For Finite Cash Flows, What is the Correct Formula for the Return to Levered Equity?

Abstract

For cash flows in perpetuity without growth, analysts typically use the following formula for the return to levered equity Ke.

Ke = Ku + (Ku ­ Kd)(1 ­ T)D/E (1)

where Ku is the return to unlevered equity, Kd is the cost of debt, T is the tax rate, D is the market value of debt and E is the market value of equity.

What is the corresponding formula for finite cash flows? Is it the same as equation 1? In other words, is equation 1 appropriate for both finite and infinite cash flows? One may be tempted to believe that equation 1 is the general formulation for the return to levered equity and applies to both cash flows in perpetuity and finite cash flows. However, this conclusion is misleading.

In this short note, using simple algebra, we derive the general formulation for the return to levered equity for finite cash flows, and show that equation 1 is not the general formulation for finite cash flows.

Keywords: Present value of the tax shield, formulation for Ke, cost of levered equity, cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity, tax savings, growth rate for the free cash flow

JEL Classification: M40, M46, M41, G12, G31, J33