The Cost of Capital
Where do Firms Get Money?
Self Financing (using internal cash flow)
Accounts for 80% (avg.) of financing in the U.S.
Difficult for start-up companies
Borrowing from banks or issuing bonds
Sharing ownership by issuing stock
Net new issues of these securities accounts for the
other 20% on average
About 80% of what is raised or generated and
retained is used for capital spending and the rest
for working capital and “other” uses
Where Do Small Businesses
0 10 20 30 40 50 60
Fraction of Funds Raised (%)
Source: 1987 SBA survey of firms with less than $500,000 in assets.
A Life Cycle of Financing
Very small, no track record Small with growth potential Medium-sized Large with Track record
Inside seed money
Short Debt Short-term commercial loans Commercial paper
Intermediate-term commercial loans Medium-term
Debt Mezzanine Finance Private Placements
Outside Equity Venture Capital Public Equity
Source: FRB Report on Private Placements, Rea et. al., 1993
The Capital Structure Question:
How should a firm structure the left hand side
of its balance sheet?
Debt vs. Equity – the choice for our purposes.
We have seen how to do capital budgeting
when the firm has debt in its capital structure.
However, we have not figured out how much
debt the firm should use.
Can the firm change shareholder value
through its financing decisions?
In particular, should the firm load up with „low
One possible answer:
It makes no difference!
Assume PCM: there are no differential taxes
and the firm‟s investment policy is unaffected
by how it finances its operations.
Both Modigliani and Miller won a Nobel Prize
The value of a firm with debt is, under these
circumstances, equal to the value of the same
firm without debt. MM Proposition I.
Since the assets are the same, regardless of
how they are financed, so are the expected
cash flows and the asset risks (asset betas)
of equivalent “levered” and “unlevered” firms.
Irrelevance Proposition II
What this means is that the expected return
on equity rises with leverage according to:
(where, B/S = leverage ratio -- market value
of debt over market value of equity, r
denotes expected return or appropriate
rEquity rAssets (rAssets rDebt )
I will try to use r0 not rA for consistency with
MM Proposition II
Why does the expected return on equity rise?
The SML tells us that the expected return on an
asset changes only when what characteristic of
the asset changes?
The beta of a portfolio is the weighted sum of the
0 S B
Rearrange this to find:
S 0 0 B
MM Proposition II with No Corporate
Taxes: Another View
Cost of capital: r (%)
rS r0 (r0 rB )
r0 rW ACC rB rS
What About The Tax
Deductibility of Interest?
n Interest is tax deductible (dividends are not).
n A valuable “debt tax shield” is created by
substituting payments of interest for payments of
dividends, i.e. debt financing for equity financing.
n Modigliani and Miller also showed that if the only
change in their analysis is an acknowledgement of
the US corporate tax structure, then:
n The value of a levered firm is: VL = VU + TcB
the value of an equivalent unlevered firm PLUS
the value of the tax shields generated by the
use of debt.
n Firm Value rises with additional borrowing! Why?
Proposition II with Taxes
When we take the tax deductibility of
interest payments into account the
equations we presented must change:
rWACC rS rB (1 Tc )
rS r0 (1 Tc )(r0 rB )
S 0 (1 Tc )( 0 B )
Cost of capital: r B
(%) rS r0 (r0 rB )
rS r0 (1 TC ) (r0 rB )
rW ACC rB (1 TC ) rS
BSL B SL
Limits to The Use of Debt
Given the treatment the U. S. corporate tax
code gives to interest payments versus
dividend payments, firms have a big incentive
to use debt financing.
Under the MM assumptions with corporate
taxes the argument goes to extremes and the
message becomes: firms should use 100%
What costs are associated with the use of
Bankruptcy costs and/or costs of
Costs associated with a trial (expert witnesses)
Reduced effectiveness in the market.
Lower value of service contracts, warranties.
Decreased willingness of suppliers to provide
Loss of value of intangible assets--e.g., patents.
Agency Costs of Debt
When bankruptcy is likely incentives may be altered.
Big Trouble Corp. (BTC) owes its creditors $5 million, due
in six months.
BTC has liquidated its assets because it could not operate
profitably. Its remaining asset is $1 million cash.
Big Bill, the lone shareholder and general manager is
considering two possible investments.
• (1) Buy six month T-bills to earn 3% interest.
• (2) Go to Vegas and wager the entire $1 million on a single
spin of the roulette wheel.
Why might Bill consider the second “investment”?
Would he have considered it in the absence of high
Slight Trouble Corp. (STC) has a small but
significant chance of bankruptcy in the next few
years. Its debt is trading far below par.
Managers are evaluating an investment project
that will cost $1 million to undertake. The
alternative is to pay $1 million out as dividends.
While the NPV of the project is positive it may
be that the shareholders are better off with the
dividend than if the project is taken.
The reason is that while shareholders pay all
the costs of the project, they will have to share
its value with bondholders, the added value will
raise bond prices as well as stock prices.
Disciplinary Power of Debt
“On the other hand” as economists are fond of
saying, debt can be a disciplinary device.
It is well recognized that an owner works harder
and makes better decisions than an employee.
This was an often cited justification for the LBO
wave of the mid 80‟s and early 90‟s.
