Operating Leverage - Investment and Project Valuation

Operating leverage is the sensitivity of an asset’s value on the market development caused by the operational cost structure, fixed and variable costs. The asset can be a company, a project or another economic unit. A production facility with high fixed costs is said to have high operating leverage. High operating leverage means a high asset beta caused by high fixed costs. The cash flows of an asset mainly consists of revenues, fixed and variable expenses:

cash flow = revenues – fixed expenses – variable expenses

Costs are variable if they depend on the output rate. Fixed costs do not depend on the output rate. The present value (PV) of the asset is the present value of its cash flows. Present values are linear, we obtain for the asset’s PV:

PV(asset) = PV(revenues) – PV(fixed expenses) – PV(variable expenses)

Rearranging leads us to:

PV(revenues) = PV(fixed expenses) + PV(variable expenses) + PV(asset)

Those who receive the fixed expenses are like debtholders in the project. They get fixed payments. Those who receive the net cash flows of the asset are like shareholders. They get whatever is left after payment of the fixed expenses. Now we analyze how the beta of the asset is related to the betas of revenues and expenses. The beta of PV(revenue) is a weighted average of the betas of its component parts:

$\beta_{revenue}=\beta_{\text{fixed exp.}}\frac{\text{PV(fixed exp.)}}{\text{PV(revenue)}}+$

$+\beta_{\text{var. exp.}}\frac{\text{PV(var. exp.)}}{\text{PV(revenue)}}+\beta_{\text{asset}}\frac{\text{PV(asset)}}{\text{PV(revenue)}}$

The fixed expense beta is close to zero, because the fixed expenses do not depend on the market development. The receivers of the fixed expenses get a fixed stream of cash flows however the market develops. That means $\beta_{\text{fixed exp.}} = 0$ . The betas of revenues and variable expenses are more or less the same, because they are both related to the output. Therefore we can substitute $\beta_{\text{revenue}}$ for $\beta_\text{var.exp.}$ .

$\beta_{\text{asset}}=\beta_{\text{revenue}}\frac{\text{PV(revenue)-PV(var.exp.)}}{\text{PV(asset)}}$

Setting PV(revenue) – PV(var.exp.) = PV(asset) + PV(fixed exp.) we obtain:

$\beta_{\text{asset}}=\beta_{\text{revenue}}\left[ 1 + \frac{\text{PV(fixed exp.)}}{\text{PV(asset)}}\right]$

This is the relationship of asset beta to the beta of turnover. The asset beta increases with increasing fixed costs. As an accounting measure we define the degree of operating leverage (DOL) as:

$\text{DOL}= 1 + \frac{\text{fixed exp.}}{\text{profits}}$

The degree of operating leverage measures the change in profits when revenues change.

Valuing the equity beta is a standard issue in DCF analysis. In many cases you take an industry segment beta and adjust it to your company or project. The adjustment of the industry beta also includes the adjustment of operating leverage. We assume that $\beta_{\text{revenue}}$ is the same for all companies in the industry segment. $\beta_{\text{revenue}}$ is the beta of the segment without operating leverage. The $\beta_{\text{asset}}^{\text{ind. segm.}}$ is the average asset beta of the industry segment, which has an average ratio of fixed expenses to profits. $\beta_{\text{asset}}^{\text{ind. segm.}}$ is provided by public databases.

For detailed information see: Brealey/Myers/Allen: Principles of Corporate Finance, 13th edition, p. 238, McGraw Hill Education, 2020)

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