The derivation of accounting profit depends upon a company's asset values and vice versa. The assets only have value in as much as they generate future income. Periodic income can only be determined by valuing the assets at two points in time.

For the purpose of acquisition pricing, this circle can be broken if management define income entirely in cash terms, rather than accounting revenue less historical costs, which also includes non-cash expenses such as provisions for capital maintenance (depreciation), bad debts, R and D and goodwill write-offs.

Using a discounted cash flow (DCF) analysis, with which you are familiar:

The basic going concern value of a target company equals the present value (PV) of future cash inflows less cash outflows resulting from the cycle of its operations.

To this value may be added the realizable value of assets to the extent that "surplus" assets may be sold post-takeover and the sale price will form part of future cash inflows. Conversely, if the total assets are inadequate, further investment (a cash outflow) at replacement cost must be incorporated into the analysis.

You should also note that the predator's decision is now based on an economic forecast, rather than adjustments to a set of stewardship-based accounts. However, once the target firm is acquired, published accounting statements for the newly merged entity will obviously be produced in accordance with generally accepted accounting principles (GAAP) based on historical costs and the accruals concept. But these may well differ from the cash projections used for the investment analysis that justified the bid price and acquisition.

Despite this disparity between accounting profits and cash flow, the latter approach to a going concern valuation is now based on a fundamental capital theory proposition explained in Chapter Two. Expressed mathematically, the value of an investment is the future net cash inflows it delivers discounted back to the present at an appropriate rate of return.

And if the yield (Ke) and cash receipts (Ct) are constant and tend to infinity, their PV simplifies to the capitalisation of a perpetual annuity:

You should also remember from Chapter Three that if cash flows are not constant over time, but grow at a constant annual rate (g) then their PV can be defined as follows:

Review Activity

Let us develop our previous numerical example using a cash flow analysis.

You will recall from earlier Activities that the following going concern valuations were derived using an earnings yield of 15 percent (equivalent to a P/E of 6.66) and a dividend yield of 3 percent respectively,

Total market value = £100 million Bid price per share = £20

Both figures were determined by an annuity capitalisation of accounting profitability. Now assume that at the valuation date:

(i) The predator company requires an earnings yield of 18 percent on a cash flow basis.

(ii) First-year net cash income after charging depreciation of £8 million to the accounts is expected to be £17 million.

(iii) Taxable accounting profits are £20 million.

(iv) The rate of corporation tax is 25 percent.

(v) Cash flows are expected to grow at 2 percent per annum.

Recalculate the total market value and bid price with reference to dividend policy.

Because accounting depreciation does not create a cash flow (i.e. it is a non-cash expense) a going concern value must be calculated based upon first-year cash flows by adding depreciation to net cash income. Taxation, which is a cash outflow but based on accounting profit, must then be subtracted to derive the true cash flow.

Using Equation (35) subject to the proviso that Ke > g for PV0 to be finite.

So, with 5 million shares in issue, the target company's valuation per share equals £25.

Note that these cash flow valuations are 25 percent higher than our previous accounting valuations, not only because of the depreciation adjustment, but also because the capitalisation rate is higher and income is assumed to grow.

Turning to dividend policy, if the current yield for similar firms is 3 percent (as stated in our previous Activities) the first-year distribution is no longer £3 million (as before) but:

£125 million x 0.03 = £3.75 million

Assuming the firm maintains a constant dividend payout ratio post-takeover from cash flows growing at 2 percent per annum, management also need to determine the long-run dividend yield (Ke). Fortunately, using Gordon's growth equation from Chapter Three (given PV0, g and D1 equal to the first-year dividend distribution) we can determine its value.

£125 million = 3.75 million / (Ke - 0.02)

Rearranging terms and solving for Ke:

As explained in Part Two, if dividends do not affect share price, there must be a unique relationship between their yield and dividend policy. What the example reveals is Gordon's proposition (1962) previously contested by MM (1961) that the long-run equity capitalisation rate used in the constant growth formula must be an increasing function of the growth rate. It will be recalled that in the original example with zero growth the dividend yield (Ke) was not 5 percent but only 3 percent.

However, these figures do not necessarily conflict with the "law of one price" and the dividend irrelevancy hypothesis proposed by MM. They would suggest that the rationale behind a higher yield relates to the profitability of investment opportunities provided by the 2% growth of retained earnings over time, rather than any increase in dividend distributions.

Summary and Conclusions

Alternative approaches to acquisition pricing are available to predator companies, which are either asset based or driven by income expectations, using conventional accounting data prepared on a non-cash basis. The latter utilize discounted revenue theory and the capitalisation of a perpetual annuity (either earnings or dividends) that can be made operational through a series of investment yields (capitalisation rates) namely:

- A capitalized earnings valuation using a P/E ratio applied to post-tax earnings

- A capitalized dividend valuation based upon dividend policy

P/E ratios and dividend yields can also be applied to the most sophisticated technique for valuing a company as a going concern.

- A present value (PV) analysis of future cash flows

However, it is important to realize that as an introduction to the subject and guide for further study, the PV analysis was kept deliberately simple. It implicitly assumed that the following information was known with certainty:

(i) All future cash flows in perpetuity, including an allowance for constant growth, which is less than the rate of

capitalisation.

(ii) A single rate of capitalisation, with capital costs and reinvestment rates equal to this (i.e. borrowing and lending rates are equal).

(iii) That sufficient funding was retained to maintain the expected future cash flows without compromising dividend policy.

(iv) The timing and amounts of any asset replacements.

(v) The realizable value and timing of the sale of surplus assets.

Relax any one of these assumptions and the valuation process not only becomes extremely complex but its cost and margin for error may outweigh the benefits. Perhaps this is why practical going concern valuations and bid prices are still underpinned by published financial statements, stock market ratios and other publicly available information.

Selected References

1. Gordon, M. J., The Investment, Financing and Valuation of a Corporation, Irwin, 1962.

2. Miller, M. H. and Modigliani, F., "Dividend policy, growth and the valuation of shares", The Journal of Business of the University of Chicago, Vol. XXXIV, No. 4 October 1961.

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