Aswath Damodaran1 Session 1: The Cost of Capital Laying the Foundation Aswath Damodaran

2 The essence of intrinsic value 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.

Aswath Damodaran3 The two faces of discounted cash flow valuation 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(CF t ) 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(CF t ) is the certainty equivalent of E(CF t ) and r f is the riskfree rate.

Aswath Damodaran4 Estimating Inputs: Discount Rates 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. 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

Aswath Damodaran5 DCF Choices: Equity Valuation versus Firm Valuation Equity valuation: Value just the equity claim in the business Firm Valuation: Value the entire business

Aswath Damodaran6 Equity Valuation Cost of equity is what equity investors require, given risk that they see in their investments.

Aswath Damodaran7 The problem with estimating “cost of equity” 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. 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.

Aswath Damodaran8 The Marginal Investor 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.

Aswath Damodaran9 Firm Valuation 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.

Aswath Damodaran10 The cost of debt 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.

Aswath Damodaran11 Cost of capital: Fundamental Propositions 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.