Calculating Tobin’s Q
Tobin’s Q is impossible to calculate with precision, as the concept of replacement value is inherently subjective. For example, rational investors are likely to disagree on the replacement value of The Coca-Cola Company, as investors will have divergent views on the value of Coke’s brand equity. As a result, the calculation of Q requires a number of estimates and approximations.
In this report, we focus on estimating Q for the market as a whole rather than any single stock.
The data used to estimate Q can be found in the Federal Reserve Board’s Z.1 statistical release entitled Flow of Funds Accounts of the United States. Before proceeding with this brief tutorial, we suggest that you access the FRB’s website and print out the relevant page from the latest Z.1 release. To do so, simply go to http://www.federalreserve.gov/releases/z1/ and click on the date of the current Z.1 release. Then click on PDF file labeled “Balance sheet tables.” The file will contain several pages, but you only need the page entitled “B.102 Balance Sheet of Nonfarm Nonfinancial Corporate Business.” All references below to lines that contain certain data relate to line numbers in the B.102 table. For your convenience, we have reproduced on the next page the data used to calculate Q from 1945 thru 2008.
- The market value of debt can be estimated by using book value of debt as a proxy for market value; book value of debt outstanding in any particular year is the sum of the following line items contained in balance sheet B.102 of statistical release Z.1: Municipal Securities (line 24), Corporate Bonds (line 25), and Mortgages (line 28). (See note below)
- The market value of equities is found in line 35 of B.102. Equity market value can be updated through the present by adjusting the value provided in the Z.1 statistical release to reflect the subsequent change in a major market index, such as the S&P 500 Index.
- Net liquid assets = total financial assets – (total liabilities – municipal securities – corporate bonds – mortgages) = line 6 – (line 21 – line 24 – line 25 – line 28)
- Land value is approximated as the market value of real estate – the replacement cost of residential and nonresidential structures, i.e., land value = line 3 – line 33 – line 34.
- The replacement cost of structures, equipment & software, and inventories is the sum of lines 4, 5, 33, and 34 of B.102.
Note: It is possible to estimate the market value of debt more accurately than by using book value as a proxy. In order to do so, long-term debt can be modeled in the form of 10-year, Baa-grade bonds with semiannual coupons. (Historical data on Moody’s Baa interest rates is available on the FRB’s website.) The market value of the debt outstanding in year t would then equal the sum of the market values of debt issued in years t-9 through t. The book value of bonds issued in year t equals the book value of debt outstanding in year t (calculated as noted in text above) minus the book value of debt outstanding in year t-1 plus the book value of debt outstanding in year t-10. The market value of debt issued in year t can be estimated as the book value of debt issued in year t. The market value of debt issued in years t-9 through t-1 can be estimated via a net present value formula using the applicable Moody’s Baa interest rates.
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