Question

How can the DCF method be applied if the growth rate was not constant? (detailed explanation needed)

I found short answer for this as: "We will find the PV of the dividends during the nonconstant growth period and add this value to the PV of the series of inflows when growth is assumed to become constant." But I am looking for a detailed explanation.

Answer 1

DCF method can be applied either on the dividends or on the free cash flows. Let's understand for the free cash flows. Whatever we do, will be applicable for the dividends as well.

Under discounted cash flow analysis to value a business or a business segment or a business combination, we look at two different types of free cash flows:

1. Free cash flow to the firm (FCFF) given by:

This is post tax operating cash flow after capital expenditure.

2. Free cash flow to equity holder (FCFE) given by:

If there is a preference share capital in the company, FCFE formula will also incorporate preferred stock dividend and will be given by:

FCFE is a cash flow which is free from all kinds of claims. It is a cash flow that ordinary equity holder can pocket safely. It’s the residual cash flow left after meeting all the liabilities, claims and investment needs of the company.

Steps involved in discounted cash flow valuation:

1. Project FCFF / FCFE for a reasonable horizon of projection.

   Let the free cash flows be represented by C. If we know the free cash flows last year say C₀ and the non constant growth rates for over say multiple years, then we can calculate the free cash flows of the future years as:

   C₁ = C₀ x (1 + g₁);

   C₂ = C₁ x (1 + g₂​);

   C₃ = C₂ x (1 + g₃);

   .........

   C_N = C₀ x (1 + g_n); where g_i is the growth rate in the period i.

2. Assume that the cash flows will grow at a constant growth rate (called terminal growth rate) beyond the horizon of projection. Calculate terminal value as present value of all the cash flows beyond the horizon period at the end of horizon period. This is given by equation:

Where TV_N is the terminal value at the end of horizon of projection of N years, C_N is the cash flow in the last year of horizon of projection (i.e. year N), “g” is terminal growth rate and “r” is the discount rate. Alternatively, terminal value can also be calculated by applying any of the relative valuation multiple on the applicable parameter. EV / EBITDA multiple can be applied on EBITDA in the last year of projection to obtain the terminal enterprise value. P / B or P / E or P / Sales can be applied on ordinary (common) stock book value or earnings or Sales respectively to get the terminal equity value. The multiple chosen for terminal value should be consistent with the cash flow being discounted. Note that when you are discounting FCFF, you should use EV / EBITDA multiple for terminal enterprise value. You should use P / E or P / B or P / Sales multiple to obtain terminal equity value when you are discounting FCFE.

3. Discount the cash flows and terminal value using the discount rate to obtain their present values at year 0. Appropriate discount rate is:
   1. WACC when FCFF is used
   2. Cost of equity when FCFE is used
4. Sum total of all the present value of future cash flows is the valuation today at year 0. When FCFF is used, the resultant valuation is called “Enterprise Value (EV)” of “Value of the firm”. All potential non-operating liabilities and claims need to be removed from the EV to get the equity value. Enterprise value = Value of the net debt (short term as well long term) + Value of preference stock (if any) + Value of the common equity. Hence, value of ordinary equity stock (or common stock) = Enterprise value – Value of net debt – value of preference stock (if any). Net debt = Total debt (short term as well as long term) – Surplus cash. Hence, When FCFE is discounted under discounted cash flow analysis, one ends up getting the “common equity value” or “ordinary equity value” directly.

This concept can be applied to valuing a business, a business segment, a company or a stock, a business combination by using the following analogous parameters:

Sl. No.	Situation	Business	Business Segment	Company / stock	Business combination
1.	Cash flows	Cash flows for the entire business that needs to be valued	Cash flows only from the business segment under consideration	Cash flows of the entire company include all businesses, segments, verticals etc.	Cash flows of the target under consideration
2.	Discount rate	Discount rate applicable to the particular business. Surrogate can be WACC of the business	Discount rate applicable to the particular business segment. Surrogate can be WACC of that particular business segment	Discount rate applicable to the overall firm. Surrogate can be WACC of the firm.	Discount rate applicable to the acquirer. Surrogate can be WACC of the acquirer or WACC of target or WACC based on funding mix for acquisition

Further note that:

• If a firm is undertaking a new project, the enterprise value (or firm’s value) or equity value of the firm will increase by a quantum equal to the NPV of the project. That’s why we have been harping in the previous sections that a positive NPV leads to shareholders’ wealth creation.
• We have already been through various forms of dividend discount models for equity valuation. All those models of equity valuation are also applicable if FCFE is used instead of dividends. FCFE is in a way maximum free cash flow available for distribution as dividend to the shareholders. Recall that all the variants of dividend discount model uses cost of equity as a discount rate.