1.24 $1.75
EPS $7.59 -$1.50 $3.05 $6.43 $7.06 -$2.31 $2.38 $6.63
Book value per share $39.93 $33.50 $36.72 $4.55 $17.59 $10.69 $14.14 $4.88
Dividend yield ? 0% n/a n/a ? 0.00% n/a n/a
CF to creditors $0.00 $0.00 $0.00 $0.00 $80.75 $80.75 $80.75 $0.00
CF to shareholders $265.65 $0.00 $132.83 $187.84 $247.00 $0.00 $123.50 $174.66
CF from assets $265.65 $0.00 $132.83 $187.84 $327.75 $80.75 $204.25 $174.66
So far we have considered only a relatively mild downturn in sales and earnings. Both Toy Inc. and all-equity Toy Inc.
appear to survive it relatively unscathed. It is time we considered a more dramatic scenario that will reveal some of the more
dramatic consequences of borrowing.
8

Parallel universes: A severe downturn
Let us imagine a severe drop in sales and how it affects Toy Inc. and all-equity Toy Inc. Consider an 80% decrease in sales
that results in a massive loss of over $2,500. The loss is so dramatic that assets plummet from $3,500 to $1,100.
Pro-forma income statement of Toy Inc. under a severe market downturn scenario
Today
Next year
Sales $5,000.00 $1,000.00
(Costs) $3,500.00 $2,450.00
(Depreciation) $1,000.00 $1,000.00
EBIT $500.00 -$2,450.00
(Interest) $80.75 $80.75
EBT $419.25 -$2,530.75
(Tax) $142.55 $0.00
Net income $276.71 -$2,530.75
Addition to RE $179.86 -$2,530.75
Dividend $96.85 $0.00
Pro-forma balance sheet of Toy Inc. under a severe market downturn scenario
Today Next year Today Next year
Cash $100.00 $0.00 A/P $300.00 $430.75
Inventory $500.00 $100.00 N/P $400.00 $400.00
A/R $400.00 $0.00 Current liabilities $700.00 $830.75
Current assets $1,000.00 $100.00
Long-term debt $1,500.00 $1,500.00
Gross fixed assets $3,000.00 $3,000.00 Other long-term $0.00 $0.00
Depreciation $1,000.00 $2,000.00 Outstanding shares $1,120.14 $1,120.14
Net fixed assets $2,000.00 $1,000.00 Retained earnings $179.86 -$2,350.89
Other assets $500.00 $0.00 Owner's equity $1,300.00 -$1,230.75
Total assets $3,500.00 $1,100.00 Total L&E $3,500.00 $1,100.00
We estimate a cash coverage ratio of -18 for next year. The company can try to increase its accounts payable, use up all
strategic cash reserves to pay its employees, write-off accounts receivables, but in the end, Toy Inc still does not have
enough money left to cover its interest obligation - at this point in time bankruptcy is most likely declared. Notice how,
under the burden of the loss, even owner's equity becomes negative. This equity deficit is a bad omen: although book value
of equity reflects only historical costs, it signals the firm might not be viable anymore. It is quite possible that the market
value of assets could be less than that of debt obligations, case in which liquidation would result in a partial loss to creditors
and a total loss to shareholders.
9

Consider now what happens to all-equity Toy Inc. Even though the loss is still staggering it does not necessarily spell the
demise of the company, at least not yet. The company will again try to use accounts payable, tap into its strategic cash
reserves, write-off account receivables, etc., but fortunately, here there is no need to worry about paying interest.
For the time being the company has wiggled its way out of a tight spot. It has another chance to pick themselves up and try
again in one year's time. It could also raise new equity to replenish cash and prepare for the eventuality that the years ahead
would again be bad. Of course, the company cannot operate like this indefinitely (unless you're a third generation
entrepreneur sitting on top of a family fortune waiting to be squandered), but for the particular period under analysis, allequity
Toy Inc. need not go bankrupt like Toy Inc.
Pro-forma income statement of all-equity Toy Inc. under a severe market downturn scenario
Today
Next year
Sales $5,000.00 $1,000.00
(Costs) $3,500.00 $2,450.00
(Depreciation) $1,000.00 $1,000.00
EBIT $500.00 -$2,450.00
(Interest) $0.00 $0.00
EBT $500.00 -$2,450.00
(Tax) $170.00 $0.00
Net income $330.00 -$2,450.00
Addition to RE $214.50 -$2,450.00
Dividend $115.50 $0.00
Pro-forma balance sheet of all-equity Toy Inc. under a severe market downturn scenario
Today Next year Today Next year
Cash $100.00 $0.00 A/P $300.00 $50.00
Inventory $500.00 $100.00 N/P $400.00 $0.00
A/R $400.00 $0.00 Current liabilities $700.00 $50.00
Current assets $1,000.00 $100.00
Long-term debt $1,500.00 $0.00
Gross fixed
assets
$3,000.00 $3,000.00 Other long-term $0.00 $0.00
Depreciation $1,000.00 $2,000.00 Outstanding shares $1,120.14 $3,285.50
Net fixed assets $2,000.00 $1,000.00 Retained earnings $179.86 -$2,235.50
Other assets $500.00 $0.00 Owner's equity $1,300.00 $1,050.00
Total assets $3,500.00 $1,100.00 Total L&E $3,500.00 $1,100.00
10

The Holy Grail of finance and the cash cow
Our analysis has established so far that Toy Inc. appears to reward its shareholders with higher returns than all-equity Toy
Inc. , but these returns are also more volatile. At the same time, Toy Inc. also produces larger total cash flows. We examined
other financial ratios and found to display similar trends. One thing that was left hanging was the issue of dividend yield.
Here, we are asking an apparently innocuous question: In a parallel universe, what is the dividend yield of all-equity Toy
Inc. ? What would be the price of its stock? To answer this question we need to know the valuation of all-equity Toy Inc.:
Dividend yield = Current dividend/Current stock price
Based on what we found until now, we have good reasons to believe that the market value of all-equity Toy Inc. would be
different than that of Toy Inc. Consider this:
P = PV(cash flows)
P = CF1/(1+ r) + CF2/(1+r) 2 + CF3/(1+r) 3 + .......etc
As already acknowledged, cash flow is not the same in the two parallel universes. Cash flow to shareholders is larger for the
all-equity Toy Inc. However, total cash flow is larger for the leveraged Toy Inc.
Total cash flow of all-equity Toy Inc. = Cash flow to shareholders
Total cash flow of levered Toy Inc. = Cash flow to shareholders + Cash flow to creditors
Return on equity volatility is not the same, as calculated earlier. It is smaller for all-equity Toy Inc. and larger for Toy Inc.
The same can be said about total cash flow. The volatility of total cash flow of Toy Inc. is larger, when we take into account
the possibility of Toy Inc. going bankrupt:
Variance (ROE) all-equity Toy Inc. < Variance (ROE) levered Toy Inc.
Variance (Total CF) all-equity Toy Inc. < Variance (Total CF) levered Toy Inc. (when bankruptcy is possible)
Unquestionably, Toy Inc is the riskier company. It has an added layer of risk. An extra risk dimension. The overall riskiness
of the firm is the sum of business risk and financial risk. Business risk is an unavoidable risk faced by any enterprise in the
course of conducting its operations. Its magnitude is given by the specific nature of its assets. An airline has a different
business risk than that of a grocery store. A pharmaceutical company has a different business risk than that of a bank. A steel
mill has a different business risk than a hedge fund. Besides the nature of assets, other factors, such as regulation, exchange
rates, inflation, wages, transportation costs, climate, and even morality play an important role in shaping the environment,
and hence the risk to which the firm is exposed. In addition to business risk, firms face an additional form of risk- financial
risk- contingent on the manner in which assets are financed. The more debt, the higher the financial risk. Debt adds more
risk, because interests payments represent a contractual, firm commitment to pay predetermined amounts at predetermined
time periods. Failure to fulfill these contractual commitments results in financial distress and failure. We have already
concluded that total cash flow has become larger for Toy Inc, yet also more volatile: if in any given year sales crash
unexpectedly, Toy Inc might not be able to make interest payments and would have to file for bankruptcy protection. To
summarize, financial risk has two important dimensions:
(i) Extra volatility in equity returns and cash flows
(ii) The real possibility that the firm could go bankrupt if unable to pay its financial obligations
It follows that the risk faced by the two companies in parallel universes is:
Total risk of all-equity Toy Inc = Business risk
Total risk of levered Toy Inc. = Business risk + Financial risk
The logical conclusion of this discussion is that the equity of Toy Inc. needs a higher discount rate to compensate for the
additional financial risk. The hard question, however, is this: how much more return would the market require in order to
compensate for financial risk? To answer, we have to know how return varies with risk. This is the holy grail of modern
finance, a question that every investor is grappling with.
11

Enter the cash cow. A cash cow is a mature company, without great growth prospects, generating a predictable and steady
stream of dividends year in and year out. Let us imagine Toy Inc. as a the proverbial cash cow. This current year, Toy Inc.
paid $96.85 to its shareholders and $80.75 to its creditors. If we assume no changes in sales, next year's cash flow will be
the same. Toy Inc.'s going discount rate on equity is implicitly given by the current market price. At the present time, the
stock of Toy Inc is selling for $25/share.
$25 = $0.97/r
r = $0.97/$25 = 3.8%
Is this number a fair discount rate? That is, if we buy the stock, are we fairly rewarded in making a return in the
neighborhood of 4% (plus whatever expected growth rate in earnings), without being unrealistically optimistic about the
future? Is the current dividend stream likely to prevail in the future? Is the volatility of this dividend payment reflected in
the current market price? Should we embrace 4% as such, just because it prevails in the market? What if the market is
replete with irrational exuberance or blinded by fear? Should we follow it unconditionally or attempt to pass our own
judgment?
Suppose tomorrow the price drops to $18. What would it mean? Several possible things:
It could be that the going rate has been revised upward to 5.4% amid fears of higher volatility in the future:
$18 = $0.97/0.054 (approximately)
Or, it could be that risk is expected to remain the same, but the expected amount of cash to be paid in the future to
shareholders is down to $0.68 per share:
$18 = $0.68/0.038
Or, it could be that both risk expectations and cash flows expectations have changed at the same time, such that:
or
or
$18 = $1.5/0.083
$18 = $1.6/0.088
$18 = $1.9/0.105
or........an infinity of other possibilities
In fact we would never know for sure how the valuation of the market has changed exactly. It could be driven by fear and
panic, by wisdom, by ignorance, by savvy, by greed, or by all of the above. The truth is, crowds are fickle and whimsical.
Investors are possessed by strong emotions and many a times exhibit herding behavior. Following the ups and down of the
market is maddening and stressful; even if we trust the market is always right, we are bound to be taken by surprise, to
always lag one step behind. Ideally, we want our own formula to tell us whether the current stock price is fair. But how can
we catch a glimpse of it? This is the big question. Every discipline grapples with its own deep questions. Philosophers ask
why is there something instead of nothing; physicists try to find a formula that would explain gravity, electromagnetism and
elementary forces in a unified way; mathematicians compare infinities and count prime numbers; engineers want to build an
engine that would run on light, wind, water, or whatever is dirt cheap but not dirty; doctors want to cure cancer and other
serious illnesses; financial economists, however, want a formula to tell them how much to pay for an asset that will
generate an uncertain payoff in the future. We want to know how much to pay for something that is not yet in existence, but
might come into existence in the future in a variety of ways. It sounds as though we want a crystal ball. Where should we
start?
12

