Inflation, Investment and Valuation

1 Inflation

At the end of June 1965, the Consumer Price Index (CPI) in the United States was 31.61. By the end of June 2020, it has risen to 257.21, an increase of 714%. This equates to an annual compound growth rate of 3.89%. It is natural to think of this inflation as being caused by a general tendency of prices to rise, but that is misleading. The real cause of inflation is the decline in the value of one good – the U.S. dollar. Because the prices of all goods and services in the United States are stated in terms of dollars, we experience the declining value of the dollar as a general increase in the price level. This means that a dollar in 1965 or 2015 is not the same thing as a dollar in 2020. Economists have recognized this fact and developed tools to deal with it, but U.S. GAAP accounting typically excludes the impact of inflation. Financial statements for U.S. companies in 1965, 2015 and 2020 are all stated in terms of “dollars” even though the dollars are not the same. This simple error creates a lot of mischief, but nowhere more so than in valuation.

2 Be Careful Defining Growth

Growth is typically measured by the percentage increase in a company’s revenue, earnings, or assets, as calculated using current dollars. The italicized part of the sentence is critical because growth in current dollars can come either from actual expansion of the business in real terms or inflation. To see the distinction, return to the example of the home delivery company. One possible source of real growth would be buying more trucks and hiring more drivers. Financing such growth requires taking a fraction of the company’s current earnings and plowing them back into the business rather than paying them out as dividends to shareholders. This is true of all real growth in steady state; it requires cash investment in the business thereby reducing the free cash flow payable to shareholders.

Unlike real growth, inflationary growth, as measured in current dollars, does not require cash investment beyond the amount necessary to maintain the firm’s assets in real terms. If prices throughout the economy are rising at 4%, then the prices charged by the home delivery company, the wages the company pays, and the prices of the trucks will also rise at 4%.^[1] This implies that the revenues, earnings, and assets of the delivery company will be rising at 4%. However, although the firm’s assets must be maintained in real terms, that growth does not require any cash plowback. It is simply an artifact of the fact that the value of the dollar is falling at 4% per year.

What makes growth tricky to deal with in the “real” world, is that it is usually due to a combination of inflation and real growth. However, to properly value a company the distinction is critical because of the fact that real growth requires cash plowback and inflationary growth does not. Failure to distinguish between the two sources of growth will lead to an erroneous estimate of value.

3 Growth Requires Investment: The Plowback Equations

Here we leave the mathematical derivations aside, they are presented in detail in Bradley and Jarrell (2008) and Cornell and Gerger (2017a, 2017b). We stress, however, that all the equations below refer to a constant growth firm in steady state as of the terminal date. The key issue involves confusion in the plowback equation included in several valuation texts, including McKinsey (2020), when applied to accounting data. The analysis begins with an equation which states that the growth rate, G, in net operating profit after tax (NOPAT) equals the fraction of NOPAT plowed back into the business, IR, times the return on the investment of the plowed back cash, ROIC, or:^[2]

In the context of valuation, equation (1) is not used directly. When the constant growth formula is applied in steady state at the terminal horizon, G and ROIC are taken as given by assumption. The task is to solve for the fraction of earnings that must be plowed back in order to finance the assumed growth. Therefore, equation (1) is solved for IR, giving:

For instance, in the seventh edition McKinsey (p. 50) says, “Since the company’s cash flows are growing at a constant rate, we can begin by valuing a company using the well-known cash flow perpetuity formula:

In equation (3), FCF is the free cash flow and WACC is the weighted average cost of capital. This equation is well known and there is no dispute regarding its validity. McKinsey then observes that to achieve growth at the rate G, the fraction IR of NOPAT must be plowed back into the business. This leads them to conclude that free cash flow equals NOPAT reduced by the plowback so that:

McKinsey then says, “build this into the definition of free cash flow,” to arrive at the final valuation equation:^[3]

The key to formulas (1)–(5) is NOPAT, ROIC, and G must be properly defined and used consistently. Specifically, if ROIC is calculated from GAAP based financial statements (“ROIC_acct”), it will likely differ from the economic ROIC (“ROIC_econ”) due to inflation and other factors.^[4] Furthermore, while it may be reasonable to assume a company’s ROIC_econ will converge with the company’s WACC in the long-run, ROIC_acct is unlikely to converge to the company’s WACC.^[5]

The fundamental error that frequently occurs in valuations that employ equation (5) is failing to recognize that if NOPAT is based on GAAP financial statements, the ROIC in equation (5) must be ROIC_acct, not ROIC_econ, and the two growth terms in the equation may differ. Specifically, G in (1 − G/ROIC) must represent growth in book value (“G _BV”)^[6] and G in (WACC − G) must represent economic growth, e.g., growth in NOPAT (“G _econ”).

