Discount Rates, Valuation, and the Cost of Capital

"Price is what you pay; value is what you get." - Warren Buffett

Why Discount Rates Matter

Valuation is fundamentally about comparing cash flows that occur at different points in time. A pound received today is worth more than a pound received in the future because today's pound can be invested and earn a return.

The present value of a future cash flow can be written as

PV = \frac{FV}{(1+r)^n},

where $PV$ is present value, $FV$ is the future cash flow, $r$ is the discount rate, and $n$ is the number of periods.

This simple relationship is central to discounted cash flowvaluation. The higher the required return, the lower the present value of the same future cash flow. This is why changes in interest rates can have an especially large impact on the valuations of long-duration growth companies.

A Simple Example

Suppose an investor expects to receive 1,000 in five years and requires an annual return of 8%. Using Equation pv,

PV = \frac{1000}{(1.08)^5} \approx 680.58.

If the required return rises to 10%, the same cash flow is worth only

PV = \frac{1000}{(1.10)^5} \approx 620.92.

The underlying cash flow has not changed; only the discount rate has.

The Weighted Average Cost of Capital

For a company financed by both debt and equity, analysts commonly use the weighted average cost of capital(WACC) as the discount rate for free cash flow to the firm.

WACC = \frac{E}{D+E}R_e + \frac{D}{D+E}R_d(1-T),

where:

$E$ is the market value of equity,
$D$ is the market value of debt,
$R_e$ is the cost of equity,
$R_d$ is the pre-tax cost of debt, and
$T$ is the corporate tax rate.

The tax adjustment reflects the fact that interest expense is generally deductible for corporate tax purposes.

Estimating the Cost of Equity

A common starting point is the Capital Asset Pricing Model:

R_e = R_f + \beta (R_m - R_f),

where $R_f$ is the risk-free rate, $\beta$ is the firm's equity beta, and $(R_m - R_f)$ is the expected market risk premium.

A stock with $\beta > 1$ is assumed to have greater systematic risk than the market, while a stock with $\beta < 1$ has lower systematic risk.

Illustrative Company Valuation

Consider a hypothetical company, Northbridge Payments plc, with the following capital structure assumptions.

Illustrative WACC Assumptions

{lr} Input	Assumption
Equity value	800m
Debt value	200m
Risk-free rate	4.0%
Equity beta	1.10
Market risk premium	5.0%
Pre-tax cost of debt	5.5%
Corporate tax rate	25.0%

Using Equation capm, the cost of equity is

R_e = 4.0\% + 1.10(5.0\%) = 9.5\%.

The after-tax cost of debt is

R_d(1-T) = 5.5\%(1-0.25) = 4.125\%.

With equity representing 80%of total capital and debt representing 20%,

WACC = 0.8(9.5\%) + 0.2(4.125\%) = 8.425\%.

Discounted Cash Flow

Assume the company is expected to generate the following free cash flows.

Forecast Free Cash Flow

{lrr} Year	Free Cash Flow (m)	Discount Factor
1	70	0.922
2	80	0.850
3	92	0.784
4	105	0.723
5	120	0.667

The present value of the explicit forecast period is therefore approximately

PV_{\text{forecast}} = 70(0.922) + 80(0.850) + 92(0.784) + 105(0.723) + 120(0.667).

Terminal Value

Because firms are normally assumed to continue beyond the explicit forecast period, analysts often calculate a terminal value using the Gordon Growth Model:

TV = \frac{FCF_{n+1}}{WACC-g},

where $g$ is the assumed perpetual growth rate.

If year-five free cash flow is 120m and long-run growth is assumed to be 2.5%,

FCF_6 = 120(1.025) = 123.

Using a WACC of 8.425%,

TV = \frac{123}{0.08425 - 0.025} \approx \pounds 2{,}075.95\text{m}.

The terminal value must then itself be discounted back to present value.

Sensitivity Analysis

DCF valuations can be extremely sensitive to small changes in assumptions. Table sensitivityshows an illustrative enterprise value sensitivity matrix.

Illustrative Enterprise Value Sensitivity (m)

{lrrr}	Perpetual Growth Rate
(lr){2-4} WACC	2.0%	2.5%	3.0%
7.5%	2,210	2,420	2,680
8.0%	2,020	2,195	2,410
8.5%	1,860	2,005	2,180
9.0%	1,720	1,845	1,995

The table demonstrates why valuation should not be interpreted as a single precise number. A more useful approach is often to present a reasonable range of outcomes based on plausible assumptions.

A Simple Empirical Specification

Suppose an analyst wants to test whether companies with higher leverage trade at lower valuation multiples. A basic cross-sectional regression could be written as

\ln(\text{EV/EBITDA}_i) = \alpha + \beta_1 \text{Leverage}_i + \beta_2 \text{Growth}_i + \beta_3 \text{ROIC}_i + \varepsilon_i.

An illustrative set of regression results is shown below.

Illustrative Regression Results

{lrr} Variable	Coefficient	Std. Error
Leverage	-0.182***	0.051
Revenue growth	0.436***	0.109
ROIC	1.214***	0.298
Constant	1.736***	0.142
Observations	120
R^2	0.61

The negative coefficient on leverage is consistent with the idea that highly indebted firms may trade at lower valuation multiples, although this example is purely illustrative and should not be interpreted as empirical evidence.

Figure Example

Illustrative relationship between discount rates and valuation

Conclusion

Discounted cash flow analysis provides a useful framework for connecting a company's expected operating performance with its valuation. However, the output is only as reliable as its assumptions.

The most important takeaway is therefore not that a DCF produces a single 'correct' value, but that it makes the assumptions behind valuation explicit. Changes in the cost of capital, long-run growth, or expected cash flows can materially alter the result.