The concept of cost of capital
The cost of capital is the required rate of return that makes investors willing to provide capital. The economic significance
of the cost of capital is straightforward: it is used to discount expected cash flows in order to determine the fair market value
of the firm. The cost of capital has two components: the cost of equity and the cost of debt (for companies that issue
preferred shares, one has to account for the cost of preferred shares as well). As already mentioned at the beginning of this
section, one has to be careful not to confuse the cost of capital with the cost of issuing capital. The cost of capital is simply
a fair financial compensation owed to the providers of capital and is proportional to the riskiness of their respective financial
claims. The cost of issuing capital is made of all direct and indirect expenses incurred by the firm in order to bring the bonds
and shares in the hands of claimholders: creditors and shareholders. The cost of issuing capital is also referred to as flotation
cost and is at its very heart an intermediation cost: commission, fees, spreads, money left on the table, etc. These costs are
paid to underwriters, regulators, lawyers, accountants, etc.
Of the two types enumerated above, the cost of debt is easier to estimate. We simply observe the interest a firm pays on its
loans or the coupon it pays on its bonds. Banks and creditors usually do a fair job at estimating the riskiness of corporate
borrowing. Of course, they all can be wrong at times, but in general the cash flow generated by debt is reasonably
predictable because it is made of fixed payments at fixed intervals. Firms have no choice but to pay their financial
obligations as they come due. The hard part is to estimate the probability that the firm will default. Some financial
institutions use sophisticated methodologies to determine the level of creditworthiness of the borrower. Everyone is familiar
with the bond rating done by Moody's, Standard & Poor, and Fitch:
Summary of credit rating: Moody's, Standard&Poor, and Fitch
Moody's rating Standard&Poor rating Fitch's rating
Aaa AAA AAA Prime
Aa1 AA+ AA+ High grade
Aa2 AA AA High grade
Aa3 AA- AA- High grade
A1 A+ A+ Upper medium grade
A2 A A Upper medium grade
A3 A- A- Upper medium grade
Baa1 BBB+ BBB+ Lower medium grade
Baa2 BBB BBB Lower medium grade
Baa3 BBB- BBB- Lower medium grade
Ba1 BB+ BB+ Non Investment grade speculative
Ba2 BB BB Non Investment grade speculative
Ba3 BB- BB- Non Investment grade speculative
B1 B+ B+ Highly Speculative
B2 B B Highly Speculative
B3 B- B- Highly Speculative
Caa1 CCC+ CCC Substantial risks
Caa2 CCC Extremely speculative
Caa3 CCC- In default with little prospect for recovery
Ca CC In default with little prospect for recovery
/ D DDD In default
/ DD In default
/ D In default
Source:Bonds online at http://www.bondsonline.com/asp/research/bondratings.asp and Wikipedia at http://en.wikipedia.org/wiki/Bond_credit_rating
Investors and banks care about credit rating because it is a good indicator of how much to require for lending money. Firms
with solid solvency ratios borrow at low rates, firms with acceptable solvency ratios borrow at higher rates, and firms on the
13

verge of financial distress usually do not have access to debt financing. In general, the higher the level of financial leverage,
the higher the marginal interest rate at which the firm can acquire new debt. This follows from the fact that more debt means
more financial risk.
The cost of equity is simply the required return on equity; that is, a return representing a fair compensation for the risk
undertaken by shareholders. The most accurate thing we can say about the cost of equity is that it must be larger than the
marginal (i.e., highest) interest rate at which the firm is able to borrow. By how much? One is at a loss to quantify the
difference for lack of a reliable return generating model, that is, a functional model measuring how return varies with risk.
Based on our discussion of business and financial risk, we contend that the cost of equity must be an increasing function of
leverage, although we are not able to specify its functional form in too much detail:
r = y(financial risk) + x(financial risk)
where:
r = cost of equity
y = the cost of debt, a function of financial risk
x = equity premium, also a function of financial risk
This method is heuristic, because it is partially based on speculative judgments; it is, without a question a subjective
approach.
Academics and practitioners, however, don't like this elusive guesswork. They want hard numbers to justify their decisions -
some equations to confer them the respectability of physics or engineering. There have been serious attempts to quantify
this relationship in a more rigorous manner. Most corporate finance textbooks use a formula proposed by Merton Miller an
Franco Modigliani 2 (the economist, not the painter):
where:
r = r(all-equity) + [r(all-equity) - y]*(D/E)*(1-Tc)
r = the cost of equity; r(all-equity) is the cost of equity for a similar all-equity firm
y = the cost of debt
D = market value of debt, a function of rational expectations
E = market value of equity, a function of rational expectations
Tc = tax rate on corporate profits
In this formula, the cost of equity is a nice, smooth, linear function of financial leverage, as measured by the debt-to-equity
ratio. The trouble is, the relationship is indeterminate. First, we cannot tell what is the fair cost of equity for the all-equity
firm; the cost of debt varies with leverage as well; and leverage is expressed in terms of market values -not those we can
directly observe in the market at a given point in time- rather those contingent on rational expectations, that is, contingent
on knowing the cost of equity. In other words, the cost of equity for the levered firm, the cost of equity for the all-equity
firm, and the fair market value of equity are jointly determined. We just cannot hold them constant for the convenience of
estimating them one at a time. We have one equation and at least three unknown variables that move together. We need
alternative approaches.
2 Modigliani, F. and Miller, M. H., (1963) "Corporate Income Taxes and the Cost of Capital: A Correction," American Economic Review, 53(3), 433–43.
14

The Nine Lives of the Capital Asset Pricing Model (CAPM)
The CAPM is at the heart of modern finance theory. It is a model of the return generating process, meaning that it aims to
quantify how the required return of each security traded in the market is commensurate to its relative risk. The CAPM is
both intuitive and simple to understand. It has a stunning mathematical elegance and a hard to equal beauty as far as
economic theory goes. It appears to be the ideal candidate to estimating the cost of equity. CAPM relies on concepts like
diversification, absolute risk, relative risk, efficient portfolios, and market portfolio.
Diversification is the most intuitive concept of all. It simply states that by combining risky assets in the same portfolio, we
might be able to reduce the total return volatility of the portfolio. Return volatility, as measured by variance (or standard
deviation) is a measure of absolute risk. Diversification works when returns accross various securities are not perfectly
correlated among them. Take the example of two assets, A and B, with return volatilities measured by σ(A) and σ(B). If the
correlation between the two is less than 1, then the combined portfolio will have an absolute risk lower than the weighted
average of the two individual risks:
At the same time:
σ(A and B) < σ(A) + σ(B)
Eret(A + B) = Eret(A) + Eret(B)
where:
Eret (A+B)
Eret(A)
Eret(B)
= expected return on the combined portfolio
= expected return on asset A
= expected return on asset B
In other words, when we construct a portfolio of risky securities, the resulting return is simply the weighted average of the
two returns, while the resulting risk is less than the weighted average of the two individual risks. The more securities we add
to our portfolio the lower the resulting volatility of the portfolio. There are limits, however, to how much we can diversify
away risk. As long as various securities exhibit a certain measure of correlation, no matter how hard we try, we reach a level
beyond which volatility cannot be reduced any further. The level of portfolio volatility that cannot be diversified away is
called systematic 3 , non-diversifiable, or market risk.
It stands to reasons that, among all possible portfolios that we can construct with all the available securities, some will
exhibit the largest level of return for a given level of standard deviation of return, or the lowest level of standard deviation
of return for a given level of return. These portfolios are called efficient portfolios, and common sense dictates that a
rational investor would only hold these efficient portfolios. Why hold just any portfolio, when for a particular level of risk
there is an efficient portfolio with a higher return? In other words, efficient portfolios are desirable because they optimize
the trade-off between risk and return.
But which efficient portfolios to hold? That depends on each individual investor's risk aversion: more risk averse individuals
will hold efficient portfolios with lower risk and lower return, while less risk averse individuals will hold efficient portfolios
with higher risk and higher return.
When there exists a (quasi) risk-free asset (such as a government-issued bond), it can be mathematically shown that,
regardless of the level of risk aversion, rational investors will hold only one portfolio: this special portfolio contains all
imaginable assets in the known universe, and is called the Market Portfolio. However, in order to accommodate each
individual's risk preferences, the theory shows that the Market Portfolio can be combined with the risk-free asset in various
proportions to generate various levels of risk and return. More prudent individuals will invest a fraction of their wealth in
the risk-free asset (that is, buy government T-bills), and the remaining portion in the Market Portfolio. More adventurous
investors would borrow money in order to increase their investment in the Market Portfolio. In any case, in a system of
coordinates with standard deviation of return on the X-axis, and expected return on the Y-axis, all resulting possible
combinations between the risk-free asset and the Market Portfolio will lie on a perfectly straight line known as the Capital
Market Line.
3 Not to be confused with systemic risk, which refers to the risk faced by financial institutions when the failure of one entity triggers a domino effect that
threatens to bring down the entire system.
15

Relative risk and β
Since return volatility can be reduced, or rather partially neutralized through diversification, it stands to reason that the
standard deviation of return is not the most relevant way to measure risk.
Instead of focusing on the standard deviation of return, we should measure the extent to which adding a given asset to a
well-diversified portfolio, such as the Market Portfolio, contributes to the overall return volatility of the portfolio. The
relative contribution of an asset to the overall return volatility of the Market Portfolio is measured by the fabled β, the
quintessential measure of relative risk. Mathematically, β is nothing else but the covariance between the return of the
Market Portfolio and that of the asset, divided by the variance of the Market Portfolio:
β = covariance(M, asset)/variance(M)
where M denotes the Market Portfolio.
By definition, β(M) = 1. This simply follows from the above equality.
When an asset has a beta larger than one, it follows that adding that asset to the Market Portfolio will increase the overall
volatility of return of the Market Portfolio. A beta less than one means that adding that asset to the Market Portfolio will
decrease the overall volatility of return of the Market Portfolio. A beta equal to one will leave the overall volatility of return
of the Market Portfolio unchanged.
Having established that relative risk is the relevant measure of risk, we now turn to analyzing return. We notice that risky
securities require a return above and beyond the return on the risk-free asset. Obviously, the risk-free rate is a compensation
for inflation and time preference 4 , but not for risk. While trivial, this observation has profound implications. It follows that
the difference between the required return on the Market Portfolio and the return on the risk-free asset shows the extra
return required only and only by market risk alone. This difference is called market risk premium:
Market risk premium = Rret(M) – Rret(risk-free asset)
Obviously, the risk premium of any given asset will vary according to risk. To be more precise, according to relative risk.
The Market Portfolio is now the main reference point. It is the yardstick for measuring return and risk. All the pieces of the
puzzle are about to fall into place.
The main contention of the CAPM is that the risk premium per unit of relative risk must be the same across all assets in the
market:
[Rret(A) – Rret(Risk-free asset)]/ β(A) = [Rret(B) – Rret(Risk-free asset)]/ β(B) = .......etc.
Since the Market Portfolio is an asset as well, it follows that:
[Rret(A) – Rret(Risk-free asset)]/ β(A) = [Rret(M) – Rret(Risk-free asset)]/ β(M)
By definition, β(M) = 1. It follows that:
or
[Rret(A) – Rret(Risk-free asset)]/ β(A) = [Rret(M) – Rret(Risk-free asset)]
Rret(A) = Rret(Risk-free asset) + β(A)*[Rret(M) – Rret(Risk-free asset)]
This conclusion is highly intuitive, almost trivial, if you think about it. While in the grocery store the price of a steak is
proportional to its weight times the price per pound, in the financial market the required return of an asset is proportional to
4 Time preference denotes the willingness to postpone or sacrifice current consumption in exchange for future consumption. It can also be viewed as the
degree of consumption impatience. Investors with high time preference will require high rates of return to compensate them for postponing current
consumption, even when there is no risk.
16