To arrive at a proper estimate of the terminal value, ROIC_acct, G _BV, and G _econ used in equation (5) must represent steady state rates. Unfortunately, steady state ROIC_acct and G _BV are difficult to calculate from a company’s financial statements because a company may not be in steady state in the real world. In fact, as demonstrated by Exhibit 1, the Parking Lot example below, many companies never reach a steady state in accounting terms so that ROIC_acct and G _BV (0.0% in the Parking Lot example) can be materially different than G_econ (4.0% in the Parking Lot example).

A careful review of equation (1) highlights the issue. According to equation (1), growth requires plowback, but if growth is measured in economic terms, i.e., a firm’s value is increasing, and IR is based on cash investment, equation (1) ignores inflationary growth by effectively assuming all growth requires plowing back cash to expand the business in real terms. But our discussion of the food delivery company, and a more complete example presented in the next section, show that this is not the case. Inflationary growth measured in terms of current dollars as financial statements are, does not require plowback, it is due entirely to the decline in the purchasing power of the dollar.

In an important paper, Jarrell and Bradley (2008) recognized that proper valuation requires carefully taking account of the distinction between real and inflationary growth. Doing so, they were able to derive the proper relation between plowback and growth in steady state. Their equation is given by:^[7]

It looks exactly like equation (1) except for the substitution of small letters for capitals, but that difference is critical. In equation (6), all the variables are real, that is adjusted for inflation. For instance, if a company expects a nominal return on investment, ROIC, of 10%, and the rate of inflation is 4%, then the real expected return on investment, roic, is 5.77%.^[8]

Notice that the Bradley–Jarrell relation immediately solves the problem with the food delivery company. If there is no real growth, that is if g = 0, then the plowback rate, ir, is also zero.

4 Data for Equations (1)–(5) Must be Carefully Defined and Applied: The Parking Lot

A simple example demonstrates that inputs for equations (1)–(5) must be carefully defined. Assume, as shown in Exhibit 1, $1000 is invested in vacant land used as a parking lot which has an expected return on invested capital, which is equal to the business’s WACC, of 10%. Also assume that inflation is expected to be 4%. For the business to operate, the parking lot requires an attendant to collect money and provide security, but the business requires no capital improvements. The business’s expected net operating profit after tax based on accounting data in period t + 1 is $60. Since the parking lot requires no capital improvements, the expected FCF in period t + 1 is also $60, resulting in the initial $1000 value based on equation (3), i.e., $60/(10%–4%).

As described above, the growth of the parking lot’s financial results is due to inflation, not cash plowback. Each year, the revenues and expenses, and therefore the profit and cash flow generated by the business are 4% greater than the last year due to inflation. For this reason, the value of the land also grows at 4% per year. There is no need for cash plowback; all the business owns is a vacant lot.

Based on equation (2), however, if growth is based on the firm’s financial results, G _econ, plowback would be equal to 40%, i.e., IR = G/R, so IR = 4%/10%. Applying the 40% plowback ratio to the net operating profit after tax results in a significant undervaluation of the business because based on equation (4) FCF in period t + 1 would equal $36, i.e., $60 * (1–40%), and based on equation (5) the value of the business is also reduced by 40%, dropping to $600, i.e., ($60 * (1–40%))/(10%–4%). When applied to accounting metrics, equation (5) is wrong because all growth in the value of a business’s invested capital is treated as the result of cash plowback – inflationary growth is ignored and the two growth terms have the same value. In this simple example, all the growth is due to inflation.

5 Bradley–Jarrell and Proper Accounting for Inflation: A “Real World” Example

The parking lot is a particularly simple example, but the same analysis carries over to more complex businesses that involve real, as well as inflationary, growth. Before turning to the example, there is one other distinction between the McKinsey analysis and the Bradley–Jarrell approach that must be taken into account. McKinsey defines plowback in relation to NOPAT, but there is a problem with that caused by the fact that inflation drives a wedge between replacement cost and depreciation as discussed earlier. This led Bradley and Jarrell to define the concept of Net Cash Flow, NCF, that takes account of the wedge. More specifically,^[9]

NCF can be thought of as the cash flow the company can distribute to investors after making all the expenditures necessary to maintain the capital stock. Cornell and Gerger (2017a) show that plowback, when based on accounting data, should be calculated as a fraction of NCF, not NOPAT because that is the distributable cash flow prior to any plowback to provide for real growth.

