Prospective Accounting Initiative 

Appendix 9

AFTF Formulas

AFTF Dual Validations Formulas 

Let,

CV_t = Company Valuation at time t

E_t = Expected cash flow at time t for prior year

H = Historic cost of capital for the previous 5-year period

A_t = Actual cash flow at time t for prior year

MV_t;= Market value at time t

 

The Expected cash flows must match the Actual cash flows,

E_-5 + E_-4 + E_-3 + E_-2 + E_-1 = A_-5 + A_-4 + A_-3 + A_-2 + A_-1

 

The Company Valuation is defined as,

CV₀ = E₁ / (1+H) + E₂ / (1+H)² + E₃ / (1+H)³ + E₄ / (1+H)⁴ + …

Where the historic cost of capital H is determined from,

CV_-5 + CV_-4 + CV_-3 + CV_-2 + CV_-1 = MV_-5 + MV_-4 + MV_-3 + MV_-2 + MV_-1

Note that the historic cost of capital is phrased in term of five consecutive company valuations, all from the same point in time so that a single model and set of cash flows is used. Note also that the historic cost of capital does not use the current year. The principal reason for this is to isolate and quantify effects other than capital market effects. In fact, if we don’t do this the Company Valuation degenerates into the Market Valuation. A second reason for not using the current year is a practical one; there would not be time enough to validate the model and determine the cost of capital at the close of the reporting year. It is expected, and in fact desirable, that the validation be done well in advance of year-end. This is desirable in order not to capture changing experience or changing expectations from the current year. We want this to be separately and explicitly captured in the new Company Valuation.

Miscellaneous Formulas 

The current actual-to-expected ratio = A₀ / E₀

The historic actual-to-expected ratio = (A_-5 + A_-4 + A_-3 + A_-2 + A_-1) / (E_-5 + E_-4 + E_-3 + E_-2 + E_-1)

The IRR (company-estimated yield) = that H for which CV₀ = MV₀

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