its relative risk times the return premium per unit of relative risk. Another nontrivial contention is that the market rewards
only systematic risk, not absolute risk. Required return is proportional to beta, not to the standard deviation of return. The
connoisseur can only wonder at the exquisite elegance, audacity and sheer scope of the mathematical apparatus deployed
here to make this simple point 5 .
Albert Einstein once quipped that “ elegance is for tailors.” The beauty and elegance of the CAPM, however, is only
equaled by its absolute lack of practicality. The CAPM first emerged as a positive (i.e. descriptive) theory of the return
generating process, but was surreptitiously perverted into a normative theory of estimating required return and measuring
performance. If there is anything for which the CAPM is ill-equipped, it has to be its inability for providing guidance in
estimating required rates of return. Without dwelling too much on its many metaphysical flaws, let us draw the attention to
some very simple, yet practical shortcomings.
Suppose you wish to estimate the cost of capital for Toy Inc. The cost of capital is the rate of returned required by Toy Inc.
shareholders. The first step is to estimate the beta of the stock. Next, estimate the market risk premium, and the risk-free
rate. Once all these variables have been accounted for, use the formula:
Rret(Toy Inc.) = Rret(Risk-free asset) + β(Toy Inc.)*[Rret(M) – Rret(Risk-free asset)]
Easier said than done. Once we start to carry on these steps we soon realize how insurmountable the practical details of our
endeavor turn out to be. The beta of Toy Inc. should reflect the rational expectations of investors regarding the relative risk
of Toy Inc. going forward. Investors' expectations are virtually unobservable quantities. Alas, we are able to observe only
realizations. Meanwhile, under the influence of new information constantly flowing into the market, investors have moved
on to new expectations. The only way out is to assume that current expectation are predicted by past expectations, and
estimate beta by regressing Toy Inc.'s past returns against Market Portfolio past returns. This statement turns out to be very
controversial. If life is filled with uncertainty, and things happen at random, then expectations about future events should
change randomly. Even when investors are not rational and are under the influence of past events, it would still hold true
that current expectations need not be the same as past realizations. Even if we take the ultimate leap of faith and equate past
realization with current expectations, we arrive at a very troubling conclusion: if the future is predicted by the past, why
bother to entertain this arcane and contrived exercise, when we could simply extrapolate past returns into the future. In fact,
technical analysts shun CAPM and other type of fundamental analysis altogether, and stick with extrapolating charts and
trends, without too much success either; but that is a whole different story.
For now let us ignore all these (otherwise legitimate) concerns, and let us plod ahead with our estimation of the required
return. In order to estimate the beta of Toy Inc. we have no choice but to regress the historical return of Toy Inc. against that
of the Market Portfolio:
Hret(Toy Inc.) = a + b*Hret(M) + e
where:
Hret(Toy Inc.) = historical returns on Toy Inc.
Hret(M) = historical return on the Market Portfolio
a, b, = regression coefficients
e
= error term, following a normal distribution with mean zero and standard deviation equal to one
But what is the Market Portfolio? The theory behind the CAPM states that the Market Portfolio is made up of ALL assets
that could be traded world-wide. This includes stocks, bonds, real estate, collectibles, art, gold, racing cars, bottle-aged
wine, and many others. To our knowledge, there is no market index (yet) that includes everything. Can we settle for an
index that approximates the market portfolio? The answer of CAPM is a resounding NO. An index similar to the Market
Portfolio is no substitute for the real thing. Close enough is not good enough. Once we make the substitution, we abandon
the CAPM, and start operating according to a different model, not yet formalized or explained. Call it Joe's Asset Pricing
Model, or Buster's Asset Pricing Model, or the Ad-Hoc Pricing Model, or the Makeshift Asset Pricing Model, but it is
definitely NOT the Capital Asset Pricing Model. In practice, however we have little choice because there is only a limited
range of indexes available. Hence, we pick one that we feel is representative and we pretend not to notice we are straying
away more and more from the gospel of the theory. Now that we have trampled over yet another legitimate objection let us
5 As the reader has probably realized by now, the above discussion is an oversimplification of the mathematically-rich derivation of the CAPM; many
steps have been skipped and replaced with a sleigh of hand.
17

settle for the S&P 500 as a proxy of the Market Portfolio.
Let us consider the following data:
Monthly returns S&P 500 and Toy Inc. (2000-2009). Source: S&P data provided by Standard & Poor Index Services, Toy Inc. is fictitious.
Month S&P 500 close Change S&P 500 monthly return Toy Inc. monthly return Risk-free rate Market risk premium
02/2009 735.09 -90.79 -10.99% -22.00% 0.03% -11.03%
01/2009 825.88 -77.37 -8.57% 2.50% 0.03% -8.60%
12/2008 903.25 7.01 0.78% 1.80% 0.03% 0.75%
11/2008 896.24 -72.51 -7.49% 2.70% 0.03% -7.51%
10/2008 968.75 -197.61 -16.94% 6.40% 0.03% -16.97%
09/2008 1166.36 -116.47 -9.08% 2.20% 0.03% -9.11%
08/2008 1282.83 15.45 1.22% -1.20% 0.03% 1.19%
07/2008 1267.38 -12.62 -0.99% 5.70% 0.04% -1.02%
06/2008 1280.00 -120.38 -8.60% 7.90% 0.04% -8.63%
05/2008 1400.38 14.79 1.07% -22.00% 0.04% 1.03%
04/2008 1385.59 62.88 4.75% 25.00% 0.04% 4.72%
03/2008 1322.70 -7.93 -0.60% 6.90% 0.05% -0.64%
02/2008 1330.63 -47.92 -3.48% 4.90% 0.05% -3.52%
01/2008 1378.55 -89.81 -6.12% 17.00% 0.05% -6.16%
12/2007 1468.36 -12.79 -0.86% 3.00% 0.05% -0.91%
11/2007 1481.14 -68.23 -4.40% 6.60% 0.05% -4.45%
10/2007 1549.38 22.63 1.48% -2.55% 0.05% 1.43%
09/2007 1526.75 52.76 3.58% -3.88% 0.09% 3.49%
08/2007 1473.99 18.72 1.29% 12.70% 0.09% 1.20%
07/2007 1455.27 -48.08 -3.20% 6.88% 0.09% -3.29%
06/2007 1503.35 -27.27 -1.78% 8.90% 0.08% -1.87%
05/2007 1530.62 48.25 3.26% -6.90% 0.08% 3.17%
04/2007 1482.37 61.50 4.33% -1.10% 0.08% 4.24%
03/2007 1420.86 14.05 1.00% -8.00% 0.25% 0.75%
02/2007 1406.82 -31.42 -2.18% 4.70% 0.25% -2.43%
01/2007 1438.24 19.94 1.41% -5.70% 0.25% 1.16%
12/2006 1418.30 17.67 1.26% -7.90% 0.25% 1.01%
11/2006 1400.63 22.69 1.65% -2.00% 0.17% 1.47%
10/2006 1377.94 42.09 3.15% -1.00% 0.17% 2.98%
09/2006 1335.85 32.03 2.46% -2.50% 0.17% 2.28%
08/2006 1303.82 27.16 2.13% -6.00% 0.17% 1.95%
07/2006 1276.66 6.46 0.51% -1.00% 0.17% 0.34%
06/2006 1270.20 0.11 0.01% -1.00% 0.17% -0.16%
05/2006 1270.09 -40.52 -3.09% 18.90% 0.20% -3.29%
04/2006 1310.61 15.78 1.22% -0.20% 0.20% 1.02%
03/2006 1294.83 14.17 1.11% -0.70% 0.20% 0.91%
02/2006 1280.66 0.58 0.05% -2.00% 0.20% -0.15%
01/2006 1280.08 31.79 2.55% -4.00% 0.20% 2.35%
12/2005 1248.29 -1.19 -0.09% 1.00% 0.26% -0.36%
18

11/2005 1249.48 42.47 3.52% -6.00% 0.26% 3.26%
10/2005 1207.01 -21.80 -1.77% 3.50% 0.20% -1.97%
09/2005 1228.81 8.48 0.69% -0.29% 0.20% 0.50%
08/2005 1220.33 -13.85 -1.12% -2.07% 0.28% -1.40%
07/2005 1234.18 42.85 3.60% 4.29% 0.15% 3.45%
06/2005 1191.33 -0.17 -0.01% -1.36% 0.15% -0.16%
05/2005 1191.50 34.65 3.00% 1.38% 0.15% 2.85%
04/2005 1156.85 -23.74 -2.01% -1.44% 0.15% -2.16%
03/2005 1180.59 -23.01 -1.91% -1.42% 0.29% -2.20%
02/2005 1203.60 22.33 1.89% 1.56% 0.29% 1.60%
01/2005 1181.27 -30.65 -2.53% -3.76% 0.29% -2.82%
12/2004 1211.92 38.10 3.25% 3.16% 0.19% 3.06%
11/2004 1173.82 43.62 3.86% 3.34% 0.19% 3.67%
10/2004 1130.20 15.62 1.40% 1.18% 0.19% 1.21%
09/2004 1114.58 10.34 0.94% 1.19% 0.19% 0.75%
08/2004 1104.24 2.52 0.23% 1.68% 0.19% 0.04%
07/2004 1101.72 -39.12 -3.43% -4.45% 0.21% -3.64%
06/2004 1140.84 20.16 1.80% 3.21% 0.21% 1.58%
05/2004 1120.68 13.38 1.21% 1.93% 0.17% 1.04%
04/2004 1107.30 -18.91 -1.68% -2.01% 0.17% -1.85%
03/2004 1126.21 -18.73 -1.64% -1.80% 0.17% -1.81%
02/2004 1144.94 13.81 1.22% 1.90% 0.17% 1.05%
01/2004 1131.13 19.21 1.73% 2.01% 0.17% 1.55%
12/2003 1111.92 53.72 5.08% 4.26% 0.17% 4.90%
11/2003 1058.20 7.49 0.71% 1.93% 0.17% 0.54%
10/2003 1050.71 54.74 5.50% 5.32% 0.17% 5.32%
09/2003 995.97 -12.04 -1.19% -0.36% 0.19% -1.38%
08/2003 1008.01 17.70 1.79% 1.58% 0.19% 1.60%
07/2003 990.31 15.81 1.62% 1.65% 0.19% 1.43%
06/2003 974.50 10.91 1.13% 1.85% 0.17% 0.96%
05/2003 963.59 46.67 5.09% 5.19% 0.17% 4.92%
04/2003 916.92 68.74 8.10% 9.13% 0.17% 7.94%
03/2003 848.18 7.03 0.84% -0.17% 0.17% 0.66%
02/2003 841.15 -14.55 -1.70% -0.93% 0.17% -1.87%
01/2003 855.70 -24.12 -2.74% -4.32% 0.17% -2.91%
12/2002 879.82 -56.49 -6.03% -4.70% 0.17% -6.20%
11/2002 936.31 50.55 5.71% 6.78% 0.25% 5.45%
10/2002 885.76 70.48 8.64% 7.11% 0.25% 8.39%
09/2002 815.28 -100.79 -11.00% -10.76% 0.20% -11.20%
08/2002 916.07 4.45 0.49% 0.40% 0.20% 0.29%
07/2002 911.62 -78.20 -7.90% -8.12% 0.20% -8.10%
06/2002 989.82 -77.32 -7.25% -6.58% 0.13% -7.38%
05/2002 1067.14 -9.78 -0.91% 0.57% 0.13% -1.04%
04/2002 1076.92 -70.47 -6.14% -5.23% 0.12% -6.27%
19

03/2002 1147.39 40.66 3.67% 2.48% 0.12% 3.56%
02/2002 1106.73 -23.47 -2.08% -1.99% 0.12% -2.19%
01/2002 1130.20 -17.88 -1.56% -0.85% 0.12% -1.67%
12/2001 1148.08 8.63 0.76% 0.19% 0.12% 0.64%
11/2001 1139.45 79.67 7.52% 7.36% 0.12% 7.40%
10/2001 1059.78 18.84 1.81% 1.59% 0.14% 1.67%
09/2001 1040.94 -92.64 -8.17% -7.42% 0.14% -8.31%
08/2001 1133.58 -77.65 -6.41% -5.08% 0.14% -6.55%
07/2001 1211.23 -13.15 -1.07% -2.27% 0.14% -1.21%
06/2001 1224.38 -31.44 -2.50% -3.12% 0.29% -2.79%
05/2001 1255.82 6.36 0.51% -0.62% 0.29% 0.22%
04/2001 1249.46 89.13 7.68% 6.05% 0.37% 7.31%
03/2001 1160.33 -79.61 -6.42% -5.56% 0.23% -6.65%
02/2001 1239.94 -126.07 -9.23% -7.88% 0.23% -9.46%
01/2001 1366.01 45.73 3.46% 3.27% 0.23% 3.23%
12/2000 1320.28 5.33 0.41% -0.36% 0.38% 0.03%
11/2000 1314.95 -114.45 -8.01% -7.59% 0.25% -8.26%
10/2000 1429.40 -7.11 -0.49% 1.07% 0.25% -0.75%
09/2000 1436.51 -81.17 -5.35% -6.74% 0.44% -5.79%
08/2000 1517.68 86.85 6.07% 7.13% 0.31% 5.76%
07/2000 1430.83 -23.77 -1.63% -0.95% 0.24% -1.87%
06/2000 1454.60 34.00 2.39% 1.08% 0.24% 2.15%
05/2000 1420.60 -31.83 -2.19% -1.45% 0.24% -2.43%
04/2000 1452.43 -46.15 -3.08% -2.97% 0.38% -3.46%
03/2000 1498.58 132.16 9.67% 8.47% 0.38% 9.30%
02/2000 1366.42 -28.04 -2.01% -2.68% 0.24% -2.25%
01/2000 1394.46 -74.79 -5.09% -6.72% 0.24%
20