Putting all the pieces together, the proper constant growth valuation equation when using accounting data is given as:

With this background, we now turn to a specific example – the valuation of Costco presented in Appendix H of McKinsey (2020). The analysis of Costco by McKinsey is extensive, but the only issue of relevance here is the continuing value. Everything but the calculation of the continuing value is held constant. There are two numbers that must be added to perform the Bradley–Jarrell calculations, an estimate of the steady-state inflation rate and the average life of Costco’s depreciable assets. Here we use 2% for the inflation rate. That rate is consistent with recent history, most forecasts, and the current rates on Treasury securities. It is also a number that McKinsey uses in other parts of the book. For the average life of depreciable assets, we use 15 years which is consistent with the ratio between Costco’s depreciable assets and its annual depreciation. Finally, in Exhibit H:14, Costco: Continuing Value and Exhibit H:16, Costco: Enterprise DCF Valuation, McKinsey uses a return on new invested capital, ROIC, of 22% to calculate Costco’s continuing value.^[10] For demonstration purposes we assume that ROIC equals the WACC of 8% in the example calculations.

Exhibits 2a and 2b present the calculations. The continuing value is calculated in 2a using both the assumption that ROIC equals the WACC and the Bradley–Jarrell plowback equations. The exhibit also takes account of the distinction between NOPAT and NCF described above. The continuing values are then plugged into the remainder of McKinsey’s DCF valuation in Exhibit 2b.

Exhibit 2a shows that use of the correct Bradley–Jarrell formula reduces the plowback rate from 50.00% to 33.33%. However, because the plowback ratios are applied to different metrics, NOPAT versus NCF, the impact of the lower plowback is somewhat offset by the difference between the two metrics. All told, the use of the incorrect formulas assuming ROIC equals WACC leads to an understatement of value of about $11 billion or 15.3% of Costco’s estimated value.

6 What Have the Delaware Courts Said?

To review, in steady state all prices will rise at the rate of inflation. With respect to estimating the continuing value of a company in steady state, this has two implications. First, the rising prices, in nominal dollars, of capital goods means that replacement cost will exceed depreciation. This must be accounted for by taking account of the difference between NOPAT and NCF. Second, inflation will also cause the stock of invested capital to rise in nominal terms. This means that for a given rate of growth in capital, cash plowback is required only for the real part of growth. The inflationary growth is funded by rising prices and maintenance of the firm’s assets.

Because the Delaware courts have not explicitly adopted the proper inflationary mathematics, decisions to this point have been inconsistent on the two mains issues. With respect to the distinction between inflation and replacement cost, in Towerview LLC v. Cox Radio, Inc., Del. Ch. June 28, 2013 and in Laidler v. Hesco Bastion, Del. Ch. May 12, 2014, the court concluded that in steady state depreciation should be set equal to capital expenditures. However, in Kleinwort Benson Ltd. v. Silgan Corp., Del. Ch. June 15, 1995 and Blueblade v. Norcraft, Del. Ch. July 27, 2018, the court concluded that capital expenditures would exceed depreciation. The Blueblade decision comes closest to the analysis presented here in that the court said, “The assumption that depreciation equals capital expenditures is only appropriate if it is also assumed that there is no growth and no inflation. However, … the normalized capital expenditures of a [perpetually] growing company must materially exceed depreciation over time.”

With respect to plowback, in Appraisal of Solera, Del. Ch. July 30, 2018, the court addressed the plowback issue but did not make a final determination as to the appropriate formula and ended up valuing the company using criteria other than a DCF analysis. In Fir Tree v. Jarden, Del. July 9, 2020, the court again based its final valuation decision on criteria other than a DCF analysis but did discuss the plowback issue and appeared to side with the use of equation (5) assuming ROIC equaled or approximated the firm’s WACC. On the other hand, In Re Appraisal of Ancestry.com, Inc., Del. Ch. January 30, 2015, the court adopted the Bradley–Jarrell analysis of plowback, noting that “[i]n order to adequately support a perpetual growth rate in excess of expected inflation (i.e., positive real growth), a firm will need to reinvest in capital expenditures at a sustainable rate that is above that of projected depreciation.”

The foregoing examples are taken from appraisal cases in Delaware, but the issue is far more general. It applies in any situation where a fundamental value must be estimated using discounted cash flow analysis be it in bankruptcy and restructuring, mergers and acquisitions, or any other area. Even with an inflation rate of only 2% as currently exists, the failure to account for inflation can have a material impact on the estimated continuing value. As Brealey, Myers and Allen (2011) warn in their best-selling textbook on corporate finance, “In real-life valuations, with big bucks involved, be careful to track growth from inflation as well as growth from investment.” What is more, if inflation were to accelerate the errors introduced by not accounting for it properly grow commensurately.