Peter Jennergren

HQ was a medium-sized Swedish banking group whose licenses were revoked in 2010. The parent company sued the board members and the audit firm for damages. NN was an expert witness for plaintiff and submitted a valuation using DCF and comparables for a but-for scenario where HQ would have survived. This valuation is an example of setting assumptions to obtain a particular result, depending on the purpose of the valuation. Two possible purposes are considered, maximizing the but-for value, and legitimizing a value that has been set in advance based on other considerations. From an analysis of unusual evidence in the DCF part of the valuation model, it appears that the purpose was to legitimize a value that had been set in advance. The author served as expert witness to defendant, with the task of rebutting NN. This paper is based on expert reports by NN and the author.

HQ was a medium-sized Swedish banking group whose banking and fund management licenses were revoked in 2010, after losses in trading in equity derivatives for its own account. The parent company of the HQ group sued the board members and the audit firm and the responsible auditor for damages. NN was an expert witness for plaintiff and submitted a DCF valuation of HQ in a but-for scenario, where the banking group would have survived. This valuation is an interesting example of choice of valuation model assumptions to obtain a specific result, i. e., calibration. The nature of the calibration depends on the purpose of the model. Two possible purposes of a DCF model used by an expert for plaintiff are mentioned, maximizing the but-for value, and legitimizing a value that has been set in advance based on other considerations. From an analysis of unusual evidence that is contained in the DCF valuation model for HQ, it appears that the purpose of that model was to legitimize a value that had been set in advance. The author served as expert witness to defendant, with the task of rebutting NN. This paper is based on expert reports by NN and the author.

The following four elementary depreciation methods are often mentioned together in the literature: Nominal linear, real linear, nominal annuity, and real annuity. All four 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 four members of this class are then ranked (to the extent possible) by their remaining values. Such a ranking indicates the relative depreciation rates of the class members.

Operating leases are quite important in some industries. There are two possible errors that should be avoided when valuing a company with operating leases. In the first place, 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. In the second place, 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 valuation models, in particular the discounted cash flow model. This procedure avoids the two possible errors that were mentioned and is shown to result in equity values that are very close to the known, exact values in a stylized example problem. Naive valuation (that makes both errors) results in equity values that can be quite far away from those same known, exact values.

The influential valuation book by an author team from McKinsey recommends the so-called value driver formula rather than the Gordon formula for the continuing value in the post-horizon period in the discounted cash flow model for firm valuation. This recommendation has had considerable impact on valuation practice. This paper points out two weaknesses of the original value driver formula. The first weakness is that it is not a significant extension of the Gordon formula. The only case where it is applicable is where the requirement for working capital is not the same for the future growth projects (that are started in the successive years of the post-horizon period) as for the existing operations that are in place already at the end of the explicit forecast period, a fairly uninteresting case. In that case, the Gordon formula gives the same valuation result, implying that the original value driver formula is not necessary. The second weakness is that the split into existing operations and growth projects that underlies the original value driver formula implies that the existing operations are valued under the assumption of zero inflation, which is unreasonable if inflation is actually positive. This paper then derives a revised value driver formula that is a more significant alternative to the Gordon formula. In the revised formula, gross margins can differ between the existing operations and the growth projects. The valuation of the existing operations takes into account positive inflation. Continuing value is a sum of two separate value driver formulas, one for the existing operations and one for the growth projects. This means that most of the steady-state character of the post-horizon period is retained. A comparison with the original value driver formula in a representative setting indicates that the difference in resulting continuing values can be non-negligible.

The conventional formula for the nominal growth rate of free cash flows (equal to dividends when there is no interest-bearing debt) says that this growth rate is equal to the product of the plowback ratio and the nominal rate of return on the assets (the latter equal to book equity when there is no debt). In a recent issue of the Journal of Applied Corporate Finance, M. Bradley and G. A. Jarrell claim that the conventional formula is wrong when there is positive inflation, proposing instead an alternative formula. In a rejoinder to that paper in the same journal, G. Friedl and B. Schwetzler assert that the conventional formula is right. In a comment on Friedl and Schwetzler, Bradley and Jarrell reassert their original position, that is, the conventional formula is wrong and the alternative one is right. This note shows that the conventional formula is right and that both formulas give the same nominal growth rate. Consequently, both are OK.