Why the period 2000-2009? There is no obvious answer to this question. In this particular case, we just found historical data
with relative ease; we could have searched harder and go back to 1990, or to 1980, to 1970, or even earlier. We have
absolutely no guidance as to how far back into the past we should go, because beta and the market risk premium are based
on market expectations going forward, not looking back. CAPM is absolutely mum on historical estimation simply because
one is not supposed to estimate beta in this way. The honest conclusion is that we have chosen this particular data arbitrarily.
Another arbitrarily choice refers to the type of return. Here we show monthly returns. We could have used annual returns, or
weekly returns, or daily returns. Again, convenience proved to be the trump card. Monthly returns were readily available,
and we simply settled for them. Let us continue then.
The relative risk of Toy Inc. is given by the strength of the correlation between the return on Toy Inc. and that of the S&P
500 index. Mathematically, beta is represented by the coefficient of S&P 500 index in the following regression model:
Hret(Toy Inc.) = a + b*Hret(S&P 500) + e
Before we proceed with running the least-squares regression analysis, we plot the data along the XY-coordinates, with
return on Toy Inc. on the Y-axis, and return on the S&P 500 on the X-axis:
0.3
Toy Inc. against the S&P 500: 2000-2009
0.2
Toy Inc. monthly return
0.1
0
-0.1
-0.2
-0.3
0.00% 2000.00% 4000.00% 6000.00% 8000.00% 10000.00% 12000.00%
S&P 500 monthly return
We use Excel or any other software with econometric functions and we obtain a result that should be similar to this one:
21

Regression output: Toy Inc. as a dependent variable 2000-2009
Regression Statistics
Multiple R 0.33
R Square 0.11
Adjusted R Square 0.1
Standard Error 0.06
Observations 110
ANOVA
df SS MS F Significance F
Regression 1 0.05 0.05 13.11 0
Residual 108 0.4 0
Total 109 0.45
Coefficients
Standard
Error
t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.01 0.01 0.93 0.35 -0.01 0.02 -0.01 0.02
S&P 0.47 0.13 3.62 0 0.21 0.72 0.21 0.72
The regression output reveals some very interesting things: approximately 11% of the variance in the monthly returns of
Toy Inc. is explained by the variance in the returns of the S&P 500 (R-square = 0.11). This influence is significant, that is.,
the model has explanatory power (F = 13.11). It is significant, but small. It follows that the remaining 89% of the variance
in the returns of Toy Inc. is explained by other factors than the S&P 500 index. One more reason to diversify your
investments.
The fitted regression model becomes:
Ret(Toy Inc.) = 0.01 + 0.47*Ret(S&P 500)
The estimated beta of Toy Inc. is equal to 0.47. The last step is to estimate the market risk premium and the risk-free rate.
The risk-free rate can be approximated as being equal to the return on the one-month Treasuries. The estimation of the
market risk premium is more problematic though. The average market risk premium (the difference between the return on
the S&P 500 and the risk-free rate) for the period 2000-2009 is -0.7%. If we take this historical estimate to infer the
expected market risk premium we end up with a paradox. Are investors really expecting a long-run negative return on the
S&P 500? If so, why are they still holding on to their stocks? As I write these lines the S&P 500 and other major indices are
all down significantly, having reached historical lows. A majority of investors still believe that next year's return will be
negative; but they eventually hope that in two or three,or maybe four years things will turn around, and in the long-run, the
expected return will average out to a positive number. No investor in his/her right mind would hold on to stocks that are
expected to return -0.7% on average over the next century. This is plain common sense. The simple fact that there are still
billions of dollars invested in S&P 500 stocks is a testimony to the expectations that – in spite of the current economic
slump – markets will eventually turn around. The later this turnaround, the lower the index will go; however, as long as
there is a glimmer of hope people will still hold stocks. But never mind all this; let us continue. We average the risk-free rate
for the entire period and we find it equal to 0.17%. Now we can estimate the required rate of return for Toy Inc.
Rret(Toy Inc.) = 0.17% + 0.46*(-0.7%) = -0.152%
On an annualized base this equals -1.8%. We find that the cost of equity for Toy Inc. is a negative 1.8%/year. This result is
evidently absurd!
22

Let us try estimating beta using another period. Let us say 2005-2009, maybe recent trends are more relevant:
30.00%
T oy Inc. against the S&P 500: 2005-2009
20.00%
T oy Inc. monthly return
10.00%
0.00%
-10.00%
-20.00%
-30.00%
-20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00%
S&P 500 monthly return
Regression output: Toy Inc. as a dependent variable 2005-2009
Regression Statistics
Multiple R 0.12
R Square 0.01
Adjusted R Square -0.01
Standard Error 0.08
Observations 50
ANOVA
df SS MS F Significance F
Regression 1 0 0 0.68 0.41
Residual 48 0.32 0.01
Total 49 0.32
Coefficient
s
Standard
Error
t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.01 0.01 0.62 0.54 -0.02 0.03 -0.02 0.03
S&P -0.22 0.27 -0.83 0.41 -0.76 0.32 -0.76 0.32
Notwithstanding the insignificant explanatory power of the model (F = 0.68), the regression line is now:
23

Ret(Toy Inc.) = 0.01 -0.22*Ret(S&P 500)
Beta is negative meaning that the return on Toy Inc. is negatively correlated to that on the S&P 500. Between 2005 and
2009 Toy Inc. moved in the opposite direction of the S&P 500: when the index rose, the stock sank; when the index
slumped, the stock rose. Obviously, this makes Toy Inc. a very good candidate for diversification. The market risk premium
averages -1.03% for the period 2005-2009, and the risk-free rate averages 0.14%.
Rret(Toy Inc.) = 0.14% -0.22*(-1.03%) = 0.37%
On an annualized basis, the required return for Toy Inc. is equal to 4.49%. This figure appears more reasonable, but make no
mistake, it is as arbitrary as the previous estimation. In fact there is absolutely no valid criteria to tell us why we should
chose one historical period over another one. Were we to use the period 2007-2009, we would have ended up with a
complete different result. Even if we stayed with the same period, but used daily returns instead of monthly returns, results
would have changed. Every time we change our estimation method, results change. Period. So, CAPM is not very helpful or
reliable.
Perhaps, we should attempt another approach.
24

The Dividend Growth Model
The valuation of equity is usually done with the help of the dividend growth model. In real life, the stream of dividend is
uneven and unpredictable, unlike the coupons paid by bonds. The smoothness and relative predictability of interest
payments makes the valuation of bonds a walk in the park compared to the valuation of common equity. The formula for
calculating the price of a bond is tight and sparse: the present value of a known annuity at known intervals of time, plus the
present value of a known face value payment at a future known date. By contrast, the present value of common equity is
given by an open ended model:
P = dividend1/(1+r) + dividend2/(1+r) 2 + dividend3/(1+r) 3 + ...... + dividendN/(1+r) n + ......
Obviously, this is not of much practical help, unless we could make it more tractable. The solution is to imagine that the
future (quasi) infinite stream of dividend can be smoothened out over long periods, by averaging out wild swings. The result
is a perpetuity with constant growth rate g. It can be shown that:
P = dividend/(1+r) + dividend(1+g)/(1+r) 2 + dividend(1+g) 2 /(1+r) 3 + ...... + dividend(1+g) n-1 /(1+r) n + ......
can be approximated by the formula:
P = dividend/(r-g)
So, if we know the required rate and the expected long-term growth rate in dividends, we can easily estimate the price of the
stock. But how can we know r? We simply turn the formula around:
r = dividend/P + g
where:
dividend/P
g
= dividend yield
= long-term growth rate in dividend
when we deal with a cash cow, that is, a mature firm, without major growth opportunities, paying more or less a level
dividend stream, the formula becomes:
r = dividend/P
This approach for estimating the cost of equity is less troublesome in some ways than the CAPM; it too, however, requires a
major leap of faith. In order to estimate the required rate of return, the value of the current stock price entered in the formula
has to reflect the true riskiness of the dividend stream. To see why this is true, consider the following example:
Toy Inc. and Super Toy Inc. expected annual dividend
Dividend paid if
recession
Probability of
recession
Dividend paid if
expansion
Probability of
expansion
Expected annual
dividend
Toy Inc. $0.9 0.5 $1.04 0.5 $0.97
Super Toy Inc. $0.0 0.5 $1.94 0.5 $0.97
Both Toy Inc. and Super Toy Inc. are expected to pay an annual dividend equal on average to $0.97. If both companies are
priced in the market at $25/share, how do we know which one is correctly priced, and which is not? According to the
dividend growth model, both firms should have a cost of equity equal to (assuming zero growth in dividends):
r(Toy Inc.) = $0.97/$25 = 3.9%
r(Super Toy Inc.) = $0.97/$25 = 3.9%
We know, however, that this is not possible since Super Toy Inc. is riskier than Toy Inc. Obviously, one of them is
mispriced. But once we admit the market is fallible, we open the door to the possibility that the market is wrong with
respect to both of them. Maybe the price of Toy Inc. is too low, and the price of Super Toy Inc. is too high. In reality it is
25

very hard to tell companies like Toy Inc. and Super Toy Inc. apart. Investors see that they both behave like cash cows and
pay comparable annual dividends, hence they infer they should be priced the same.
The problem gets worse when we deal with growth companies. Not only should we question the fairness of market pricing,
but we also have to (gu)estimate the growth rate in earnings/dividends. While we might have an inkling about "next year,"
trying to project earnings growth over longer periods is a highly uncertain exercise. We could predict more accurately the
trajectory of asteroid Achaemenides from the Kuiper Belt (some 3 billion miles away) in 200 years from now than
forecasting the earnings of General Motors in two years from now. The fog of the future is simply too thick, and the
complexity of economic activity simply too monstrous to comprehend.
When used for valuation purposes, the dividend growth model leads to a paradox. Remember that we need to estimate the
required rate of return to discount cash flow in order to estimate the current stock price. We must assume that the stock is
fairly priced in order to calculate the required rate. But if we make this assumption, what is the point of the entire exercise?
We might as well acknowledge the stock price is fair and save us the trouble of doing all these mind numbing calculations.
The contradiction, however, does not end here. Things get hairy when we assume the stock is fairly priced, we estimate the
required rate, we discount cash flow, and we find the stock to be under- or overpriced. Then we know for sure that we
messed up somewhere along the way because one cannot start with a correct assumption and end up with a contradiction.
Either the assumption is wrong, the deduction process is flawed, or both.
The problem lies in the nature of the model we are using - it is indeterminate. It is presented to us in the form of ONE
equation and THREE unknown variables, which in real-life are jointly determined. There is an infinity a possible
combinations that will satisfy the dividend growth model equation. The trouble is, we cannot tell them apart.
We should not give up without attempting to approximate the boundaries of the cost of equity. An alternative to the dividend
growth model is the following variation. We know that at any time, the market value of the firm's equity should be given
by:
MVE = Max[(MVA-D); PV(CF to shareholders)]
where:
MVE
MVA
D
= market value of equity
= market value of assets
= market value of debt
(MVA-D) is simply the net market value of firm's assets, or if you wish, firm's liquidation value. If, at a given point in time
we decide to terminate the company, liquidate its assets, pay all obligations, and walk away with our pockets full of cash,
this is what we would get. If investors are rational, the price paid to acquire the equity of the firm (including control over its
operation) should be the maximum between liquidation value and value as a going concern (given by the present value of
future cash flow). An obvious consequence is that the firm should be liquidated whenever its going concerns value falls
below its liquidation value. When that happens, it is said the firm is worth more dead than alive 6 .
That is, it makes sense to keep the firm as a going concern only if the present value of its cash flow is larger than the
liquidation value of its assets. The formula becomes:
MVE = Max[(MVA-D); Dividend/(r-g)]
where:
r
g
= discount rate of equity
= growth rate in earnings/dividends
To justify the firm as a going concern, the following condition must be satisfied:
Dividend/(r-g) > MVA-D
6 Hence, we should all stop shedding tears over the fate of giant corporate dinosaurs like General Motors and AIG. Most likely they are worth more dead
than alive, and keeping them on life support is only draining away valuable resources that otherwise could be invested more efficiently.
26

