The Cash to Equity method for the valuation of an enterprise is a variant of the Discounted Cash Flow method. Alternative Discounted Cash Flow methods (like the WACC method and the Adjusted Present Value method) are based on free cash flows to the firm FCFF: the cash flows that become available to all providers of capital: shareholders and providers of interest-bearing debt, like banks or leasing companies. The Cash to Equity valuation method is based on the determination of the net present value of future cash flows that become available to the providers of equity, i.e. the shareholders. This is the so called free cash to equity FCTE. The relation between the cash to firm and the cash to equity is also clarified in the wikipedia article on Cash to Equity.

So, by definition, the Cash to Equity method is therefore the only direct valuation method to determine the value of equity, i.e. the shares.

## Cash To Equity valuation

The free cash to equity (FCTE) is the available free cash flow for the providers of share capital (equity): the shareholders. In formula:

FCTE = net profit + depreciation – investments in fixed (tangible and intangible) assets – investment in net (induced) working capital + new debt – repayments on loans.

Here, we see a first difference with the WACC method and the Adjusted Present Value method. These variants present the enterprise value. Which is something else than the equity value.

The WACC value or Adjusted Present Valuevalue was the result of adjusting (discounting) the (future) free cash flows available to all providers of capital (debt and equity).

Applying the Cash to Equity method, only the cash flows for the providers of equity are determined. With the objective to value their shares. So, this Cash to Equity method directly gives the value of equity.

## Free cash to equity

Let us take a look at the privately held limited liable company BriWiFra in our article about the WACC method. As we may remember, BriWiFra is the company of Brian: Brian’s Window Frames. BriWiFra produces hardwood window frames for the construction industry. If we now calculate the free cash to equity, we end up with the following results:

Cash to Equity in €/1000 |
Yr 1 |
Yr 2 |
Yr 3 |

Net income | 387 | 413 | 477 |

Depreciation | 160 | 170 | 175 |

Investments | |||

NCW | -60 | -35 | -55 |

Fixed assets | -185 | -195 | -200 |

Repayments on loans | -120 | -120 | -120 |

Free Cash To Equity FCTE | 182 | 233 | 277 |

In the period after the forecasting period, the so called remainder period, BriWiFra will undoubtedly continue to generate free cash to equity. To arrive at an estimation, we must make several assumptions. In any case, this is always a challenging exercise. But, let us let us be brave and assume the following:

- BriWiFra continues to repay its bank loan in the following years year 4 through year 9;
- From year 4 onwards, the operating income (or EBIT) continues to be the same as in year 3;
- From year 4 onwards, the investments in fixed assets equals to the depreciation. So the volume of fixed assets is constant;
- From year 4 onwards, the volume of induced net working capital is constant. The company’s turnover and direct and indirect costs are invariable in future years. This seems to be plausible enough;
- From year 10 onwards, the enterprise infinitely continues to generate cash at a constant level. This so called zero growth perpetuity is less probable. But let us take this for true;

Based on this, the next free cash to equity FCTE can be calculated:

Cash to Equity |
Yr 4 |
Yr 5 |
Yr 6 |
Yr 7 |
Yr 8 |
Yr 9 |
Yr 10 and later |

Free Cash To Equity FCTE | 363 | 368 | 374 | 380 | 386 | 391 | 511 |

## Required rate of return on equity

Now the following question arises: *which discount rate should we use to calculate the Net Present Value of these future FTCE’s?* Let us try the unlevered Requ = 16%. And if we do so, we end up with the following results:

NPV CTE | |

Year 1 through year 3 | 508 |

Year 4 through year 9 | 884 |

Remainder period | 840 |

Cash | 20 |

CTE Value of shares | 2252 |

The equity value is then 2252. And that is a bit strange. Because, according to the WACC method, the value of equity was 1965. So, using the CTE method with the unlevered Requ, we end up with a much higher (probably: too optimistic?) valuation outcome.

So, then the question arises: *what is the reason for this?* The difference is easy to understand. Because in the article about the WACC method, we learned that the required rate on return on equity increases when the enterprise is financed with interest bearing debt. And in the case of the levered enterprise BriWiFra, the levered required rate of return on equity Reql is higher, i.e. 21.8%.

So, apparently, we applied a too optimistic discount rate! And, if we recalculate the CTE Value of Equity with the higher Reql, we end up with the following valuation outcome:

NPV CTE | |

Year 1 through year 3 | 460 |

Year 4 through year 9 | 658 |

Remainder period | 398 |

Cash | 20 |

CTE Value of shares | 1536 |

And again, this is strange. Because this is now significant less than the 1965 according to the WACC method. Now, the question arises: *what is the reason for this?* And again, the explanation is quite simple.

In the subsequent years, the capital structure changes. The debt is diminishing, so the levered rate on equity will then be lower. And calculating all subsequent free cash to equity with the initial (and to high-pitched) Reql will yield a too low CTE Value of shares. Again ending up with a wrong value!

So, what can we do? One could make a choice for taking a discount rate in between, a bit of an average, for instance 18.9%. Then the CTE Value of shares ends up with 1833. Which is a bit closer to the 1965 according to the WACC method. But this is by far not justifiable and yet not accurate. So, as a professional business valuator, I would never recommend such an approach! And above all: a prove of misunderstanding the Cash to Equity valuation method!

## Correct valuation method

The formal correct approach is to execute a yearly re-calculation of the levered rate of return Reql. And apply those different and diminishing Reqls for the calculation of the individual and yearly net present values of all individual future FCTEs.

Note that this requires an iterative calculation process, equal to the WACC method. This is because of the following.

The valuation outcome is the economical value of equity which influences the Reql, which we used to calculate that valuation outcome, i.e. the economical value of equity. So, we must surrender into an iterative calculus: repeat this calculation to end up with an exact Cash To Equity valuation appraisal.

But at the end, the equity value outcome of the Cash To Equity method will be very much closer (yet not exact equal) to the valuation outcome according the WACC method. However, when properly executed, this Cash to Equity value will be exactly the same to the valuation outcome according the Adjusted Present Value method.

## Capital structure

The capital structure has an influence on the Cash To Equity value. This proves to be evident. This seems to be in contradiction with the Modigliani and Miller theorem, the capital structure irrelevance. However, in our world where profit tax exists, debt will help to increase value due to the tax shield. But we will come to that in the article about the Adjusted Present Value method.

For now, as an experiment, we assume that BriWiFra manages to maintain its debt from year 4 onwards at a volume of 720. So, the redemption on its loan is stopped. The future free cash to equity FCTE will rise with 120 during the years 4 through year 9. This has an increasing effect on the CTE Value of shares. If we calculate this CTE Value of shares, with the –disputable- Reql of 18.9%, the valuation outcome will be 2022 according to:

Without redemption | |

Year 1 through year 3 | 483 |

Remainder period | 1519 |

Cash | 20 |

CTE Value of shares | 2022 |

So, the valuation outcome is then 188 more compared to the situation where BriWiFra continues to redeem its bank loan. It is therefore understandable that shareholders –in general- strive for a maximum leverage. And also, prefer to receive dividends in order to invest in projects with an excessive return on investment ROI. This, instead of leaving cash in the enterprise for repayments on interest bearing loans.