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Unformatted text preview: discounted at the weighted average cost of debt and
shareholders’ equity before tax (WACCBT).
 E0 + D0 = PV[WACCBTt; CCFt]
The definition of WACCBT is :
 WACCBT t = [Et-1 Ket + Dt-1 Kdt] / [Et-1 + Dt-1]
Expression  is obtained by making  equal to . WACCBT represents the discount rate that
ensures that the value of the company obtained using the two expressions is the same:
E0 + D0 = PV[WACCBTt ; CCFt] = PV[WACCt; FCFt]
One way of defining the WACCBT is: the WACCBT is the rate at which the CCF must be
discounted so that equation  gives the same result as that given by the sum of  and .
The expression that relates the CCF with the ECF and the FCF is :
 CCFt = ECFt + CFdt = ECFt - ∆Dt + It = FCFt + It T
∆Dt = Dt - Dt-1; It = Dt-1 Kdt Method 4. Adjusted present value (APV)
The adjusted present value (APV) in equation  indicates that the value of the debt (D) plus
that of the shareholders’ equity (E) is equal to the value of the unlevered company’s
shareholders’ equity, Vu, plus the present value of the value of the tax shield (VTS):
 E0 + D0 = Vu0 + VTS0
We can see in Appendices 1 and 2 that there are several theories for calculating the VTS.
If Ku is the required return on equity in the debt-free company (also called the required return
on assets), Vu is given by :
 Vu0 = PV0 [Kut; FCFt]
Consequently, VTS0 = E0 + D0 - Vu0 = PV0 [WACCt; FCFt] - PV0 [Kut; FCFt]
We can talk of a fifth method (using the business risk-adjusted free cash flow), although this is
not actually a new method but is derived from the previous methods: Method 5. Using the business risk-adjusted free cash flow and Ku (required return on assets).
Equation  indicates that the value of the debt (D) plus that of the shareholders’ equity (E) is
the present value of the expected business risk-adjusted free cash flows (FCF\\Ku) that will be
generated by the company, discounted at the required return on assets (Ku):
 E0 + D0 = PV0 [Kut ; FCFt\\Ku]
The definition of the business risk-adjusted free cash flows (FCF\\Ku) is [1...
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- Fall '11