WACC - “after-tax” cost of debt is not correct to be used?

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WACC: “After-tax” Cost of Debt is not Correct to
be Used?
Pendahuluan
Issue
With delayed payment in corporate income tax, after-tax cost of debt in WACC (Weighted
Average Cost of Capital) is apparently wrong.
How is going to address it in your business valuation?
Response
Ignacio Vélez-Pareja
Yes, the traditional formula for WACC has some assumptions:
Sukarnen
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 There is enough EBIT to offset interest payments and hence earn Tax Shields, TS;
 Taxes are paid the same year as accrued;
 The only and one source of financial expenses (FE) are interest payments (with Kd as
cost of debt)
This means that if you have losses, you might be earning zero or less than KdDT as TS.
The rule to use for defining TS is
 If FE<EBIT + Other Income (OI) TS = TxFE
 If FE > EBIT + OI > 0 TS = EBITxT
 If EBIT+OI<0 TS = 0-
"Lost" TS can be recovered if Losses Carried Forward are accepted in the Accounting Rules.
The best to take that into account all this when using FCF is (assuming Ku as discount rate for
TS) to use the following formulation for WACC:
WACC = Ku - TS_t/V_t-1
In this way, you can even include financial expenses different from interest payments (for
instance, losses in exchange, inflation adjustments to the financial statements, bank
commissions, etc.).
BUT, the very first option to solve that problem is to use Capital Cash Flow (CCF) and WACC
for the CCF that is Ku (when assuming Ku as discount rate for TS) instead of FCF and WACC
for the FCF.
The proposed formula collapses to the traditional one when FE are identical to interest and
taxes are paid the same year and EBIT>FE.
Ku - TS/V (I drop sub-indexes) is, when those conditions apply, TS = TKdD and you have that
Ku is what they call the before tax WACC or KdD% + KeE%, hence,
Ku - TS/V = KdD% + KeE% - KdTD/V = KdD% + KeE% - TKdD% = Kd(1-T)D% + KeE%.
A beauty, isn't it?

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[Karnen: Your approach is amazing, can't remember any corporate finance or valuation books
have ever taught it. I guess Damodaran has ever touched that topic gently but just ignore it for
the practicality purposes. Expert style, I guess. For the sake of practicality!]
Jakarta, November 2015

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Reading References
Vélez-Pareja, Ignacio; and Joseph Tham. A New WACC with Losses Carried Forward for Firm
Valuation. 2001.
Vélez-Pareja, Ignacio. Calculating Tax Shields from Financial Expenses with Losses Carried
Forward. Version: August 3, 2013.
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