3. Coping with Excess Cash

3.3. Step 2: Current Cost of Capital

From our preceding analysis, we know the following about the firm under the current capital structure:

  • Market value of equity (E) = 600 billion
  • Net debt (D) = -150 billion
  • Debt tax shield (DTS) = -45 billion
  • Cost of equity (kE) = 10%
  • Cost of debt (kD) = 2%
  • Discount rate for interest tax savings: kD (since the firm pursues a financing policy with target debt levels)
  • Tax rate (τ) = 30%.

 

With this information, we can compute the firm's overall cost of capital (kA) as well as its WACC, using the expressions from the referenced sections:

  

\( k_A = k_D \times \frac{D-DTS}{D-DTS+E} + k_E \times \frac{E}{D-DTS+E} \)

  

\( WACC = k_A \times (1- \tau \times \frac{D}{D+E}) \)

 

Plugging Pear's values into these equations, we find a cost of assets of 11.7% and a WACC of 12.9%:

  

\( k_A = 0.02 \times \frac{-150+45}{-150+45+600} + 0.10 \times \frac{600}{-150+45+600} \) = 11.7%

 

\( WACC = 0.117 \times (1- 0.3 \times \frac{-150}{-150+600}) \) = 12.9%.

 

Note that under the current financing policy, Pear's cost of equity (10%) is actually lower than the cost of assets (11.7%). The reason is that shareholders currently own a portfolio that consists of the firm's operating assets (with a required return of 11.7%) and excess cash (with a required return of 2%). 

Similarly, it is not surprising that, under the current financing policy, the WACC is larger than the cost of assets. The reason is that the current financing policy carries a tax burden. The actual return earned on excess cash is not the pre-tax return of 2% but only the after-tax return of 1.4% [= 0.02 × (1 - 0.3)]. 

  

Now that we understand the status quo, let us see how the proposed recapitalization (borrow 100 billion and repurchase 250 billion worth of shares) affects the valuation of Pear as well as its cost of capital.