From here we see that:
r < Dividend/(MVA-D) + g
The above inequality is less insightful than it appears at first glance. We must be extremely careful how to interpret it. It
does not say that the cost of equity should be less than the ratio of expected dividends to the liquidation value of the firm. It
only says that firms with valuable net assets (in terms of market value) should have either a high dividend payout, or good
growth opportunities in order to justify their operation as a going concern.
To better understand this contention consider the following crude example: You own a house worth $500,000 at current
market prices (net of obligations). You can rent it or you can sell it. If the highest net rent you can obtain is only
$1,500/year, you might be better off selling it, since you only realize 3%/year, which is not dramatically higher than the
return on a GIC. Your cash flow is definitely riskier than that of a GIC. Your tenants might leave without paying, they might
scratch the walls, break some windows, or your basement might get flooded, in which case you will incur significant
additional repair costs. Of course, if you expect a significant appreciation in the value of your property you might be betteroff
renting it; what you forgo in rent return you could realize in capital appreciation.
The only minor improvement this variation has introduced over the dividend growth model is the replacement of the price
of stock with the net market value of firm's assets. By circumventing the stock price we are somewhat avoiding the circular
reference between the market value of equity and the required return on equity. Some assets have multiple uses, and hence,
their market value is only partially dependent on the payoff generated in a specific investment context. The real problem we
encounter here is determining the market value of firm's assets. In the simple example of a building, market value is easier
to infer. When dealing with complex operations,and specific technologies, where there is no market for the assets of the
firm, ascertaining market value is very difficult indeed.
At this point in time the reader might succumb to cynicism after seeing how the most cherished tenets of modern finance -
the familiar and reassuring models that populate your average finance textbook - are being criticized and ruthlessly
battered.
27

Capital structure and firm value
The initial question remains: how is capital structure affecting the valuation of the firm. To simplify this issue we transform
Toy Inc and all-equity Toy Inc into perfect cash cows: Let us assume zero retention and no growth in sales next year. All
earnings are paid out as dividends, and the dividend stays constant in perpetuity. These two companies continue to exist in
parallel universes.
Pro-forma income statement: Toy Inc. and all-equity Toy Inc. as cash cows with zero retention and constant dividend
Toy Inc today All-equity Toy Inc today Toy Inc. next year All-equity Toy Inc. next year
Sales $5,000.00 $5,000.00 $5,000.00 $5,000.00
(Costs) $3,500.00 $3,500.00 $3,500.00 $3,500.00
(Depreciation) $1,000.00 $1,000.00 $1,000.00 $1,000.00
EBIT $500.00 $500.00 $500.00 $500.00
(Interest) $80.75 $0.00 $80.75 $0.00
EBT $419.25 $500.00 $419.25 $500.00
(Tax) $142.55 $170.00 $142.55 $170.00
Net income $276.71 $330.00 $276.71 $330.00
Addition to RE $0.00 $0.00 $0.00 $0.00
Dividend $276.71 $330.00 $276.71 $330.00
Pro-forma balance sheet: Toy Inc. and all-equity Toy Inc. as cash cows with zero retention and constant dividend
Toy Inc.
today
All-equity toy
today
Toy Inc. next
year
All-equity toy
next year
Toy Inc.
today
All-equity Toy
Inc. today
Toy Inc. next
year
All-equity Toy Inc.
next year
Cash $100.00 $100.00 $1,100.00 $1,100.00 A/P $300.00 $0.00 $300.00 $0.00
Inventory $500.00 $500.00 $500.00 $500.00 N/P $400.00 $0.00 $400.00 $0.00
A/R $400.00 $400.00 $400.00 $400.00
Current assets $1,000.00 $1,000.00 $2,000.00 $2,000.00
Gross fixed assets $3,000.00 $3,000.00 $3,000.00 $3,000.00
Depreciation $1,000.00 $1,000.00 $2,000.00 $2,000.00
Net fixed assets $2,000.00 $2,000.00 $1,000.00 $1,000.00
Current
liabilities
Long-term
debt
Other longterm
Outstanding
shares
Retained
earnings
$700.00 $0.00 $700.00 $0.00
$1,500.00 $0.00 $1,500.00 $0.00
$0.00 $0.00 $0.00 $0.00
$1,300.00 $3,500.00 $1,300.00 $3,500.00
$0.00 $0.00 $0.00 $0.00
Other assets $500.00 $500.00 $500.00 $500.00 Owner's equity $1,300.00 $3,500.00 $1,300.00 $3,500.00
Total assets $3,500.00 $3,500.00 $3,500.00 $3,500.00 Total L&E $3,500.00 $3,500.00 $3,500.00 $3,500.00
28

Cash flows: Toy Inc. and all-equity Toy Inc. as cash cows with zero retention and constant dividend
Toy Inc. today All-equity Toy Inc. today Toy Inc. next year All-equity Toy Inc. next year
OCF $1,330.00 $1,330.00 $1,330.00 $1,330.00
Net Capital Spending -$338.00 -$338.00 $0.00 $0.00
Increase in NWC -$662.00 -$662.00 -$1,000.00 -$1,000.00
Interest tax shield $27.46 $0.00 $27.46 $0.00
CF from assets $357.46 $330.00 $357.46 $330.00
CF to creditors $80.75 $0.00 $80.75 $0.00
CF to shareholders $276.71 $330.00 $276.71 $330.00
CF from assets $357.46 $330.00 $357.46 $330.00
As expected, you will immediately notice that:
Net income (All-equity Toy Inc.) > Net income (Toy Inc.)
Difference in net income = $330 - $276.71 = $53.3. The significance of this number is straight forward: $80.75(1-0.34) =
$53.3. The difference in the two net incomes is due to the presence of interest. In the case of Toy Inc., interest is an
additional cost that reduces the net income by exactly:
Difference in net income = $interest*(1-Tax rate)
At the same time, as already seen earlier, total cash flows are higher for Toy Inc.
Difference in total cash flow = $357.46 - $330 = $27.46
The difference in total cash flow is also easy to spot: $80.75*(0.34). In other words, Toy Inc. will have larger cash flows
than all-equity Toy Inc., and the difference will be equal to:
Difference in total cash flow = $interest*(Tax rate)
This difference is called debt tax shield. The very presence of interest, which is deductible from pre-tax income, creates a
small increase in total cash flow - a small savings of sorts for claimholders. We can now generalize:
CF(Toy Inc.) = CF to shareholders + CF to creditors = (EBIT - $interest)*(1-Tax rate) + $interest
CF (All-equity Toy Inc.) = EBIT(1-Tax rate) - $interest*(1-Tax rate) + $interest = EBIT*(1-Tax rate) + $interest*(Tax rate)
however:
hence:
EBIT*(1-T) = CF(All-equity Toy Inc.)
CF(Toy Inc. ) = CF(All-equity Toy Inc.) + $interest*(Tax rate)
or:
CF(Toy Inc. ) = CF(All-equity Toy Inc.) + interest tax shield
where:
$interest*(Tax rate) = interest tax shield, also called debt tax shield
29

Total cash flows and borrowing: Implications for the ideal world
We analyze now cash flows and leverage while keeping all other variables constant. We assume that interest rates, tax rates,
costs, sales, etc. are not affected by leverage. This is obviously an ideal case. At the very least, interest rates would increase
with leverage to reflect higher financial risk. For now, however, it is interesting to assess the implications of such an ideal
set up. Next, we simulate cash flows as a function of total debt ratios, and plot the relationship in a two-dimensional graph:
Total cash flow of Toy Inc. for various levels of debt: the ideal world
Total debt
ratio
Cost of
borrowing
$interest Tax rate Debt tax shield
All-equity cash
flow
Total cash flow
Cash flow to
shareholders
Cash flow to
creditors
5.00% 4.25% $7.44 34.00% $2.53 $330.00 $332.53 $325.09 $7.44
10.00% 4.25% $14.88 34.00% $5.06 $330.00 $335.06 $320.18 $14.88
15.00% 4.25% $22.31 34.00% $7.59 $330.00 $337.59 $315.28 $22.31
20.00% 4.25% $29.75 34.00% $10.12 $330.00 $340.12 $310.37 $29.75
25.00% 4.25% $37.19 34.00% $12.64 $330.00 $342.64 $305.45 $37.19
30.00% 4.25% $44.63 34.00% $15.17 $330.00 $345.17 $300.54 $44.63
35.00% 4.25% $52.06 34.00% $17.70 $330.00 $347.70 $295.64 $52.06
40.00% 4.25% $59.50 34.00% $20.23 $330.00 $350.23 $290.73 $59.50
45.00% 4.25% $66.94 34.00% $22.76 $330.00 $352.76 $285.82 $66.94
50.00% 4.25% $74.38 34.00% $25.29 $330.00 $355.29 $280.91 $74.38
55.00% 4.25% $81.81 34.00% $27.82 $330.00 $357.82 $276.01 $81.81
60.00% 4.25% $89.25 34.00% $30.35 $330.00 $360.35 $271.10 $89.25
65.00% 4.25% $96.69 34.00% $32.87 $330.00 $362.87 $266.18 $96.69
70.00% 4.25% $104.13 34.00% $35.40 $330.00 $365.40 $261.27 $104.13
75.00% 4.25% $111.56 34.00% $37.93 $330.00 $367.93 $256.37 $111.56
80.00% 4.25% $119.00 34.00% $40.46 $330.00 $370.46 $251.46 $119.00
85.00% 4.25% $126.44 34.00% $42.99 $330.00 $372.99 $246.55 $126.44
90.00% 4.25% $133.88 34.00% $45.52 $330.00 $375.52 $241.64 $133.88
95.00% 4.25% $141.31 34.00% $48.05 $330.00 $378.05 $236.74 $141.31
99.00% 4.25% $147.26 34.00% $50.07 $330.00 $380.07 $232.81 $147.26
100.00% 4.25% $148.75 34.00% $50.58 $330.00 $380.58 $231.83 $148.75
30

Total cash flow as a function of leverage: the ideal world
400
350
300
$
250
200
150
Debt tax shield
All-equity cash flow
Total cash flow
100
50
0
10.00%
Total debt ratio
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
99.00%
The ideal case shows that cash flows are monotonously increasing as a function of leverage. If our goal is to maximize total
cash flows, we should borrow up to 100% of total assets. Of course, this could never happen, but let us examine what
happens when we get very close to 100% debt.
The interesting case of overwhelming debt
Next, we present the financial standing of Toy Inc. with a total debt ratio of 99%.
Income Statement of Toy Inc. at 99% debt: the ideal world
Today
Next year
Sales $5,000.00 $5,000.00
(Costs) $3,500.00 $3,500.00
(Depreciation) $1,000.00 $1,000.00
EBIT $500.00 $500.00
(Interest) $147.26 $147.26
EBT $352.74 $352.74
(Tax) $119.93 $119.93
Net income $232.81 $232.81
Addition to RE $0.00 $0.00
Dividend $232.81 $232.81
31

Balance sheet of Toy Inc. at 99% debt: the ideal world
Today Next year Today Next year
Cash $100.00 $1,100.00 A/P $0.00 $0.00
Inventory $500.00 $500.00 N/P $0.00 $0.00
A/R $400.00 $400.00 Current liabilities $0.00 $0.00
Current assets $1,000.00 $2,000.00
Long-term debt $3,465.00 $3,465.00
Gross fixed assets $3,000.00 $3,000.00 Other long-term $0.00 $0.00
Depreciation $1,000.00 $2,000.00 Outstanding shares $35.00 $35.00
Net fixed assets $2,000.00 $1,000.00 Retained earnings $0.00 $0.00
Other assets $500.00 $500.00 Owner's equity $35.00 $35.00
Total assets $3,500.00 $3,500.00 Total L&E $3,500.00 $3,500.00
Selected financial ratios of Toy Inc. at 99% debt: the ideal world
Today
Next year
TAT 1.43 1.43
FAT 2.50 5.00
D/E 99.00 99.00
Total debt ratio 0.99 0.99
LT debt ratio 0.99 0.99
TIE 3.40 3.40
Cash coverage 10.19 10.19
Profit margin 4.66% 4.66%
ROA 6.65% 6.65%
ROE 665.16% 665.16%
Dividend per share $2.33 $2.33
EPS $2.33 $2.33
Book value per share $0.35 $0.35
Dividend yield ? ?
Cash flows of Toy Inc. at 99% debt: the ideal world
Today
Next year
OCF $1,330.00 $1,330.00
Net Capital Spending -$338.00 $0.00
Increase in NWC -$662.00 -$1,000.00
Interest tax shield $50.07 $50.07
CF from assets $380.07 $380.07
CF to creditors $147.26 $147.26
CF to shareholders $232.81 $232.81
CF from assets $380.07 $380.07
32

