Consistent Valuation and Cost of Capital Expressions with Corporate and Personal Taxes

By Taggart, Robert A., Jr. | Financial Management, Autumn 1991 | Go to article overview

Consistent Valuation and Cost of Capital Expressions with Corporate and Personal Taxes


Taggart, Robert A., Jr., Financial Management


* The adjusted present value, adjusted discount rate and flows to equity valuation methods represent three different approaches to valuing firms and other assets.(1) If they are to be used interchangeably, all three methods should result in identical values for a given asset; achieving such consistency in practice can prove elusive for several reasons.

First, each method incorporates the asset's business risk and the tax effects of its financing mix in a different way, and each relies on a different cost of capital measure. It is thus necessary to understand how these measures are related to one another. Second, the interrelationships among different cost of capital measures are not unique. There are several distinct sets of valuation and cost of capital expressions, each derived under differing assumptions about the asset's cash flow and financing pattern and the applicable tax regime. Consistent valuation, of course, requires cost of capital expressions that are all based on the same assumptions. Finally, in many practical situations, it is cumbersome or even impossible to use all of the valuation methods. In such cases, they are not interchangeable, and the analyst should know which one is superior.

The potential for confusion resulting from this array of techniques and assumptions is heightened by the fragmented approach to the topic in textbooks and the literature. The literature has dealt most extensively with the case in which financing affects value only through corporate taxes.(2) Three distinct sets of cost of capital expressions have been derived for this case, each resting on a different assumption about the riskiness of future debt tax shields. For the case that includes both corporate and personal taxes, however, a complete set of analogous expressions has yet to be derived and differences in assumptions about the risk of debt tax shields have not received substantial emphasis.(3) The purpose of this paper is to fill that gap.

Section I describes the three valuation methods, and Section II surveys and summarizes existing results on valuation with corporate but not personal taxes. This includes two cases in which all future debt tax shields are known with certainty and two in which they are uncertain. Section III introduces personal taxes and derives cost of capital expressions for different assumptions about the risk of future debt tax shields. Section IV offers recommendations for choosing among the different valuation approaches, and Section V summarizes the principal findings.

I. Three Valuation Methods

All three basic valuation methods seek to discount after-corporate-tax cash flows at pre-investor-tax discount rates, but they make different adjustments for the effects of financing. Myers' [22] adjusted present value (APV) method calls for first computing a base-case value under the assumption of 100% equity financing, and then separately adding the present values of any costs and benefits from the actual financing package. The base-case value is calculated by discounting the asset's expected after-corporate-tax operating cash flows, [C.sub.n] for each period n at an all-equity, or unlevered, discount rate, r.(4)

The adjusted discount rate (ADR) method discounts expected operating cash flows, [C.sub.n], at a rate that reflects the asset's financing combination. Both the APV and ADR methods thus discount the same cash flows. However, the APV method adjusts for financing in one or more separate discounted cash flow terms, while the ADR method does so entirely in the discount rate.

Finally, the flows to equity (FTE) method calculates equity value directly by discounting cash flows to the equityholders at a cost of equity capital. The cash flows are in turn calculated by subtracting after-corporate-tax financing charges from the all-equity cash flows, [C.sub.n], and thus they represent actual cash flows to shareholders. By contrast, the cash flows used under the other two methods are hypothetical, all-equity cash flows. …

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