Feb 7th, 2008
Errors and Omissions in DCF Calculations: A Critique of Delaware’s Dr Pepper Appraisal
By Gilbert Matthews, CFA
The recent statutory appraisal of Dr Pepper Bottling Holdings, Inc. (“Holdings”) by the Delaware Chancery Court in Crescent/Mach I Partnership v. Turner 1 raises several conceptual and computational issues concerning discounted cash flow (DCF) valuations in an appraisal context. An analysis of the Court’s calculations reveals the caution with which valuation practitioners should apply the DCF method, and the enduring benefit of using comparable market analyses as a reasonableness check.
Unusual case arising from constraints on sale
The cash-out merger that led to this appraisal was unusual because it was arms’ length; most statutory appraisal cases stem from freeze-outs of minority shareholders by controlling interests. In the Crescent/Mach I case, Jim L. Turner, Holding’s controlling shareholder and chief executive, decided to sell the company because he feared “competitive challenges posed primarily by Coke and Pepsi,” including “a price war in which Holdings would not have the same support and resources as its nationally-backed competition.” In addition, “troubling” economic conditions and external constraints limited the prospects for sale. Cadbury Schweppes PLC (“Cadbury”), the franchisor for Holdings’ primary soft drink brands, “made it clear to Turner that it would not likely consent to a private equity acquisition.” Coca Cola and PepsiCo could not acquire Holdings for antitrust reasons. The only bidder was an entity owned by Cadbury and the Carlyle Group, which acquired Holdings in a cash merger at $25 per share on October 1999. Turner sold his shares at the same $25 price, subject to severe restrictions. “Turner obtained the best price that he could from Cadbury/Carlyle,” the Vice Chancellor noted, “but how often will the only buyer pay full price?”
Dissenting shareholders sought appraisal 2 under the Delaware statute (8 Del. C. §262), and the Court undertook what it called “an independent valuation exercise.”
In determining fair value, the Court may look to the opinions advanced by the parties’ experts, select one party’s expert opinion as a framework, fashion its own framework or adopt, piecemeal, some portion of an expert’s model methodology or mathematical calculations. The Court, however, may not adopt an “either-or” approach and must use its judgment in an independent valuation exercise to reach its conclusion.
At trial, experts for both sides used a comparable company approach as well as a DCF; one expert also utilized comparable transactions. Similarly, the investment bank retained by Holdings to render a fairness opinion relied on all three approaches.
The Court rejected application of the market approach because of Holdings’ unique market position and the lack of appropriate guideline comparables. Citing prior Delaware decisions, the Court reiterated its preference for the DCF method and its general opinion that “other methodologies—all based on comparables of one form or another—are of limited value.” Adopting certain of the experts’ inputs as to projections, discount rates, terminal value, taxes, and debt, the Court arrived at intermediate numbers for other inputs, and accepted the company’s projections used by Holdings’ expert. It determined a fair value of $32.31 per share, or 29% more than the transaction price (and far less than the dissenting shareholders’ expert valuation at $48.69 per-share). The Court’s conclusion was “within the range of reason,” it said, in part because it fell within the ranges of the original fairness opinion: $19.32 and $31.05 for the DCF analysis, $22.29 and $34.84 for comparable transactions, and $19.75 and $28.53 for comparable companies. The Court further supported its $32.31 fair value determination by stating that Holdings “implicitly concedes that the merger consideration was less than fair value by sponsoring an expert who concluded that the fair value was in excess of the merger price.”
However, in fact, the Court’s $32.31 valuation is above the high end of two of the three very wide fairness opinion ranges. The Court’s DCF-based conclusion was 4% above the high of the DCF range and 32% above its $25.19 midpoint. As to Holdings’ implicit concession, its expert testified that the fair value of Holdings based on a DCF was $25.10 per share, only 0.4% above the $25.00 transaction price.
Errors in the Court’s valuation
A review of the inputs selected by the Court and Holdings’ expert reveals that the differences between them were not sizeable. In particular, the Court used a discount rate of 9.75% (vs. 10% by Holdings’ expert), a tax rate of 39% (vs. 40%), and a faster use of operating loss carryforwards ($6.215 million per year vs. $4.5 million). Given these fairly close numbers, one would not expect the Court’s valuation to be 29% higher than that of Holdings’ expert.
The Court helpfully appended a summary of its calculations to the published decision. A close reading discovered two calculation errors, the first one minor. In calculating the after-tax debt-free cash flow for the 1999 stub period following the transaction date, the Court omitted the portion of pretax income sheltered by the loss carryforward. (It accurately totaled the projected data for years 2000-2004.) Correcting this small miscalculation lowers the Court’s per-share value by $0.13.