At 4.25% cost of borrowing and 34% corporate tax, most ratios are not any different than what we have been accustomed to
see until now. Interest payments are still well covered by revenues, profitability sits at a reasonable 4.7%, and ROA at
6.65%. But notice the hefty 665.2% return on equity. We are looking at a firm where you invest a mere $35 of your own
equity and expect to receive a $232.8 dividend! This must be a dream come true. In an ideal world, we would expect that all
companies would try to leverage their capital structure to capture these fabulous rates of return.
Amazingly, reality sometimes comes dangerously close to approximating this case - at least for limited periods of time. We
argued that the cost of debt increases with leverage, which might increase the probability of bankruptcy. Lenders tend to see
the borrowers as riskier the more debt they have. While this is always true in reality, the extent of risk aversion in the market
can vary greatly. The latest financial debacle is a stern reminder than even the most conservative bankers can lose their
compass and throw common sense and prudence out the window. Unbelievably, many firms actually did push indebtedness
to new highs, especially in the financial sector. For some time they were able to realize good returns, and pay some
incredible salaries to their managers. Eventually things unraveled fairly brutally under the weight of too much debt. This is
part of the reason why markets are in a free fall since 2008.
The history of financial markets is one of alternating periods of optimism and pessimism. Bulls and bears. During prolonged
periods of optimism, investors acquire a false sense of security and begin to perceive uncertainty as mild and benign. They
start to behave recklessly by taking on huge risks, without even realizing their scope and implications. In a speech delivered
on December 5, 1996, Alan Greenspan, then chairman of the US Federal Reserve, coined the term "irrational exuberance 7 ."
When the world is in such a state, money abounds, and credit is usually cheap. The spread between investment and
speculative grade bonds is laughably small. Almost everyone can borrow. It is enough to ask, and the money will be handed
to you. What Greenspan never acknowledged, however, is that he might have contributed to such an outcome by keeping
the cost of money low.
After periods of optimism, there comes a cataclysmic event that shakes everyone's confidence and forces the market into a
period of contraction. It happened in 1870, in 1929, in 2000, and in 2008. For sure, it will happen again, as soon as people
will forget about crises being possible. Sometimes, when the shock is not quite structural, cheap borrowing endures. In other
times, the crisis begins as a liquidity crisis, just like the sub-prime meltdown of 2008. Big financial players succumb under
the burden of exposure to bad debt, and before long, threaten by financial panic and bank runs, the whole system is in
tatters.
We see here two distinct worlds, both driven by human expectations and emotions: greed and fear. Common sense dictates
that the dynamic between debt and firm value follows a different logic in each situation. In order to understand these
(possibly diverging) logics in more depth we need to consider each case in turn.
First, we will assume that the cost of debt increases with leverage, but this increase is mild and smooth. This represents a
world driven mainly by greed, with high tolerance for risk,: either because investors are less risk averse, or because they do
not perceive risk realistically. Next, we will move to a world driven by fear, in which borrowing becomes extremely
expensive as risk increases even to moderate levels.
7 See "The Challenge of Central Banking in a Democratic Society" Remarks by Chairman Alan Greenspan At the Annual Dinner and Francis Boyer
Lecture of The American Enterprise Institute for Public Policy Research, Washington, D.C. December 5, 1996. Robert J. Schiller credits this speech with a
mini-crash in financial markets around the world the next morning (http://www.irrationalexuberance.com/definition.htm)
33

Borrowing with high tolerance for risk
The degree of financial leverage is partially contingent on how much debt one can borrow at a low cost. In periods of
"exuberant investor irrationality," when credit is abundant, when even Ebenezer Scrooge is upbeat about the future, both
lenders and investors tend to underestimate risk, or overestimate their business savvy. Cheap credit floods the market and
everyone borrows with gusto. The spread between firms with good credit rating and those with a more precarious situation
is rather narrow. Suppose that in the case of Toy Inc. the cost of borrowing looked like this:
Toy Inc. as a cash cow: Cash flows as a function of leverage when there is high tolerance for risk
Total debt ratio Interest rate $interest Tax rate Debt tax shield
All-equity
cash flow
Total cash flow
CF to
shareholders
CF to creditors
0.00% 4.25% $0.00 34.00% $0.00 $330.00 $330.00 $330.00 $0.00
10.00% 4.25% $14.88 34.00% $5.06 $330.00 $335.06 $320.18 $14.88
15.00% 4.25% $22.31 34.00% $7.59 $330.00 $337.59 $315.27 $22.31
20.00% 4.50% $31.50 34.00% $10.71 $330.00 $340.71 $309.21 $31.50
25.00% 4.50% $39.38 34.00% $13.39 $330.00 $343.39 $304.01 $39.38
30.00% 4.50% $47.25 34.00% $16.07 $330.00 $346.07 $298.82 $47.25
35.00% 4.50% $55.13 34.00% $18.74 $330.00 $348.74 $293.62 $55.13
40.00% 4.50% $63.00 34.00% $21.42 $330.00 $351.42 $288.42 $63.00
45.00% 5.00% $78.75 34.00% $26.78 $330.00 $356.78 $278.03 $78.75
50.00% 5.00% $87.50 34.00% $29.75 $330.00 $359.75 $272.25 $87.50
55.00% 5.00% $96.25 34.00% $32.73 $330.00 $362.73 $266.48 $96.25
60.00% 5.00% $105.00 34.00% $35.70 $330.00 $365.70 $260.70 $105.00
65.00% 5.00% $113.75 34.00% $38.68 $330.00 $368.68 $254.93 $113.75
70.00% 5.00% $122.50 34.00% $41.65 $330.00 $371.65 $249.15 $122.50
75.00% 5.00% $131.25 34.00% $44.63 $330.00 $374.63 $243.38 $131.25
80.00% 5.00% $140.00 34.00% $47.60 $330.00 $377.60 $237.60 $140.00
85.00% 5.00% $148.75 34.00% $50.58 $330.00 $380.58 $231.83 $148.75
90.00% 5.00% $157.50 34.00% $53.55 $330.00 $383.55 $226.05 $157.50
95.00% 5.50% $182.88 34.00% $62.18 $330.00 $392.18 $209.30 $182.88
99.00% 6.00% $207.90 34.00% $70.69 $330.00 $400.69 $192.79 $207.90
100.00% 6.25% $218.75 34.00% $74.38 $330.00 $404.38 $185.63 $218.75
34

Total cash flow as a function of leverage when there is high tolerance for risk
450
400
350
300
$
250
200
Debt tax shield
All-equity cash flow
Total cash flow
150
100
50
0
10.00%
Total debt ratio
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
99.00%
The difference between a world with high tolerance for risk and the ideal world is hardly noticeable. The cash flows of Toy
Inc. increase with leverage almost as smoothly as in the ideal world.
35

The hurdle rate: the weighted average cost of capital
We turn now to estimating the cost of capital and the fair market value of the firm. Consistent with earlier arguments, we
estimate the cost of equity heuristically:
r = y + risk premium for leverage
The risk premium is an arbitrary quantity, chosen based on common sense.
Toy Inc. as a cash cow: Cost of equity, cost of borrowing, and present values as a function of leverage when there is high tolerance for risk
Total debt ratio
Total cash flow
CF to
shareholders
CF to
creditors
Cost of
debt
MV(Debt) Cost of equity MV equity Total firm value
Implied hurdle
rate
0.00% $330.00 $330.00 $0.00 4.25% $0.00 9.43% $3,499.47 $3,499.47 9.43%
10.00% $335.06 $320.18 $14.88 4.25% $350.00 9.93% $3,224.40 $3,574.40 9.37%
15.00% $337.59 $315.27 $22.31 4.25% $525.00 10.18% $3,096.99 $3,621.99 9.32%
20.00% $340.71 $309.21 $31.50 4.50% $700.00 10.68% $2,895.22 $3,595.22 9.48%
25.00% $343.39 $304.01 $39.38 4.50% $875.00 10.93% $2,781.45 $3,656.45 9.39%
30.00% $346.07 $298.82 $47.25 4.50% $1,050.00 11.18% $2,672.76 $3,722.76 9.30%
35.00% $348.74 $293.62 $55.13 4.50% $1,225.00 11.43% $2,568.83 $3,793.83 9.19%
40.00% $351.42 $288.42 $63.00 4.50% $1,400.00 11.68% $2,469.35 $3,869.35 9.08%
45.00% $356.78 $278.03 $78.75 5.00% $1,575.00 12.43% $2,236.73 $3,811.73 9.36%
50.00% $359.75 $272.25 $87.50 5.00% $1,750.00 12.68% $2,147.08 $3,897.08 9.23%
55.00% $362.73 $266.48 $96.25 5.00% $1,925.00 12.93% $2,060.90 $3,985.90 9.10%
60.00% $365.70 $260.70 $105.00 5.00% $2,100.00 13.18% $1,978.00 $4,078.00 8.97%
65.00% $368.68 $254.93 $113.75 5.00% $2,275.00 13.43% $1,898.18 $4,173.18 8.83%
70.00% $371.65 $249.15 $122.50 5.00% $2,450.00 13.68% $1,821.27 $4,271.27 8.70%
75.00% $374.63 $243.38 $131.25 5.00% $2,625.00 13.93% $1,747.13 $4,372.13 8.57%
80.00% $377.60 $237.60 $140.00 5.00% $2,800.00 14.18% $1,675.60 $4,475.60 8.44%
85.00% $380.58 $231.83 $148.75 5.00% $2,975.00 14.43% $1,606.55 $4,581.55 8.31%
90.00% $383.55 $226.05 $157.50 5.00% $3,150.00 14.68% $1,539.85 $4,689.85 8.18%
95.00% $392.18 $209.30 $182.88 5.50% $3,325.00 15.43% $1,356.46 $4,681.46 8.38%
99.00% $400.69 $192.79 $207.90 6.00% $3,465.00 16.13% $1,195.20 $4,660.20 8.60%
100.00% $404.38 $185.63 $218.75 6.25% $3,500.00 16.43% $1,129.79 $4,629.79 8.73%
Notice that we have introduced a new variable, called "implied hurdle rate." This addition warrants an explanation.
Remember that:
It follows that:
Total CF(Toy Inc.) = CF(shareholders Toy Inc.) + CF(creditors Toy Inc.)
Total MV(Toy Inc.) = MVE(Toy Inc.) + MVD(Toy Inc.)
where:
MV = total market value
MVE = market value of equity
MVD = market value of debt
That is, the total market value of Toy Inc. can be decomposed into market value of equity and market value of debt.
36

However, in the case of the cash cow:
MVE(Toy Inc.) = CF(shareholders)/r
MVD(Toy Inc) = $interest/y
where:
r = cost of equity
y = cost of debt
By definition, there must be a discount rate - let us call it hurdle rate -such that:
Total (CF Toy Inc.)/wacc = CF(shareholders Toy Inc.)/r + $interest/y
where:
wacc = hurdle rate
It can be easily shown that:
wacc = a*y + (1-a)*r
where:
a = is the implied weight of debt in the capital structure of Toy Inc. Obviously, a +(1-a) = 100%
The hurdle rate is also known as the weighted average cost of capital or wacc. The economic significance of wacc is
straightforward: it is an average cost of capital that could be used in estimating the present value of total cash flows, that is
the total market value of the company.
So far, we have described two approaches to calculating the total market value of the firm:
(i) We could discount cash flows to shareholders using the cost of equity to find the fair market value of equity. We could
discount cash flows to creditors using the cost of debt to estimate the fair market value of debt. We could then add the fair
market value of debt and the fair market value of equity to estimate the fair total market value of the firm; or
(ii) We could discount total cash flows using the weighted average cost of capital (wacc) to estimate the fair total market
value of the firm;
In most finance textbooks, the weighted average cost of capital (wacc) is adjusted to reflect the tax-saving effect of interest
payments:
wacc' = a*y (1-Tc) + (1-a)*r*
where:
wacc'
Tc
= tax-adjusted wacc
= corporate tax rate
When using wacc', the estimation of total market value needs to be adjusted as well. The total market value of the firm can
be now estimated by discounting all-equity total cash flows, instead of total cash flows. This is so because we do not want
to count twice the tax-saving effect of debt. Remember that:
or
Total CF(Toy Inc.) = CF(shareholders Toy Inc.) + CF(creditors Toy Inc.)
Total CF(Toy Inc.) = Total CF(all-equity Toy Inc.) + interest tax shield
37

