Terminal value

A discounted cash flow model forecasts cash flows for five or ten years. The business does not stop there. Terminal value is the single number that stands in for every year after the forecast ends.

It is uncomfortable to look at, because in most models it is the majority of the answer. The carefully built year-by-year forecast turns out to be the smaller half of the valuation, and the larger half rests on one growth assumption applied to infinity.

The workbook gives two routes.

Perpetual growth (Gordon) method. Take the last forecast year's cash flow, grow it one more year, and divide by the discount rate minus the perpetual growth rate. The growth rate must be below the discount rate or the arithmetic breaks. The workbook adds a discipline: the perpetual growth rate is often capped at the long-term nominal GDP growth rate of the markets the company operates in, because no business can outgrow its economy forever. A lower rate may be used where the analyst judges it appropriate.

Exit multiple method. Multiply EBITDA (or EBIT) at the end of the high-growth period by an appropriate EV/EBITDA (or EV/EBIT) multiple drawn from comparable firms.

Either way, one step is compulsory and constantly forgotten: the terminal value has to be discounted back to the present, because it is a value struck at the end of year n, not today.

Terminal value at year n = FCFF(n) × (1 + g) ÷ (WACC − g)

Present value of TV      = Terminal value ÷ (1 + WACC)^n

Exit multiple method     = EBITDA(n) × comparable EV/EBITDA

A consumer company is forecast in detail for five years. Year 5 free cash flow to the firm is Rs 300 crore, WACC is 12%, and the analyst uses a perpetual growth rate of 5%.

TV at year 5 = 300 × 1.05 ÷ (0.12 − 0.05) = 315 ÷ 0.07 = Rs 4,500 crore
PV of TV     = 4,500 ÷ 1.12^5 = 4,500 ÷ 1.7623 = Rs 2,553 crore

If the present value of years 1 to 5 is Rs 950 crore, the enterprise value is Rs 3,503 crore — and 72.9% of it is the terminal value.

Change one number. Push the perpetual growth rate from 5% to 6%:

TV = 300 × 1.06 ÷ 0.06 = Rs 5,300 crore
PV = 5,300 ÷ 1.7623   = Rs 3,007 crore
Enterprise value      = Rs 3,957 crore

One percentage point on a rate that applies to years nobody will forecast moved the whole valuation by Rs 454 crore, or 13%.

The exit multiple route, for comparison: year 5 EBITDA of Rs 600 crore at a peer multiple of 8× gives a terminal value of Rs 4,800 crore, whose present value is Rs 2,724 crore — Rs 171 crore more than the perpetuity route. Two defensible methods, two different answers.

Chapter 10 (section 10.5) introduces terminal value as the second half of a two-stage FCFE or FCFF valuation, and gives both the perpetual growth and the exit multiple routes along with the GDP cap. Expect a computation, and a conceptual question on why the perpetual growth rate cannot exceed the long-term nominal growth rate of the economy.

• Discount it. Terminal value is struck at the end of year n. Adding it to the present values of years 1 to n without discounting inflates the answer enormously — at 12% over five years, by 76%.
• g must be less than the discount rate. Set them equal and the denominator is zero; set g higher and the model returns a negative value. The Gordon model in Chapter 10.5 states the assumption explicitly.
• The workbook caps perpetual growth at long-term nominal GDP growth of the relevant market. A 9% perpetual growth assumption is not conservative, it is impossible.
• Terminal value usually dominates. When it is 70% or more of the answer, the "detailed" DCF is mostly one assumption in a smart suit.
• Match the cash flow to the rate. FCFF with WACC gives a firm terminal value; FCFE with cost of equity gives an equity one. Mixing them corrupts both stages.
• The exit multiple method imports today's market mood into a valuation meant to be independent of it. Cross-check it against the perpetuity answer.