The Proper Treatment of Cash Holdings in DCF Valuation Theory and Practice

Valuation I

Based on these assumptions, the present value of the operations of this company is $126.97, which is its operating business value in Table 1 (Valuation I) presented at the end of this Appendix. The $126.97 operating business value plus the $90.91 in cash equals an asset value of $217.88. The asset value in Valuation I includes 100% of the company’s cash, even though cash is clearly needed to pay near-term expenses. We will next demonstrate how Valuation I correctly includes all of the company’s cash without excluding any “operating cash.” Valuation I represents what we regard as the standard, correct DCF valuation of this business.

Valuation II

In Valuation II, to explicitly address the need to provide funding for expenses in years one and two, we assume that the company borrows $100 at a 10% interest rate at the end of year one to pay the projected $100 cash outflow, and borrows another $100 at the end of year two to pay that projected $100 cash outflow. Both of these loans are repaid, with principal and interest totaling $231 (i.e., $100 × [1 + 10%]^{2 years} + $100 × [1 + 10%]), at the end of year three once the company receives the $400 inflow. As shown in Table 1 (Valuation II), the $126.97 operating business value plus $90.91 in cash equals an asset value of $217.88, which is identical to the asset value in Valuation I where we did not assume any financing details. This is regardless of whether one accounts for the financing of operational cash needs indirectly (as in Valuation I) or directly (as in Valuation II). Comparing Valuation I to II demonstrates how the math of discounting operates to fully account for all of the financing costs of operating this business. Also notice that Valuation I is a much simpler model to implement in practice because one does not need to complicate the model with details of the financing embedded in the cash-flow projections as in Valuation II.

Valuation III

In Valuation III, the company invests its $90.91 of cash and earns 10% interest on this money so that by the end of year one the future value of this cash will equal $100 (i.e., $90.91 × [1 + 10%]). The $100 future value of cash will then be used to pay the projected $100 cash outflow at the end of year one. Unlike Valuations I and II, where the company’s cash was not explicitly used for operations, in Valuation III the company literally earmarks all of its cash for operations, thereby reducing the amount of borrowing to only the amount needed for year two. That is, the company only borrows $100 at the end of year two to pay that year’s projected $100 cash outflow, and repays this loan with principal and interest totaling $110 (i.e., $100 × [1 + 10%]) at the end of year three once the company receives the $400 inflow. As shown in Table 1 (Valuation III), the $217.88 operating business value plus $0.00 in cash equals an asset value of $217.88 that is exactly the same as it is in the prior two valuations. All three valuations yield the correct asset value of $217.88, and none double-count operating expenses.

This further demonstrates that so long as one obeys the symmetry principle and avoids double-counting expenses, a properly designed DCF model can either include “operating cash” or exclude “operating cash” from the valuation. Obviously, it is a much easier exercise to simply include all cash as a non-operating asset rather than trying to earmark such cash for specifically identified future expenses.

Valuation IV

The error made by the traditional approach of excluding “operating cash” can now be clearly demonstrated in Table 1 (Valuation IV) below, where even though all four valuations represent otherwise identical companies, Valuation IV’s asset value of $126.97 is understated by exactly the amount of the excluded cash.

Specifically, Valuation IV represents the traditional approach where operating business value of $126.97 is identical to operating business value in Valuation I, but the $90.91 of cash-on-hand is excluded from non-operating assets because it is earmarked to pay year one operating expenses, and thus is “used for operations.” Thus, by this traditional approach, the asset value is equal to the $126.97 operating business value. Although the operating business value of $126.97 can be regarded as correct, the total asset value is understated by $90.91 because the analyst does not include this $90.91 of “operating cash” to operating business value to arrive at the total asset value, according to Valuation IV, based on the misleading logic that the $90.91 initial cash will be used for operating purposes in the near term as shown in Table 1 (Valuation IV) below:

This error can be corrected in one of two ways, both of which are consistent with the symmetry principle. The analyst could simply refrain from excluding “operating cash” from asset value as in Valuations I and II, or one could exclude operating cash while also identifying and eliminating the projected cash outflows this cash has been earmarked to cover as in Valuation III.

Although in our simple numerical example it is easy to identify and eliminate the period 1 cash outflow that offsets the deduction of $90.91 of operating cash from asset value as in Valuation III, we do not recommend this approach be used for real-world DCF valuations for practical reasons. We recommend the approach taken in Valuation I. This is because in actual valuations it is extremely difficult, if not impossible, to precisely identify the cash outflows that actually are expected to be covered by the “operating cash” estimation. Indeed, none of the various ways to estimate operating cash suggested in the valuation literature involve attempting to identify precisely the actual expected near-term expenses that are to be used to estimate operating cash, no doubt reflecting both the vagueness of the definition of “operating cash” and the difficulty of the implied accounting tasks.^[44] Fortunately, correctly including all of a company’s cash-on-hand at the valuation date in non-operating asset value makes identifying specific near-term operating expenses that might be covered by cash-on-hand unnecessary when doing a DCF valuation.