The idea is that one of the most contentious
issues between managers and shareholders is
the payout of excess cash. Consider Hollinger
International and Conrad Black‟s behavior.
Debt allows manager to commit to the payout in
a way that cannot be accomplished with a
MM with Taxes and Costs of Financial Distress
Value of firm (V) Value of firm under
MM with corporate
Present value of tax taxes and debt
shield on debt
VL = VU + TCB
Maximum Present value of
firm value financial distress costs
V = Actual value of firm
VU = Value of firm with no debt
0 Debt (B)
Optimal amount of debt
Choosing an Amount of
The theory provides no clear formula (unlike NPV)
but the tradeoffs are clear; the benefits versus the
costs of debt.
The theory does tell us to use more debt if:
effective tax rates (without debt) are higher,
operating cash flows are more predictable,
tangible assets make up most of your asset base,
agency costs can be controlled by contracts.
A safe strategy might be to emulate the industry
average. After all these are the firms who have
survived. From there you make alterations as
your own situation dictates.
Leverage Ratios for
Building Construction 52.8
Hotels and Lodging 56.0
Air transport 47.7
Gold-Silver mining 42.2
Biological products 4.0
Source: Ibbotson Associates 2003
Pecking Order Theory says that there is no
optimal capital structure, just the
culmination of all your financing decisions.
Internally generated funds.
External Equity as a last resort.
Data shows that preferences such as these
are there but a subject of debate is whether
they are necessarily inconsistent with there
being an optimal capital structure.
Ralph‟s firm has been in the food processing business
for 10 years. It has maintained a conservative capital
structure financing 60% of its value with equity.
Ralph has recently considered investing in the IPO of
a start-up company that will develop and manufacture
internet infrastructure. In discussions with the start-
up‟s manager, Ralph‟s nephew, it is revealed that the
start-up will use either no or 20% debt financing.
For simplicity, assume the firm is expected to generate
free cash flow of $1M each year in perpetuity.
You have been called in to help identify an appropriate
cost of capital for evaluating this investment.
Currently Ralph‟s equity beta is estimated at
0.95. We cannot estimate the beta for this
private company (the start-up) directly but
we know that Cisco has an equity beta of
The risk free rate is 6% and the market risk
premium is 7%. The tax rate for all
corporations is 35%.
How can we approach determining the
appropriate discount rate?
Ralph‟s Dilemma cont…
Start with the following:
Assets S (1 T ) B Equity
We can reasonably assume that the asset
beta for Cisco will be a close estimate for
the asset beta for the start-up.
We know that the equity beta for Cisco is
1.92. What is Cisco‟s asset beta?
Ralph‟s Dilemma cont…
Now we know that the asset beta for the start-
up can be estimated at 1.92. What is the equity
We have two scenarios to consider, a debt to
value ratio of either 0% or 20%.
If it is zero, the equity beta equals the asset
beta or 1.92.
If it is 20%, we need to use:
B(1 TC ) .2(1 .35 )
Equity Assets 1 1.92 1 2.23
Ralph‟s Dilemma cont…
Now we need a weighted average cost of
For the case of no debt rS = rA = r0 = rWACC:
rS = 6% + 1.92(7%) = 19.44%.
With 20% debt:
rS = 6% + 2.23(7%) = 21.61.
rB = 6% (since we assumed the debt was riskless).
rWACC = 21.61%(.8) + 6%(1-.35)(.2) = 18.07%.
Why was I sure that I did something wrong when I
calculated the rWACC as 20.50% on the first try?
Using the $1M per year perpetual free
cash flow assumption the valuation of
this firm is easily done.
With no debt in the start-up firm‟s capital
structure its value is:
VNoDebt $5.14 M
With 20% debt:
V20% Debt $5.53 M
An Alternative Valuation
The Adjusted Present Value (APV):
Follows from the MM equation
VL = VU + TCB.
Take the value of the firm or project, if it
were unlevered, then add the value of
the debt tax shields (more completely
the additional effects of debt).
This can be a very useful approach to
valuation in some situations.
APV Versus WACC
The difference between these valuation
techniques lies in how we value the tax shields
associated with the use of debt financing.
In the WACC approach we use Free Cash Flow and a
discount rate (WACC) that is below the unlevered
cost of capital (r0). The lower discount rate inflates
the present value of the future free cash flows by just
enough to account for the value of the tax shields
associated with the chosen debt to equity ratio.
In the APV we value the Free Cash Flow at the
appropriate discount rate for an unlevered firm (r0)
which gives us the correct present value of the Free
Cash Flow. We then add the value of the tax shields
associated with the firm‟s use of debt financing.
APV – Example
To implement this approach we do two things.
First, find the value of the firm if it is unlevered.
Second, find the present value of the debt tax
shields that will be generated by the use of debt
The value of the unlevered firm, as before, is:
VNoDebt $5.14 M
With $1.1M in debt capital used by the start-up firm its
value would become:
VDebt VNoDebt Tc B
(0.35 )($ 1.1M )
$5.14 M $0.39 M $5.53 M
The Alternative Approach
The APV approach is most useful when
you know the dollar amount of debt that
will be used each year over the life of the
e.g., an LBO or other highly levered
The WACC approach is easier to use
when the firm has a target debt ratio that it
can reasonably be expected to maintain.