Simple Example

A simple example illustrates the APV and enterprise DCF approaches. Company K earns $100 per year of NOPLAT in perpetuity, with no growth.

Since growth is zero, free cash flow (FCF) also equals $100. If the unlevered cost of equity (ku) is 10 percent, the unlevered value of company K (Vu) is $1,000, as follows:

Company K also has $400 of debt (B), which pays interest at 7 percent pre-tax (kb), with a 40 percent tax shield (T). Using the APV model, we value the debt tax shield by discounting it at some rate. Let's assume that we can either discount the tax shield at the cost of debt (7 percent) or the unlevered cost of equity (10 percent). (We will discuss the pros and cons of the two approaches later). If we discount it at the cost of debt, the value of the tax shield (Vtb) is $160, as follows:

The enterprise value (V ) of Company K would then be $1,160, the sum of the unlevered value ($1,000) and the present value of the tax shields ($160). The value of equity (S ) would be $760, the enterprise value ($1,160) less the value of debt ($400).

To arrive at the same value using the enterprise DCF approach, the WACC would have to be 8.621 percent, derived as follows:

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