Session 1: The Cost of Capital
Laying the Foundation
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The essence of intrinsic value
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In intrinsic valuation, you value an asset based upon its intrinsic
characteristics.
For cash flow generating assets, the intrinsic value will be a function
of the magnitude of the expected cash flows on the asset over its
lifetime and the uncertainty about receiving those cash flows.
Discounted cash flow valuation is a tool for estimating intrinsic value,
where the expected value of an asset is written as the present value of
the expected cash flows on the asset, with either the cash flows or the
discount rate adjusted to reflect the risk.
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The two faces of discounted cash flow valuation
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The value of a risky asset can be estimated by discounting the expected cash
flows on the asset over its life at a risk-adjusted discount rate:
where the asset has a n-year life, E(CFt) is the expected cash flow in period t and r
is a discount rate that reflects the risk of the cash flows.
 Alternatively, we can replace the expected cash flows with the guaranteed
cash flows we would have accepted as an alternative (certainty equivalents)
and discount these at the riskfree rate:
where CE(CFt) is the certainty equivalent of E(CFt) and rf is the riskfree rate.
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Estimating Inputs: Discount Rates
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Critical ingredient in discounted cashflow valuation. Errors in estimating the
discount rate or mismatching cashflows and discount rates can lead to serious
errors in valuation.
At an intuitive level, the discount rate used should be consistent with both the
riskiness and the type of cashflow being discounted.
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Equity versus Firm: If the cash flows being discounted are cash flows to equity, the
appropriate discount rate is a cost of equity. If the cash flows are cash flows to the
firm, the appropriate discount rate is the cost of capital.
Currency: The currency in which the cash flows are estimated should also be the
currency in which the discount rate is estimated.
Nominal versus Real: If the cash flows being discounted are nominal cash flows
(i.e., reflect expected inflation), the discount rate should be nominal
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DCF Choices: Equity Valuation versus Firm Valuation
Firm Valuation: Value the entire business
Assets
Value of investments already
made by the company over it's
history. The value is updated to
reflect their current cash flow
potential.
Value of investments the
company is expected to take into
the future. This value rests on
perceptions of growth
opportunities.
Liabilities
Assets in Place
Debt
Lenders, both short and long
term, get first claim whatever
cash flow is generated by the
firm.
Growth Assets
Equity
Equity investors get whatever is
left over, after meeting the debt
obligations.
Equity valuation: Value just the
equity claim in the business
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Equity Valuation
Figure 5.5: Equity Valuation
Assets
Cash flows considered are
cashflows from assets,
after debt payments and
after making reinvestments
needed for future growth
Assets in Place
Growth Assets
Liabilities
Debt
Equity
Cost of equity is what
equity investors require,
given risk that they see
in their investments.
Discount rate reflects only the
cost of raising equity financing
Present value is value of just the equity claims on the firm
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The problem with estimating “cost of equity”
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Implicit vs Explicit cost: Unlike the cost of debt, which is an explicit
cost (you can see it as an interest rate on a current loan), the cost of
equity is implicit.
Multiple investors? If you have more than one equity investor, the
problem becomes even more complex, since each of the equity
investors can have different “required” rates of returns.
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With publicly traded companies, which have thousands of investors, the problem is
magnified, since these investors can range the spectrum from individuals to
institutions, with very different views on risk.
Even with solely owned private businesses, there are usually multiple potential
buyers with very different assessments of risk and cost of equity.
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The Marginal Investor
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While risk is usually defined in terms of the variance of actual returns around
an expected return, risk and return models in finance assume that the risk that
should be rewarded (and thus built into the discount rate) in valuation should
be the risk perceived by the marginal investor in the investment.
If you assume that the marginal investor is well diversified, and that the only
risk that he or she perceives in an investment is risk that cannot be diversified
away (i.e, market or non-diversifiable risk), the only risk built into the cost of
equity should be the non-diversifiable risk. The standard risk and return
models in finance (the CAPM, Arbitrage pricing model and most Multi-factor
models) make this assumption. Thus, the beta or betas in these models
measure only the non-diversifiable risk in an equity investment.
If the marginal investor is not well diversified, the cost of equity will
incorporate the risk that he or she perceives in the equity, even if that risk is
diversifiable risk.
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Firm Valuation
Figure 5.6: Firm Valuation
Assets
Cash flows considered are
cashflows from assets,
prior to any debt payments
but after firm has
reinvested to create growth
assets
Assets in Place
Growth Assets
Liabilities
Debt
Equity
Discount rate reflects the cost
of raising both debt and equity
financing, in proportion to their
use
The cost of capital is a
composite cost of all
financing, with the cost of
debt reflecting the default
risk that lenders perceive
in the firm.
Present value is value of the entire firm, and reflects the value of
all claims on the firm.
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The cost of debt
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What it is: The cost of debt is the interest rate, at which a firm can
borrow money, long term, today. It is not the rate at which you
borrowed money at in the past. To get to the cost of debt, you will start
with a risk free rate and add a default spread, to reflect the credit risk
in the borrowing firm.
Tax advantage: To the extent that the tax law favors borrowing (by
allowing interest expenses to be tax deductible), the after-tax cost of
borrowing will be lower than the pre-tax cost of borrowing.
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Cost of capital: Fundamental Propositions
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Vary across businesses: The cost of capital should vary across
businesses, largely as a function of the risk of the businesses and the
financing mix chosen to fund these businesses.
For the same business, vary across investors: The cost of capital can
vary across investors in the same business, depending upon their risk
aversion and how diversified they are.
For the same business, vary across time: The cost of capital will vary
over time, as the fundamentals of a business change.
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