Peter Jennergren

Professional service firms are common in some areas, in particular auditing and law. They are organized as partnerships, private corporations, or public corporations. This paper discusses the first category of these three. When a partner leaves the partnership, her/his shares are redeemed. Two alternatives for redemption are at book value, the traditional alternative, or at fair market value. By means of a novel discounted dividends model that includes risk taking, it is shown that there may be an economic incentive for risk taking when the redemption value is equal to book value. There may also be an incentive for risk taking when the redemption value is equal to fair market value. However, the level of risk taking in the latter alternative is not higher than the level of risk taking in the former alternative. Switching from book value to fair market value as redemption value is hence suggested as one way to reduce client propensity for litigation. This paper’s incentive for risk taking in a professional partnership has apparently not been noted in the literature.

Depreciation methods are used for allocating acquisition costs of long-lived assets to individual years that benefit from those assets, e.g., in connection with product pricing and regulation of public utilities. The following depreciation methods are sometimes mentioned together in the literature: Nominal linear, real linear, nominal annuity, and real annuity. All are shown to be special cases of one generic formula. For that reason, they are referred to collectively as the linear and annuity class of depreciation methods. The members of this class are ranked (to the extent possible) by their book values. Such a ranking indicates the relative depreciation rates of the class members, and also relative savings due to tax-deductible depreciation. Two applications of members of the linear and annuity class are discussed, to product pricing in classical equilibrium theory, and to incentives for undertaking an investment project. The essential insight from this note is that it is meaningful to group the members of the linear and annuity class into one well-defined class of depreciation methods.

Traditional firm valuation discounts forecasted cash consequences that are understood as expected values under some scenario. It is not clear how, and to what extent, uncertainty is incorporated in the valuation. This article constructs a new valuation model where uncertainty, in particular bankruptcy risk, is explicitly included. Bankruptcy denotes a failure situation where a company ceases to operate and its assets are liquidated. At the end of each year, there is a jump to one of three possible states of the world at the end of the following year. A state is a combination of sales revenue for the firm being valued and return on the market index. The third state implies bankruptcy for the firm. The new model includes both the non-steady-state explicit forecast period and the steady-state post-horizon period and derives consistent values for the unlevered firm, the debt, the tax shields, the equity, and the levered firm. All discount rates, and the promised debt interest rate, are derived from certain basic parameters, using the CAPM. The model structure, in particular the manner in which sales revenue serves as driving variable, implies that one needs to perform only one discounting operation for each year, like in Fama (Journal of Financial Economics 5:3-24, 1977). A small annual bankruptcy probability is seen to lead to a noticeable value decrease. There is also a discussion of how to combine traditional firm valuation with inputs from the new valuation model, so as to take bankruptcy risk into account.

A team from McKinsey (Koller et al. 2010) recommended the value driver formula for continuing value. The idea is as follows: The company is almost in a steady state. However, the existing operations and the subsequent ones, referred to as growth projects, can be somewhat different. That is, the return on new invested capital (RONIC; refers to growth projects) can be lower than the return on invested capital (ROIC; refers to existing operations). Two weaknesses are associated with the McKinsey formula. Firstly, the only permissible case of RONIC < ROIC is where the working capital requirement is different between the growth projects and the existing operations. The usual Gordon formula then gives the same result, so the McKinsey formula is not necessary. Secondly, the implied split into existing operations and growth projects means that the former are valued under the unreasonable assumption of zero inflation. A more significant extended value driver formula is derived that rectifies these weaknesses.

Operating leases are quite important in some industries. There are two possible errors that should be avoided when valuing a company with operating leases. First, one should not neglect the implied lease debt. Such neglect distorts the calculation of free cash flow, required rate of return on the equity under partial debt financing, WACC, and residual equity value in the discounted cash flow model. Second, lease expense and implied lease debt should not be forecasted as constant, historical fractions of sales revenue in the (non-steady-state) explicit forecast period. This paper outlines an approximate procedure for handling operating leases in the discounted cash flow model. This procedure avoids the two possible errors that were mentioned.

In the abnormal earnings growth (AEG) valuation model of Ohlson and Juettner-Nauroth (2005), there is one (constant) discount rate and no company or personal taxes. The parsimonious model specification focuses on bottom-line earnings and growth in abnormal bottom-line earnings and can hence be viewed as an equity-level model. Disregarding taxes, we first extend this model to a firm-level model based on operating earnings and growth in abnormal operating earnings, allowing for two exogenous discount rates: the required rate of return under all-equity financing and the borrowing rate. Dividend policy irrelevance holds for this model. Using the firm-level model as a stepping stone, a new equity-level model is developed where dividends are discounted at a leverage-dependent varying cost of equity capital. Dividend policy irrelevance holds for this model, too. Finally, the firm-level and equity-level models are extended to a situation with company and personal taxes. Dividend policy irrelevance then no longer holds, except in the tax-neutrality case in Miller (1977).

Loan subsidies are sometimes offered in connection with investment projects. It is convenient to view such subsidies as financing side effects providing value additions to project net present values without loan subsidies. A number of different methods for loan subsidy valuation have been suggested in the literature and by project appraisal practice. Four methods are outlined and applied to a subsidized loan example taken from a prominent text book. A combination of two of those methods is recommended for practical applications. The other two methods are not recommended.

The book presents a survey of usable multilevel methods for modeling and solving decision problems in economics and management. The methods are largely extensions of linear programming and fall within the realm of column generation and decomposition. About one third of the book is concerned with methods and the rest describes case studies where these methods have actually been used. They are taken from areas such as national and regional economic planning, production planning, and transportation planning.