Discount rates and terminal values

Which discount rate goes with which cash flow?

The rate must match the claim in the numerator. This is the discount rate consistent with the claim . Cash flows that belong only to shareholders (dividends, free cash flow to equity (FCFE), residual income) are discounted at the required return on equity, $r_e$. Free cash flow to the firm (FCFF) belongs to lenders and shareholders and is discounted at the weighted average cost of capital (WACC) , a single required return for all capital providers. Earnings before interest, taxes, depreciation, and amortization (EBITDA), a before-tax measure, needs a before-tax rate (lesson 2).

Discount ratematch the claim in the numerator

• Required return on equity, r_e Memorize dividends, FCFE, residual income
• WACC Memorize FCFF; then subtract the market value of debt
• A pre-tax rate Know the idea EBITDA

WACC uses current market values for the weights (market value weights ), and the cost of debt after tax (after-tax cost of debt , $r_d(1 - \text{Tax rate})$) because interest is tax deductible.

$$\text{WACC} = \frac{MV_{Debt}}{MV_{Debt} + MV_{Equity}}\, r_d(1 - \text{Tax rate}) + \frac{MV_{Equity}}{MV_{Debt} + MV_{Equity}}\, r_e$$

The Corporate Issuers module introduced WACC; Learning Module 12 estimates $r_e$.

Debt is a contractual, less risky claim, so its cost is below the cost of equity, and so WACC ≤ $r_e$. This is the rule of WACC at or below the cost of equity . They are equal only for a firm with no debt. The gap grows with the share of debt and with the difference between the costs of debt and equity; a higher tax rate also lowers the after-tax cost of debt and so WACC.

Go deeper Why WACC can never exceed the cost of equity

WACC averages the cost of equity with the after-tax cost of debt. Lenders are paid first and by contract, so they accept less than shareholders, and interest also saves tax. An average that mixes in a cheaper source can only fall below $r_e$ or, with no debt, equal it.

How do you get from firm value to equity value?

Discounting FCFF at WACC gives the value of the whole firm, its enterprise value from FCFF . Firm value is the market value of debt plus the market value of equity, so subtract the market value of debt to get the value of equity.

$$IV_t = \left[\sum_{i=1}^{n} \frac{\text{FCFF}_{t+i}}{(1 + \text{WACC})^{i}} + \frac{E(P_{t+n})}{(1 + \text{WACC})^{n}}\right] - MV_{Debt}$$

That is the rule that equity value equals firm value minus market value of debt .

Valued with consistent assumptions, FCFE at $r_e$ and FCFF at WACC should give similar equity values; this is the consistency of FCFE and FCFF valuations . Calderon’s FCFE is expected to be 70 next year, growing 3%: 70 ÷ (0.12 − 0.03) = 777.78, close to 775. In practice the two often drift apart, and a big gap means the assumptions need another look. The FCFF growth rate that would make the two match exactly is the implied FCFF growth : using lesson 3’s formula at WACC on a firm value of 777.78 + 250, about 2.52%.

The classic error is discounting FCFE at WACC. WACC is lower than $r_e$, so the value comes out too high, and the rate no longer matches the claim: 70 ÷ (0.105 − 0.03) = 933.33, 20% too high.

What is a terminal value, and how much of the value is it?

The terminal value is the expected value of the share (or of the equity or firm) at the end of the forecast horizon; it stands for every cash flow after that. Analysts estimate it in two standard ways: as a present value with constant growth (this module) or with market multiples (Learning Module 7).

How much it weighs depends on the horizon: the shorter the forecast horizon, the larger the share of value that sits in the terminal value. This is the link between terminal value share and forecast horizon . Take a cash flow of 10 growing 8% a year before settling at 3%, discounted at 9%. The terminal value is 85% of the value with a three-year horizon, 77% with five and 62% with ten. And because the terminal value is cash flow ÷ (required return − g), that gap is one of the main drivers of the whole value.

Exam tip When the terminal value is most of the answer, test its growth rate and discount rate before anything else.

How do you choose the long-run growth rate?

From the company’s sustainable growth rate (SGR), its history or the economy. Analysts often keep it between the expected inflation rate and nominal gross domestic product (GDP) growth of the markets where the company earns its money: this is the range for terminal growth between inflation and nominal GDP growth .

Long-run growth g_lbelow the discount rate

• Sources Know the idea SGR, history, the economy
• Usual range Memorize expected inflation to nominal GDP growth
• Which economies Use it where the company sells, weighted
• Declining firm Use it can be below inflation or negative

Four rules. Use long-run averages, not this year’s rates, which may not last. Weight the economies where the company actually sells, not just its home country. The rate can be below inflation and even negative for a declining firm. And it must stay below the discount rate.

Negative growth

A stable negative terminal growth rate describes a firm in slow decline that will eventually stop operating; it does not imply a negative share price.

The value under the most likely assumptions is the base case; alternatives for the length of the fast stage, the first-stage growth rate and the long-run rate give a range around it. Report the base case and value range together. For Pellworth, if some analysts see decline slowing to −1% and others speeding up to −7%, the range is 120 × 0.99 ÷ 0.12 = 990 to 120 × 0.93 ÷ 0.18 = 620, around the base case of 768.