Direct or Indirect—CAPM or WACC?

BY JAMES W. KUKULL

Taking the Temperature of Health Care Valuations” (JofA, Oct.01, page 79) indicates the capital asset pricing model (CAPM) was used to derive the discount rate, which resulted in an “enterprise value” that included both the value of equity capital and debt capital. I believe this is incorrect.

The purpose of the appraisal in the article evidently is to estimate the company’s equity value at the appraisal date. Equity can be valued under the income approach either directly or indirectly. When the indirect approach is used, the value of invested capital (equity and interest-bearing debt) is computed, and then the value of the interest-bearing debt is subtracted to arrive at the equity value.

The income stream used in the direct method is after subtracting interest expense. The income stream for the indirect approach is before subtracting interest expense because interest expense is the return to the debt holders rather than the equity holders. In the indirect approach, the income stream includes the return for both the debt holders and equity shareholders.

The methodology used in the article is CAPM. By applying the CAPM, an appraiser will arrive at a discount rate for equity, which should be used in the direct approach to valuation.

The article appears to apply this rate to the cash flow after interest expense has been subtracted (the direct approach) to derive “enterprise value.” Then, the value of interest-bearing debt is subtracted to arrive at the value of stockholder’s equity. This is incorrect since the discount rate and the cash flow stream being discounted apparently arrive directly at the value of equity.

The article should have derived the discount rate by use of the weighted average cost of capital (WACC) if the indirect method was to be used, and the income stream should have been before interest expense was subtracted. The WACC is the cost of equity capital times its market weighting plus the cost of debt capital times its market weighting.

For example, if debt and equity are weighted 50% each and the cost of debt is 10% and the cost of equity is 24.8% and long-term growth is 3%, then the WACC is 17.4% (the discount rate) and the capitalization rate is 14.4% (the discount rate minus growth).

The article apparently uses a capitalization rate that directly values equity capital and then incorrectly treats this value as though it was total invested capital (stockholder’s equity plus interest-bearing debt). By subtracting the interest-bearing debt from the initial amount, the value of a stockholder’s equity is understated.

James W. Kukull, CPA, ASA
Kirkland, Washington

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