The second error was material. The Court included the post-2004 cash flow benefit of the tax loss carry forward as a line item in the calculation of equity value, reflecting the present value of the carryforwards after the end of the projection period. However, the numerator of the growth model (the 2004 free cash flow number) included the full amount of the pretax income being sheltered by the loss carryforward. Therefore, free cash flow for the perpetuity calculation was overstated by $2,424,850, i.e., 39% (the assumed tax rate) of the annual sheltered income ($6,215,000). The present value of the second error caused the Court’s valuation to be $2.40 per share too high.
After adjusting for these two errors, the fair value of the transaction is $30.04 per share, 7.4% below the Court’s award of $32.31 per-share.
Conceptual questions left open
Based on a reading of the case, the experts failed to analyze and address certain conceptual issues. As a result, it appears that the Court may have adopted conceptually flawed inputs that may have increased its valuation. Analysts should review these factors for future valuations, where relevant, to aid the trier-of-fact in its independent determination of value under the DCF approach.
1. Effect on Discount rate of a weak competitive position. The opinion acknowledged that Holdings was in a weak competitive position. Faced with the supermarket industry’s consolidation and preference for national bottlers, the company “would encounter substantial market difficulties.” Cadbury’s support for Holdings was about to decline or end, further impairing Holdings’ ability to compete.
In determining its discount rate, the Court looked in part to testimony regarding the volatility of national bottlers (Coca Cola and PepsiCo), which occupied a stronger market position than Holdings’. Given the stronger positions of the national bottlers, it would have been reasonable to adjust Holdings’ discount rate upward.
Application of a 10% discount rate rather than 9.75% (and correcting for the two errors, discussed above) would have reduced the Court’s calculated value of Holdings from $30.04 to $27.56 per share; a 10.25% discount rate would have further reduced it to $25.27 per share.
2. Perpetual growth rate. In calculating terminal value, the Court applied a perpetual growth rate of 3.5% to free cash flow, although it used a 3% EBITDA growth rate for the projection period. Based on the accepted management projections, the growth rate in projected free cash flow from 2000 to 2004 was 3.98%, but this resulted from using flat capital expenditures and increasing depreciation. If depreciation, capital expenditures, and changes in working capital in the projection had been increased by 3.0% annually, free cash flow would have increased at 2.7% per annum.3 Applying a 3.0% (rather than 3.5%) perpetual growth rate and correcting for the two calculation errors, the Court’s valuation of Holdings would have declined from $30.04 to $26.21 per share.
It is rare (except in turnaround situations) to find a long-term growth rate exceeding the anticipated growth rate for the medium-term projection period. Competitive factors, changes in consumer preferences, and obsolescence should normally cause the long-term growth rate to be lower than the medium-term rate.
3. Capital expenditures and depreciation. The Court adopted management’s projection that capital expenditures would be $25 million each year of the projection period and that depreciation would increase each year. Although increasing revenues normally require increasing capital expenditures, the Court’s (and management’s) assumption that capital expenditures would not grow was not supported by a schedule of future capital expenditures. The assumption of flat capital expenditures is clearly inconsistent with management’s projection that depreciation would increase each year, since it is almost impossible for depreciation to increase unless capital expenditures increase.4
In a perpetuity model (such as the Gordon Growth Model that the Court used), capital expenditures must be materially higher than depreciation because, in an inflationary economy, new capital expenditures must reflect increasing capital asset costs, while depreciation must reflect the amortization of lower historical capital asset costs.5 In a perpetuity model with a 3% growth rate and assuming a 10-year average life for fixed assets, capital expenditures would exceed depreciation by 15.5% using straight line depreciation and 11.6% using the double-declining method.6 The Court’s opinion gave no indication that the experts considered the appropriate relationship between capital expenditures and depreciation, which is a common error of omission in DCF analyses.
If capital expenditures and depreciation were both projected to increase at 3% per year after the first full year of the projection period (using the Court’s 9.75% discount rate and correcting for the two errors), the calculated value of Holdings would drop from $30.04 to $27.20 per share. Combining this adjustment with a 3% perpetual growth, the calculated value of Holdings would have fallen to $23.56, less than the $25.00 transaction price.
In evaluating any projections, the practitioner should consider both the reasoning behind the projected capital expenditures and the relationship between capital expenditures and depreciation. When possible, management should explain its assumptions. It should always be able to calculate depreciation accurately based on historical and projected capital expenditures. When trial experts later examine management projections, they should consider making appropriate adjustments if the assumptions are questionable, and be prepared to support any revisions in court.
4. Amortization has a limited life. The Court’s valuation model included $5.4 million of annual tax-deductible amortization as a non-cash charge. Amortization necessarily has a limited life, but the Court, by including it in the free cash flow in the growth model, effectively assumed that it was perpetual, thereby understating taxes and overstating value. (Without knowing how long the amortization was scheduled to continue, the overstatement cannot be quantified.) Moreover, applying a growth rate to free cash flow erroneously assumes that amortization will grow at the same growth rate, thereby further overstating terminal value.
