 # Understanding discounted cash flows

| Updated on October 13, 2012 Published on October 13, 2012

When companies look to acquire or merge with other companies, the difficult question they face is — how to value the new business.

There are a number of methods available in finance literature to answer this question. A company can be valued based on book value or net worth, liquidation value, replacement value, discounted cash flow, relative valuation and adjusted present value. Among these, DCF is a common method used by players.

### Inputs for Calculation

Discounted Cash Flow method is based on the following inputs: Free cash flow, discount rate or Weighted Average Cost of Capital and the growth rate in earnings.

Free Cash Flow or FCF

It is defined as the cash flow that is available freely for company to deploy in the deal. FCF is computed by subtracting the capital expenditure and additional working capital requirement from the after-tax operating profit adjusted for depreciation and other non-cash expenses of a company. We can also compute the Free Cash Flow to Equity Shareholders by subtracting the value of debt from the FCFF.

Free cash flow to the firm (FCFF) is used for valuing the entire firm while FCFE is used for valuing the equity portion of the firm.

FCFE enables a company to arrive at the equity valuation while floating an initial public offer or structuring M&A deals, where shares are exchanged as consideration instead of cash payments.

Phases of growth

A DCF estimate also requires us to estimate the company’s growth over the long-term. Any business goes through two phases of growth i.e. Higher or Explicit Growth Phase and Normal or implicit growth phase. The hypothetical business in our example may grow at 8 per cent a year for the next five years.

Thereafter it may grow at 5 per cent, the normal growth phase. It is difficult for us to predict the duration of the stable growth phase as businesses are expected to live forever. Practitioners normally solve this by approximating the normal phase cash flow to a Terminal cash flow. Terminal Cash Flow is computed by multiplying the cash flow of the last year of the higher growth phase with the normal or implied growth rate and dividing this number by the excess of WACC over implied Growth Rate.

Normal or implied Growth Rate

It is the growth rate the company is expected to deliver on its operating income after the higher growth phase. It is computed by multiplying the return on invested capital with the re-investment rate. Let us assume ROIC of 10 per cent and re-investment rate of 50 per cent for the hypothetical company, then its implied growth rate would be 5 per cent.

Discount Rate or WACC

This is the last input required for the DCF calculation. WACC is the overall cost of capital of the company.

Let’s assume the hypothetical company has 70 per cent equity and 30 per cent debt in its capital structure. Further its after-tax cost of debt is 8 per cent and its cost of equity is 16 per cent. Then WACC would be = [0.7*0.16] + [0.3*0.08] that is 13.6 per cent.

### DCF value

We have now with us the following:

Growth Rate = 5 per cent; WACC=13.6 per cent and FCFF for the next year [year 1 of the explicit growth phase] = Rs 1,800 crore [assumed].

By using the above calculations, we get the FCFF for the next 4 years of the explicit or higher growth phase of the hypothetical company. Accordingly the FCFF for the 5 years [@8 per cent growth rate] would be Rs1,800 crore, Rs 1,944 crore, Rs 2,099.5 crore, Rs 2,267.5 crore and Rs 2,448.8 crore respectively.

Once we have the FCFF for the explicit growth phase then we can calculate the Terminal Cash Flow for the hypothetical company. It is Rs 30,387 crore.

The last thing we have to obtain to arrive at the DCF value is to discount the yearly FCFF and the Terminal value. The total value of the business is the sum of the present value of the yearly FCFF and the terminal value = Rs 23,253.4 crore. This is the FCFF of the business and if we can deduct the value of debt from the FCFF we would get the FCFE of the business. In this case it is Rs 23,253.4 – 1,000 crore [assumed]. The result is Rs 22,253.4 crore.

Though DCF valuation is a commonly used method to value a business in M&A, Adjusted Present Value is an improvement over it, as it also takes into account the effect of financial side effects of the deal. As an alternative to these two methods, Relative Valuation enables the appraiser to arrive at a comparative value on the basis of multiples.

(The authors teach accounting and finance courses at IIM-Ranchi.)

Published on October 13, 2012