We investigate a disaggregated version of the abnormal earnings growth (AEG) model of Ohlson and Juettner-Nauroth (2005). The value of the firm then becomes discounted free cash flows minus initial debt. Discounted free cash flows are equal to capitalized operating earnings from the initial stock of operating assets plus the present value of an infinite sequence of growth projects, where each growth project is valued by discounted economic value added. Sufficient conditions for the present value of the free cash flows to be equal to the sum of these two components are investigated. The Gordon growth formula is found to be one special case. Another case concerns lumpy growth projects with depreciation according to the annuity method. We then allow for three different interest rates, the required rate of return on equity under all-equity financing, the borrowing rate, and the required rate of return on equity under partial debt financing (the latter given by MM's Proposition 2). In the model of Ohlson and Juettner-Nauroth, these rates are the same. A firm-level model is developed that focuses on operating earnings and free cash flows with discounting at the required rate of return under all-equity financing. An equity-level model is then developed that focuses on bottom-line earnings and dividends with discounting at the required rate of return under partial debt financing. Relationships between the two models are explored. Dividend policy irrelevance holds only in a limited sense for the equity-level model.

The Swedish finance company crisis was a kind of "run" that happened in September, 1990. It marked the beginning of the Swedish banking crisis of the early 1990's. The crisis was initially focused on the finance company Nyckeln. The specific negative information about Nyckeln is identified, as well as how it spread only very late, or not at all, to the supervisory authority and to the banks that were involved in lending to the finance companies. The paper then inquires whether there were warning signs of the forthcoming crisis in capital market information and other public information, by means of the usual event study methodology. The data that are used include indices for the banking industry and the real estate and construction industry, and share prices and trading volume for finance companies. The conclusion is that the crisis really came as a surprise, with very little advance warning.

Two changes happened in 1998 that affect pension planning in a Swedish municipality. In the first place, there were changes in laws that affect accounting for pensions: Accrued pension rights that have been earned from 1998 have to be entered as a liability in the balance sheet. Pension rights that are earned in a given year must appear as a cost in the income statement, and similarly for interest cost relating to the pension debt. Also, the budget of a municipality has to balance. That is, budgeted revenues have to exceed budgeted costs. The result of these law changes is to necessitate a strengthening of municipal balance sheets. More precisely, municipalities are required to start funding the pensions of their employees, as pensions rights are earned. In the second place, a new pension agreement was signed between municipalities and labor unions representing municipal employees. This agreement, named PFA 98, is based on annual pension dues that accrue over time until retirement and are then transferred into a monthly pension amount, rather than on a specific pension promise that is given already at the time when the pension rights are earned. (That is, a pension promise is only given when an employee retires.) It is hence fairly simple to simulate the evolution of the municipal pension debt under the PFA 98 agreement. This report undertakes such a simulation. It shows annual forecasts for municipal pension debt, pension costs, and pension payments until 2043, for the total set of municipalities in Sweden. The report also investigates the consequences of the changes in laws mentioned earlier as regards the asset side of a municipal balance sheet. For instance, due to the manner in which the relevant laws are written, there may arise an overfunding of the pension debt. The report also includes a comparison with pension foundations in private companies (these are one particular manner, with some associated tax advantages, of managing a portfolio of assets acquired as pension debt funding). It is also argued that the strengthening of municipal balance sheets mentioned earlier will probably to a large extent take place through the reduction of external debt.

All steps of the discounted cash flow model are outlined. Essential steps are: calculation of free cash flow, forecasting of future accounting data (income statements and balance sheets), and discounting of free cash flow. There is particular emphasis on forecasting those balance sheet items which relate to Property, Plant, and Equipment. There is an exemplifying valuation included (of a company called McKay), as an illustration. A number of other valuation models (abnormal earnings, adjusted present value, economic value added, and discounted dividends) are also discussed. Earlier versions of this working paper were entitled "A Tutorial on the McKinsey Model for Valuation of Companies".