Relevant to ACCA Qualification Paper F9 and P4

Theoretically, the free cash flow (FCF) model is the best valuation model to estimate the intrinsic value of a business. This article will address the detailed approach of how to use FCF to value a firm.

FORMAT OF FCF

Firstly we should review the format of free cash flow, we usually distinguish the free cash flow into free cash flow to firm (FCFTF) and free cash flow to equity (FCFTE), and the formulae are shows below:

Free cash flow to firm

Free cash flow to equity

The difference of two formulas is that interest charge is deducted in calculating the FCF to equity and hence less tax payment. When using FCF to equity model, we normally assume the debt/equity ratio is constant overtime, therefore no need to subtract debt repaid or add debt raised.

<!--page-->

SELECTING FREE CASH FLOW AND APPROPRIATE DISCOUNT RATE

Students should bear in mind that two types FCF are discounted at different rate:

1. FCF to firm should be discounted at WACC; the total present value is called corporate value or entity value. Then to find value of equity, we subtract the market value of debt from the corporate value.

2. FCF to equity should be discounted at cost of equity (Ke). The total present value is just the value of equity.

If the company's debt/equity ratio is constant over time, the FCF to equity method should give the same answer as discounting FCF to firm at WACC and then subtracting debt. In real exam, we usually use the first method, i.e. discounting FCF to firm at WACC, and use second method if the question tells students to do so, or question does not give enough information to calculate the WACC.

STEPS OF CALCULATING VALUE OF EQUITY USING FCF

The following steps are based on discounting FCF to firm at WACC.

1. Estimate the FCF and its growth rate at and beyond horizon period.

The horizon period is normally 3-6 years, where the firm experiences a higher growth rate, beyond the horizon periond, the growth rate is expected to reach a steady stale.

The growth rate at horizon period can be computed using Gordon growth model:

g = rb

where: r= return on reinvested funds (normally use ROE or Ke)

b=proportion of funds retained

The growth rate after horizon period may be decreased at a low level, e.g. the growth rate of GDP.

2. Discounting FCF at WACC to find the value in horizon period.

3. Calculating the terminal value beyond the horizon period.

We normally assume the FCF after horizon period is in perpetuity, therefore the formulae is shown below:

Terminal value =  discount factor at last year of horizon period

FCF in this formulae is used the FCF in the last year of horizon period.

4. Added the horizon value and residual value together to find the corporate value.

5. Add the market value of short-term investment. (if any).

6. The value of equity is then determined by deducting the value of debt from corporate value.

After finishing the calculation, students are recommended do following assumption to capture some professional marks:

l The current operating cash flows are solid.

l The investment in non-current asset and working capital will be in a consistent manner in future.

l The Debt/equity ratio will remain constant.

l The growth rate will be reasonable for horizon period and be constant after that.

l The rate of return required by investors is constant throughout the life of the busine

l The business has an indefinite life after horizon period.

If students discount the FCF to equity at Ke, the approaches are similar; the differences are listed as below:

l Using FCF to equity

l Discounting at cost of equity

l Do not deduct the debt.

Example 1 (discount FCF at WACC)

L plc is currently considering a take-over bid for a competitor in its sector, O plc, the finance team of L has produced the following forecasts of financial data for the activities of O plc if it is taken over for the first four years:

The corporate taxation is at rate of 30% per year, the weighted average cost of capital for O plc after acquisition is estimated at 14%. The market value of debt in O plc is 60m, and the cash flow is expected to grow at 3% per year after year 4.

Required:

Calculate the value of equity of O plc.

Solution:

Calculate the horizon value:

Calculate the terminal value

Terminal value =  discount factor at last year of horizon period

                            =  0.592 = 177

Corporate value = horizon value + terminal value

= 79+177 = 256

Value of equity = corporate value - value of debt

              = 256 - 60 = 196

Example 2: (discounting FCF to equity at Ke)

S plc is a UK-based telecommunication company; the company is considering the purchase of B Ltd, an unlisted company. It is expected that the turnover of B Ltd grow by 25% per year for three years and by 10% thereafter. Summarised profit and loss accounts for the year ended 31 March 2006 are shown below:

Profit and loss account for the years ended 31 March 2006

Other information:

1) Non-cash expenses, including depreciation, were $820,000 in current year.

2) Operating profit is expected to be approximately 8% of turnover in 2006, and to remain at the same percentage in future years.

3) Corporate taxation is at the rate of 30% per year.

4) Capital investment was $1 million in current year, and incremental working capital investment was 138,000, and they are expected to grow at approximately the same rate as turnover.

5) Interest and non-cash expense are expected to increase at same rate as turnover.

6) The estimate cost of equity of B is 14%

Required:

Estimate the value of B Ltd using present value of free cash flow.

Solution:

Calculate the horizon value:

Calculate the terminal value

Terminal value =  discount factor at last year of horizon period

                           =  0.675 = 27008k

Value of equity = horizon value + terminal value

               = 2694+27008 = 29702k

CONCLUSION

The FCF is theoretical the best valuation model, it is based on the future cash flow and the risk associated with the cash flow. However, this depends on accurate estimate of growth rate, cash flows and discount rate, we may not have access to all the information required to forecast future cash flows.

Moreover, a little change in assumption can result a large change in value of a firm, for example, growth rate decreasing by 1% could lead to a significant fall in value. In real world, smart financial managers try to check their results by calculating value in several different way in additional to FCF model.

Given all these problems, we realise that the FCF model is a scientific valuation method. However, it is important to appreciate that the purpose of discounted cashflow is to estimate market value - to estimate what investors would pay for a business. When we can observe what they actually pay for similar companies, we gain valuable evidence. In order to figure a way to use it, one way to do so is through valuation rules of thumb base on multiples. Two common approaches are P/E ratio model and P/B ratio model:

P/E ratio model: Value of equity = PAT×suitable industry P/E ratio

P/B ratio model: Corporate value (market capitalisation) = Book value of asset×Market to book ratio

REFERENCE

1. Brealey / Myers / Allen Corporate Finance: 8th edition, McGraw Hill International Edition, pp 507-512, 2006.