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Estimating Beta

In order to use the CAPM to calculate ROA or ROE, one needs to estimate the asset (unlevered) beta or the equity (levered) beta of the firm. The beta that often is reported for a stock is the levered beta for the firm. When estimating a beta for a particular line of business, it is better to use the beta of an existing firm in that exact line of business (a pure play) rather than an average beta of several firms in similar lines of business. Expressing the levered beta, unlevered beta, and debt beta in terms of the covariance of their corresponding returns with that of the market, one can derive an expression relating the three betas. This relationship between the betas is:

betalevered = betaunlevered (1 + (1– t) D/E)– betadebt(1 – t) D/E

betaunlevered = (betalevered + betadebt(1 – t) D/E) / (1 + (1– t) D/E)

The debt beta can be estimated using CAPM given the risk-free rate, bond yield, and market risk premium.

Unlevered Free Cash Flows

To value the operations of the firm using a discounted cash flow model, the unlevered free cash flow is used. The unlevered free cash flow represents the cash generated by the firm’s operations and is the cash that is free to be paid to stock and bond holders after all other operating cash outlays have been performed.

Terminal Value

The value of the firm at the end of the last year for which unique cash flows are projected is known as the terminal value. The terminal value is important because it can represent 50% or more of the total value of the firm.

Three Discounted Cash Flow Methods for Valuing Levered Assets

APV (Adjusted Present Value) Method

The APV approach first performs the valuation under an unlevered all-equity

assumption, then adjusts this value for the effect of the interest tax shield:

VL = VU + PVITS

where VL = value if levered;

VU = value if financed 100% with equity;

PVITS = present value of interest tax shield.

The unlevered value is found by discounting the unlevered free cash flow at the required return on assets. The present value of the interest tax shield is found by discounting the interest tax shield savings at the required return on debt, rD.

The APV method is useful for valuing firms with a changing capital structure since the return on assets is independent of capital structure. For example, in a leveraged buyout, the debt to equity ratio gradually declines, so the required ROE and the WACC change as the lenders are repaid. However, when calculating the terminal value it may be appropriate to assume a stable capital structure, so in calculating the terminal value in a leveraged buyout situation the WACC method may be a better approach.

Flows to Equity Method

The flows to equity method sums the NPV of the cash flows to equity and debt.

Then,

VL = E + D

WACC Method

The WACC method discounts the unlevered free cash flow at the weighted average cost of capital to arrive at the levered value of the firm.

Cash Flows to Debt and Equity

When calculating the amount of cash flowing to debt and equity holders, it is not appropriate to use the unlevered free cash flows because these cash flows do not reflect the tax savings from the interest paid. Starting with the UFCF, add back the taxes saved to obtain the total amount of cash available to suppliers of capital.

Hurdle Price

At times a firm may wish to know at what price it would have to sell its product for a particular investment to have a positive NPV. To determine this price, express the operating cash flow in terms of price. Write out the expression for the NPV using the appropriate discount rate. For the longer operating period, one can calculate an annuity factor to multiply by the operating cash flow expression. Solve the expression for the cash flow that would result in an NPV of zero. Since the operating cash flow was written in terms of price, the price now can be found.

Debt Valuation

While debt may be issued at a particular face value and coupon rate, the debt value changes as market interest rates change. The debt can be valued by determining the present value of the cash flows, discounting the coupon payments at the market rate of interest for debt of the same duration and rating. The final period’s cash flow will include the final coupon payment and the face value of the bond.

Optimal Capital Structure

The total value of a firm is the sum of the value of its equity and the value of its debt. The optimal capital structure is the amount of debt and equity that maximizes the value of the firm.

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