For the cash cow:
Total CF(Toy Inc.)/wacc = Total CF(all-equity Toy Inc.)/wacc' = MV(Toy Inc.)
This approach to estimating total market value represents one of the major tenets of modern finance.
Practical problems associated with the wacc
In our example, we did not calculate wacc as a weighted average because we did not know what weights to use. We have
heuristically determined the cost of equity, observed the cost of debt, estimated cash flows to shareholders, cash flows to
creditors and we inferred or implied the weighted cost of capital from the formula:
or
Total (CF Toy Inc.)/wacc = CF(shareholders Toy Inc.)/r + $interest/y
wacc = r*y*Total CF(Toy Inc.)/[y*CF(shareholders Toy Inc.) + r*$interest]
You have probably guessed by now that wacc is plagued by the same circular reference problem we have encountered
before. In order to estimate wacc using the formula:
or
wacc = a*y + (1-a)*r
wacc = a*y + (1-a)*r*(1-Tc)
we need to know the fair market value of equity in total fair market value of the firm. Sure enough, the fair market value of
equity is a function of the fair cost of equity. But the fair cost of equity in turn is a function of financial risk as measured by
leverage, that is, as measured by the weight of fair market value of equity:
and
1-a = f(r)
r = f(1-a)
The circular reference problem rears its ugly head again. We have more unknown variables to estimate than we can
formulate independent equations containing them. How do we solve this quandary? We could calculate weights based on
book values with the understanding that book values would greatly distort our results. Or, we could base or weight
calculations on observed market values of debt and equity, but this approach has two flaws. First, in doing so, we implicitly
acknowledge that observed market values represent fair market values; which, of course, defeats the purpose of the
valuation exercise. Second, market values fluctuate so wildly, that for all practical matters, this approach is essentially
unpalatable.
38

The graph below shows the heuristically estimated cost of equity and the implied wacc when there is high tolerance for risk.
note that the cost of debt and the cost of equity increase only so slightly with leverage. The weighted cost of capital is
almost flat, decreasing by only a percentage point or so as total debt ratios approaches 100%.
30.00%
Cost of equity, cost of borrow ing and implied hurdle rate when there is high tolerance for risk
20.00%
10.00%
0.00%
Cost of debt
Cost of equity
Implied wacc
-10.00%
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
Market value of equity, debt and total firm value as a function of leverage when there is high tolerance for risk
5000
4500
4000
3500
3000
$
2500
2000
1500
1000
500
0
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
MV(Debt)
MV equity
Total firm value
39

Accordingly, the total market value of the firm is relatively flat, edging up as total debt ratio approaches 100%. But the real
story is captured by return on equity. As financial leverage approaches 100%, ROE literally skyrockets. This is something
that all shareholders want to hear - and partially explains the reckless behavior usually seen towards the end of a bull run.
600.00%
ROE as a function of leverage when there is high tolerance for risk
500.00%
400.00%
ROE
300.00%
ROE
200.00%
100.00%
0.00%
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
These numbers tell any manager that debt is good; pushing the borrowing envelope to the limit is only making everyone
better-off. Total market value of the firm remains more or less the same, regardless of how much debt you stack up; it might
even go up if creditors continue to lend you money at good rates. Shareholders, on the other hand, are in heaven. The more
you borrow the higher their return. Things can only get better, as long as the market remains exuberant and optimistic.
40

Borrowing with low tolerance for risk
It is always the case that after sun there comes rain or even snow. Bull markets always end when investors and managers
become overly infatuated with themselves and part company with common sense and basic prudence. Greed suddenly turns
into visceral fear. As markets tank and bankruptcies pile up, the cost of borrowing even modest amounts becomes
prohibitive, unless firm's creditworthiness has the resilience of Teflon. The spread between investment-grade and
speculative credit widens into a precipice. It is not only the cost of debt that is affected, however.
Revenues: When borrowing with a low tolerance for risk, the investment decisions of the firm are not be same as in the case
when there is no debt. Mangers probably choose lower risk projects that will be viewed as safe by creditors. At higher levels
of indebtedness, the firm is starting to lose revenue as the management and marketing becomes strained and less focused,
and some customers start to avoid the product or service; nobody wants to be stuck with a product for which warranty and
service could vanish.
Costs: At higher levels of indebtedness, the firm struggles to keep its best employees, morale is lower, suppliers are
reluctant to sell to a company that might not be able to pay back, and management becomes unfocused.
Borrowing costs: The firm faces a very steep cost of borrowing the more debt it has. Banks would require a larger interest
for more indebted firms, to compensate for the higher probability of default. At some very high levels of leverage, the bank,
or the creditors would not be willing to lend at any rate. Period.
Tax rates: Tax rates are progressive. This means higher income puts the firm in higher tax brackets. It also means that lower
income is associated with lower tax brackets.
Toy Inc. as a cash cow: Revenues, costs, cost of borrowing, and tax rates as a function of leverage when there is a very low tolerance for risk.
Revenues Costs Total debt ratio Interest rate Expected interest Tax rate
$5,000.00 $3,500.00 0.00% 4.25% $0.00 34.00%
$5,000.00 $3,500.00 10.00% 4.25% $14.88 34.00%
$5,000.00 $3,500.00 15.00% 6.00% $31.50 34.00%
$5,000.00 $3,500.00 20.00% 6.00% $42.00 34.00%
$5,000.00 $3,500.00 25.00% 6.00% $52.50 34.00%
$5,000.00 $3,500.00 30.00% 10.00% $105.00 27.20%
$5,000.00 $3,500.00 35.00% 10.00% $122.50 27.20%
$5,000.00 $3,500.00 40.00% 10.00% $140.00 27.20%
$5,000.00 $3,500.00 45.00% 15.00% $236.25 17.00%
$4,901.96 $3,500.00 50.00% 15.00% $262.50 17.00%
$4,892.37 $3,500.00 55.00% 15.00% $288.75 17.00%
$4,882.81 $3,500.00 60.00% 20.00% $420.00 0.00%
$4,873.29 $4,182.50 65.00% 20.00% $455.00 0.00%
$4,863.81 $4,235.00 70.00% 20.00% $490.00 0.00%
$4,854.37 $4,287.50 75.00% 25.00% $656.25 0.00%
$4,844.96 $4,340.00 80.00% 25.00% $700.00 0.00%
$4,835.59 $4,392.50 85.00% 30.00% $892.50 0.00%
$4,826.25 $4,445.00 90.00% 30.00% $945.00 0.00%
$4,816.96 $4,497.50 95.00% 50.00% $1,662.50 0.00%
$4,809.54 $4,539.50 99.00% 55.00% $1,905.75 0.00%
$4,807.69 $4,550.00 100.00% n/a n/a 0.00%
41

Cost and revenues, as a function of leverage when there is very low tolerance for risk
$6,000.00
$5,000.00
$4,000.00
$3,000.00
Revenues
Costs
$2,000.00
$1,000.00
$0.00
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
100.00%
90.00%
80.00%
Cost of borrowing and taxes as a function of leverage
when there is a very low tolerance for risk
70.00%
60.00%
Interest rate
Tax rate
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
42

Toy Inc. at 65% debt when there is very low tolerance for risk
Before drawing some more general conclusions about the cost of capital and market values, it would be interesting to
evaluate Toy Inc.'s financial standing at some higher level of indebtedness. Let us first consider the case of 65% total debt
ratio, and then the case of 90% total debt ratio.
Pro-forma income statement of Toy Inc. at 65% debt when there is very low tolerance for risk
Today
Next year
Sales $4,873.29 $4,873.29
(Costs) $4,182.50 $4,182.50
(Depreciation) $1,000.00 $1,000.00
EBIT -$309.21 -$309.21
(Interest) $682.50 $682.50
EBT -$991.71 -$991.71
(Tax) $0.00 $0.00
Net income -$991.71 -$991.71
Addition to RE -$991.71 -$991.71
Dividend $0.00 $0.00
Pro-forma balance sheet of Toy Inc. at 65% debt when there is very low tolerance for risk
Today Next year Today Next year
Cash $100.00 $108.29 A/P $0.00 $0.00
Inventory $500.00 $500.00 N/P $0.00 $0.00
A/R $400.00 $400.00 Current liabilities $0.00 $0.00
Current assets $1,000.00 $1,008.29
Long-term debt $2,275.00 $2,275.00
Gross fixed
assets
$3,000.00 $3,000.00 Other long-term $0.00 $0.00
Depreciation $1,000.00 $2,000.00 Outstanding shares $2,216.71 $2,216.71
Net fixed assets $2,000.00 $1,000.00 Retained earnings -$991.71 -$1,983.42
Other assets $500.00 $500.00 Owner's equity $1,225.00 $233.29
Total assets $3,500.00 $2,508.29 Total L&E $3,500.00 $2,508.29
43

Ratio analysis of Toy Inc. at 65% debt when there is very low tolerance for risk
Today
Next year
D/E 1.86 9.75
Total debt ratio 0.65 0.91
LT debt ratio 0.65 0.91
TIE -0.45 -0.45
Cash coverage 1.01 1.01
Profit margin -20.35% -20.35%
ROA -28.33% -39.54%
ROE -80.96% -425.10%
Dividend per share $0.00 $0.00
EPS -$9.92 -$9.92
Book value per share $12.25 $2.33
Dividend yield ? ?
Cash flow of Toy Inc. at 65% debt when there is very low tolerance for risk
Today
Next year
OCF $690.79 $690.79
Net Capital Spending $0.00 $0.00
Increase in NWC -$8.29 -$8.29
Interest tax shield $0.00 $0.00
CF from assets $682.50 $682.50
CF to creditors $682.50 $682.50
CF to shareholders $0.00 $0.00
CF from assets $682.50 $682.50
At 65% total debt ratio, Toy Inc. pays an average of 20% interest on its debt. The company barely has enough money to
make interest payments. A modest decrease in sales would most likely put the company in default. Because taxable income
is in the red, it pays no tax on profit. There is nothing left to pay the shareholders.
44

Toy Inc. at 90% debt when there is very low tolerance for risk
Pro-forma income statement of Toy Inc. at 90% debt when there is very low tolerance for risk
Today
Next year
Sales $4,826.25 $4,826.25
(Costs) $4,445.00 $4,445.00
(Depreciation) $1,000.00 $1,000.00
EBIT -$618.75 -$618.75
(Interest) $945.00 $945.00
EBT -$1,563.75 -$1,563.75
(Tax) $0.00 $0.00
Net income -$1,563.75 -$1,563.75
Addition to RE -$1,563.75 -$1,563.75
Dividend $0.00 $0.00
Pro-forma balance sheet of Toy Inc. at 90% debt when there is very low tolerance for risk
Today Next year Today Next year
Cash $100.00 $0.00 A/P $0.00 $0.00
Inventory $500.00 $500.00 N/P $0.00 $0.00
A/R $400.00 $400.00 Current liabilities $0.00 $0.00
Current assets $1,000.00 $900.00
Long-term debt $3,150.00 $3,150.00
Gross fixed assets $3,000.00 $3,000.00 Other long-term $0.00 $0.00
Depreciation $1,000.00 $2,000.00 Outstanding shares $1,913.75 $1,913.75
Net fixed assets $2,000.00 $1,000.00 Retained earnings -$1,563.75 -$3,127.50
Other assets $500.00 $500.00 Owner's equity $350.00 -$1,213.75
Total assets $3,500.00 $2,400.00 Total L&E $3,500.00 $1,936.25
At 90% total debt ratio, there is not enough cash to cover the $945 interest payment. The firm is in default, and will be again
in default next year. The creditors will most likely trigger bankruptcy.
45