In fact, amortization in a projection should normally be a constant or declining number.7 The appropriate manner to value amortization subsequent to the projection period is to exclude it from the growth model calculation, and, instead, to determine the present value of the scheduled amortization over its life.
Since the Court did not explain the amortization’s specific application or its scheduled life, it is not possible to quantify its impact on the valuation. However, assuming that the amortization continued for five years beyond the end of the projection periods, the calculated value of Holdings (corrected for the two errors discussed above) would be reduced from $30.04 to $28.44 per share.
Caution when using DCF
This discussion demonstrates that practitioners must use caution in valuing a business based on discounted cash flow. A DCF analysis assumes the validity of the financial projections. However, any projection depends on the reasonableness of the underlying inputs, such as growth rate, profit margins, and capital expenditures. A DCF valuation is highly dependent on terminal value, which is a direct function of the final year of a projection; the final year is clearly more difficult to forecast than the near future. The selection of a discount rate is also subjective, particularly for smaller, less diversified companies.
Discounted cash flow is a valuable tool, but small changes in the inputs can materially affect the valuation conclusion. As this critique shows, with all other inputs in the case held constant, adjusting the perpetual growth rate assumption from 3.5% to 3.0% reduces the calculated value by 13%, and adjusting the discount rate from 9.75% to 10.25% reduces the calculated value by 16%. The subjectivity of many DCF inputs frequently makes the approach unreliable, producing a wide range of calculated results and rendering any mathematical precision illusory.
When analysts employ different approaches that lead to materially different conclusions, they should examine the inputs to determine the causes of the discrepancy. Alternative valuation methods serve as helpful “reality checks” to confirm whether a specific conclusion is reasonable. An examination of the implied multiples of data points in the final year of the underlying projection should help to establish whether a DCF valuation is reasonable. In valuing Holdings, it appears that the Vice Chancellor did not use the EBITDA multiple inherent in his DCF valuation as a reasonableness check. He called the dissenters’ expert’s valuation of Holdings at 8.9x EBITDA “somewhat high” because the comparable companies had “an implicit value premium stemming from the liquidity advantage of a closer relationship with their ‘parent’ companies.” However, based on EBITDA in the final year of the projection, the EBITDA multiple was 8.6x, not far from the 8.9x that the Court rejected. If the Court’s calculation is corrected for the two errors and if a 3% perpetual growth is applied, then the EBITDA multiple would be 7.6x.
In its seminal Weinberger decision, the Delaware Supreme Court held that “the methodology to be used for measuring fair value should be generally accepted techniques used in the financial community.”8 A review of the summaries of investment bankers’ fairness opinions in proxy statements shows that an overwhelming majority of public company transactions rely on comparable companies and comparable transactions analyses. In recent years, several Delaware Chancery Court decisions have used DCF as the sole analytical measure of value. Sound practice, however, calls for using more than one method. Experts and courts should consider the widely used comparable company and comparable transaction methods whenever possible. Expert witnesses should be prepared to explain the basis for their selection of comparables and the adjustments that they consider appropriate and necessary in applying the comparables’ multiples to the subject company. A well-reasoned and appropriately adjusted comparables analysis should be helpful to a court both as a basic valuation approach and as a crosscheck on DCF calculations.
1 2007 Del. Ch. LEXIS 63 (Del Ch. May 2, 2007). The case abstract appears in the Sept. 2007 Business Valuation Update.
2 Former shareholders also claimed that Turner breached his fiduciary duties, but the Court dismissed these claims.
3 Free cash flow would increase at a slower rate than EBITDA because amortization and the loss carryforward were projected to be constant.
4 Theoretically, depreciation might increase when capital expenditures are flat if a substantial portion of capital expenditures are for shorter-life assets than prior capital expenditures had been, e.g., buying trucks instead of building plants.
5 See M. Mark Lee, “The Ratio of Depreciation and Capital Expenditures in DCF Terminal Values,” Financial Valuation and Litigation Expert, August-September 2007, pp. 7-8. See also, Daniel L McConaughy and Lorena Bordi, “The Long Term Relationships between Capital Expenditures and Depreciation Across Industries: Important Data for Capitalized Income Based Valuations,” Business Valuation Review, March 2004, pp. 14-24.
6 Gilbert E. Matthews, “Fairness Opinions: Common Errors and Omissions,” in The Handbook of Business Valuation and Intellectual Property Analysis, R. Reilly and R. Schweihs, eds. (McGraw Hill, 2004), pp.223-4.
7 Amortization could increase during the projection period where the forecast assumed future events, such as acquisitions, that will lead to additional amortization.
8 Lawrence A. Hamermesh & Michael L. Wachter, The Fair Value of Cornfields in Delaware Appraisal Law, 31 Iowa J. Corp. L. 119, 123-4 (2005), citing Weinberger v. UOP, Inc., 457 A.2d 701, 712 (Del. 1983).