Capital structure and cash flows when there is very low tolerance for risk
A summary of cost of capital and cash flows is presented below. Notice how interest payments increase with total debt ratio
to the point where the firm becomes incapable of making interest payments. From that point on Toy Inc. is in default. Its
cash flow are crashing along with its growing inability to meet its obligations.
Toy Inc. as a cash cow: Cash flows as a function of leverage when there is very low tolerance for risk
Total debt ratio Interest rate $interest Tax rate
Debt tax
shield
All-equity cash
flow
Total cash flow
CF to
shareholders
CF to creditors
0.00% 4.25% $0.00 34.00% $0.00 $330.00 $330.00 $330.00 $0.00
10.00% 4.25% $14.88 34.00% $5.06 $330.00 $335.06 $320.18 $14.88
15.00% 6.00% $31.50 34.00% $10.71 $330.00 $340.71 $309.21 $31.50
20.00% 6.00% $42.00 34.00% $14.28 $330.00 $344.28 $302.28 $42.00
25.00% 6.00% $52.50 34.00% $17.85 $330.00 $347.85 $295.35 $52.50
30.00% 10.00% $105.00 27.20% $28.56 $330.00 $392.56 $287.56 $105.00
35.00% 10.00% $122.50 27.20% $33.32 $330.00 $397.32 $274.82 $122.50
40.00% 10.00% $140.00 27.20% $38.08 $330.00 $402.08 $262.08 $140.00
45.00% 15.00% $236.25 17.00% $40.16 $330.00 $455.16 $218.91 $236.25
50.00% 15.00% $262.50 17.00% $44.63 $330.00 $378.25 $115.75 $262.50
55.00% 15.00% $288.75 17.00% $49.09 $330.00 $374.75 $86.00 $288.75
60.00% 20.00% $420.00 0.00% $0.00 $330.00 $420.00 $0.00 $420.00
65.00% 20.00% $455.00 0.00% $0.00 $330.00 $455.00 $0.00 $455.00
70.00% 20.00% $490.00 0.00% $0.00 $330.00 $490.00 $0.00 $490.00
75.00% 25.00% $656.25 0.00% $0.00 $330.00 $566.87 $0.00 $566.87 DEFAULT
80.00% 25.00% $700.00 0.00% $0.00 $330.00 $504.96 $0.00 $504.96 DEFAULT
85.00% 30.00% $892.50 0.00% $0.00 $330.00 $443.09 $0.00 $443.09 DEFAULT
90.00% 30.00% $945.00 0.00% $0.00 $330.00 $381.25 $0.00 $381.25 DEFAULT
95.00% 50.00% $1,662.50 0.00% $0.00 $330.00 $319.46 $0.00 $319.46 DEFAULT
99.00% 55.00% $1,905.75 0.00% $0.00 $330.00 $270.04 $0.00 $270.04 DEFAULT
100.00% 1000.00% $35,000.00 0.00% $0.00 $330.00 $257.69 $0.00 $257.69 DEFAULT
46

Toy Inc. as a cash cow : Total cash flow as a function of leverage when there is very low tolerance for risk
600
500
400
$
300
DE FA U LT
All-equity cash flow
Total cash flow
200
100
0
10.00%
Total debt ratio
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
99.00%
47

Valuation of Toy Inc. when there is very low tolerance for risk
The market value of Toy Inc. mirrors the trajectory of its cash flows and cost of capital.
Total debt
ratio
Toy Inc. as a cash cow: Cost of equity, cost of borrowing, and present values as a function of leverage when there is very low tolerance for risk
Total cash
flow
CF to
shareholders
CF to
creditors
Cost of
debt
PV(Debt) Cost of equity PV(equity)
Total firm
value
Calculated
weight of
debt
Implied
hurdle rate
0.00% $330.00 $330.00 $0.00 4.25% $0.00 9.43% $3,499.47 $3,499.47 0.00% 9.43% 0.00%
10.00% $335.06 $320.18 $14.88 4.25% $350.00 9.83% $3,257.20 $3,607.20 10.75% 9.29% 9.70%
Implied
weight of
debt
15.00% $340.71 $309.21 $31.50 6.00% $525.00 11.78% $2,624.87 $3,149.87 20.00% 10.82% 16.67%
20.00% $344.28 $302.28 $42.00 6.00% $700.00 11.98% $2,523.21 $3,223.21 27.74% 10.68% 21.72%
25.00% $347.85 $295.35 $52.50 6.00% $875.00 12.18% $2,424.88 $3,299.88 36.08% 10.54% 26.52%
30.00% $392.56 $287.56 $105.00 10.00% $1,050.00 16.38% $1,755.56 $2,805.56 59.81% 13.99% 37.43%
35.00% $397.32 $274.82 $122.50 10.00% $1,225.00 16.58% $1,657.54 $2,882.54 73.90% 13.78% 42.50%
40.00% $402.08 $262.08 $140.00 10.00% $1,400.00 16.78% $1,561.86 $2,961.86 89.64% 13.58% 47.27%
45.00% $455.16 $218.91 $236.25 15.00% $1,575.00 21.98% $995.96 $2,570.96 158.14% 17.70% 61.26%
50.00% $378.25 $115.75 $262.50 15.00% $1,750.00 22.18% $521.88 $2,271.88 335.33% 16.65% 77.03%
55.00% $374.75 $86.00 $288.75 15.00% $1,925.00 22.38% $384.28 $2,309.28 500.93% 16.23% 83.36%
60.00% $420.00 $0.00 $420.00 20.00% $2,100.00 27.58% $0.00 $2,100.00 0.00% 20.00% 100.00%
65.00% $455.00 $0.00 $455.00 20.00% $2,275.00 27.78% $0.00 $2,275.00 0.00% 20.00% 100.00%
70.00% $490.00 $0.00 $490.00 20.00% $2,450.00 27.98% $0.00 $2,450.00 0.00% 20.00% 100.00%
75.00% $566.87 $0.00 $566.87 25.00% $2,267.48 33.18% $0.00 $2,267.48 0.00% 25.00% 100.00%
80.00% $504.96 $0.00 $504.96 25.00% $2,019.84 33.38% $0.00 $2,019.84 0.00% 25.00% 100.00%
85.00% $443.09 $0.00 $443.09 30.00% $1,476.97 38.58% $0.00 $1,476.97 0.00% 30.00% 100.00%
90.00% $381.25 $0.00 $381.25 30.00% $1,270.85 38.78% $0.00 $1,270.85 0.00% 30.00% 100.00%
95.00% $319.46 $0.00 $319.46 50.00% $638.91 58.98% $0.00 $638.91 0.00% 50.00% 100.00%
99.00% $270.04 $0.00 $270.04 55.00% $490.99 64.14% $0.00 $490.99 0.00% 55.00% 100.00%
100.00% $257.69 $0.00 $257.69 1000.00% $25.77 1009.18% $0.00 $25.77 0.00% 1000.00% 100.00%
48

Cost of equity, cost of borrowing and implied hurdle (wacc) rate when there is very low tolerance for risk
150.00%
140.00%
130.00%
120.00%
110.00%
100.00%
90.00%
80.00%
70.00%
60.00%
DE FA U LT
Cost of debt
Cost of equity
Implied wacc
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
The cost of borrowing, cost of equity, and wacc skyrocket as total debt ratio approaches 100%. At the same time, the market
value of equity drops to virtually zero, followed by total market value.
49

At close to 100% debt, even outstanding debt is worthless; not only Toy Inc. is not able to meet its obligation, but also it
looks more likely that liquidation would bring very little to its creditors, not to mention its shareholders.
4000
Market value of equity, debt and total firm value as a function of leverage when there is a very low tolerance for risk
3500
3000
2500
$
2000
1500
DE FA U LT
MV(Debt)
MV equity
Total firm value
1000
500
0
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
14.00%
ROE as a function of leverage when there is a very low tolerance for risk
12.00%
10.00%
8.00%
ROE
6.00%
ROE
4.00%
2.00%
0.00%
10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 99.00%
0.00% 15.00% 25.00% 35.00% 45.00% 55.00% 65.00% 75.00% 85.00% 95.00% 100.00%
Total debt ratio
50

Afterword
We ask a legitimate question: does the capital structure of a firm have a significant and persistent effect on its market
valuation? Can one devise a financial policy exclusively based on financing choices that would increase the total market
value of the firm and/or make shareholders better off? Beyond countless theoretical ramifications, this questions has serious
practical implications: how should we finance the assets of the firm?
There is some evidence suggesting debt matters: it is well documented that the announcement of equity issues are generally
met with a negative price reaction. On the other hand, debt issues, especially bank loans are meet with a weak positive
reaction, or equanimity at worst, suggesting that there might be a pecking order with respect to external financing. Since
equity issues are bad news to some extent, managers would prefer to minimize the cost of adverse selection by issuing debt
first.
On a different level, there is a unequivocal relationship between the level of debt and the likelihood of bankruptcy.
Unquestionably, a good proportion of firms that go bankrupt do so because they cannot discharge of their financial
obligation in due time. Plain, old-fashioned common sense suggests that too much debt is ruinous because it can lead to
bankruptcy.
What are we to make of all this? How should we combine statistical evidence with practical insights? We start by
identifying all the potential ways in which debt affects the variables driving the valuation of the firm. These variables are
represented by cash flows and discount rates. Cash flows to shareholders discounted using the cost of equity approximate
the fair market value of equity; and cash flows to creditors discounted at the cost of debt approximate the fair market value
of firm's debt. Together, the fair market value of equity and the fair market value of debt combine into the total market
value of the firm.
It is a matter of fact that debt increases the variability of cash flows to shareholders. When the possibility of bankruptcy is
taken into account, it can be shown that total cash flows become more volatile as well. Because it adds a new risk dimension
to the already existing business risk, debt is in fact rising the risk premium required by shareholders as a compensation for
more risk. On the other hand, debt is cheaper than equity; so, it is legitimate to ask what happens when we move from a
capital structure dominated by moderately priced equity to one dominated by cheaper debt, in which the remaining equity
portion has become more expensive. We intuitively grasp the notion that a smaller proportion of more and more expensive
equity might be offset by a larger and larger proportion of cheaper debt. But what is the net effect? The only way to answer
this question is to keep ALL other variables constant, and vary the level of debt in order to quantify its effect. Unfortunately
this is a rather utopic, if not naïve approach. All variables are linked together and move together. It is not realistic to think
that changes in the level of debt will leave sales and costs unaffected. When the total risk of the firm is going up, the
investment behavior of the management undergoes changes: some are more subtle; others are not so subtle. At very high
levels of debt, when the firm is on the verge of financial distress, things begin to unravel: management becomes unfocused,
morale slips, sales sink, and costs go up. The separation between the investment decision and the financing decision is not
tenable in practice.
The cost of equity varies with financial leverage, but in spite of commendable efforts aimed at turning finance into a
rigorous science, we are not able to quantify the relationship between risk and required return any better than we can
measure the relationship between virtue and salvation. All the models we are able to generate are indeterminate: not only
there are more unknown variables to estimate than there are equations, but also many inputs into these models are
unobservable quantities. The best solution is a heuristic approach in which we take the cost of equity to be larger than the
cost of debt by some arbitrary quantity.
The analysis of firm value as a function of leverage largely depends on the mood of the market. When the market is overly
optimistic and tolerates higher levels of financial risk - either because investors have distorted perceptions, underestimate
the probability of large losses, or are overconfident - the relationship between leverage and total firm value is approximately
flat, increasing only so slightly as leverage approaches 100%. The big winners are the shareholders who see their returns fly
off the charts.
When the market is possessed by fear, the cost of borrowing skyrockets as leverage increases. For moderate amounts of
debt, total market value goes up indeed, but beyond a certain level, under the burden of higher and higher interest payments,
lower sales, and higher costs, the firm becomes financially distressed and its total value plummets to nothing. At higher
51

levels of debt, shareholders are totally wiped out.
We strive to provide a normative account of debt financing, but so far we have largely managed to come up only with a
description of what happens when this or that happens. What are the practical implications of capital structure policy?
(i) The cost of equity is always larger than the cost of borrowing. As the marginal cost of borrowing goes up, so does the
cost of equity. The weighted average cost of capital is somewhere in between the cost of debt and the cost of equity.
(ii) Total firm value does vary with leverage; the extent and the nature of this relationship is fuzzy and complex, depending
on the economic context in which the firm operates.
(iii) The capital structure of a firm is often a residual variable, driven by the mood of the market, past profit and losses, and
past financing decisions.
(iv) To minimize the cost of borrowing, firms should match their long-term borrowing with the expected economic life of
tangible assets - these assets can be also used as collateral. The trouble is, during a recession the price of all assets is lower,
hence debt becomes even riskier because the market value of collateral is sinking as well.
(v) Too much debt is always perilous; of course, what is too much remains a business judgment, dependent on the context in
which the firm operates.
52