196  Frameworks for Valuation
of debt and equity. If the company’s debt has an expected return of 5 percent 
and the company’s equity has an expected return of 15 percent, its weighted 
average cost of capital would be 10 percent. Suppose the company decides 
to issue more debt, using the proceeds to repurchase shares. Since the cost of 
debt is lower than the cost of equity, it would appear that issuing debt to retire 
equity should lower the WACC, raising the company’s value.
This line of thinking is flawed, however. In a world without taxes, a change 
in capital structure would not change the cash flow generated by operations, 
nor the risk of those cash flows. Therefore, neither the company’s enterprise 
value nor its cost of capital would change. So why would we think it would? 
When adding debt, we adjusted the weights, but we failed to properly in-
crease the cost of equity. Since debt payments have priority over cash flows 
to equity, adding leverage increases the risk to equity holders. When leverage 
rises, they demand a higher return. Modigliani and Miller postulated that this 
increase would perfectly offset the change in weights.
In reality, taxes play a role in determining capital structure. Since inter-
est is tax deductible, profitable companies can lower taxes by raising debt. 
But if the company relies too heavily on debt, the company’s customers and 
suppliers may fear financial distress and be reluctant to do business with the 
company, reducing future cash flow (academics call this distress costs or dead-
weight costs). Rather than model the effect of capital-structure changes in the 
weighted average cost of capital, APV explicitly measures and values the cash 
flow effects of financing separately.
To build an APV valuation, value the company as if it were all-equity 
financed. Do this by discounting free cash flow by the unlevered cost of equity 
(what the cost of equity would be if the company had no debt).13 To this value, 
add any value created by the company’s use of debt. Exhibit 10.15 values 
GlobalCo using adjusted present value.
Since we assume (for expositional purposes) that GlobalCo will manage 
its capital structure to a target debt-to-value level of 25 percent, the APV-
based valuation leads to the same value for equity as did enterprise DCF (see 
Exhibit 10.4) and economic profit (see Exhibit 10.14). A simplified proof of 
equivalence between enterprise DCF and adjusted present value can be found 
in Appendix B. The following subsections explain adjusted present value in 
detail.
Valuing Free Cash Flow at Unlevered Cost of Equity
When valuing a company using the APV, explicitly separate the unlevered 
value of operations (Vu) from any value created by financing, such as tax 
13 Free cash flow projections in the APV model are identical to those presented in Exhibit 10.4. Continuing 
value is computed using the key value driver formula. Only the cost of capital is used for discounting 
changes.

Adjusted-Present-Value Model  197
EXHIBIT 10.15  GlobalCo: Valuation Using Adjusted Present Value
$ million, except where noted
Year
Free cash 
flow (FCF)
Interest tax 
shield (ITS)
Discount 
factor 
at 8.0%
Present 
value of FCF
Present 
value of ITS
Year 1
(2.0)
2.0
0.926
(1.9)
1.9
Year 2
22.5
2.2
0.857
19.3
1.9
Year 3
54.6
2.3
0.794
43.4
1.8
Continuing value
1,135.6
40.6
0.794
901.5
32.2
Present value
962.3
37.7
Present value of free cash flow
962.3
Present value of interest tax shield
37.7
Value of operations
1,000.0
shields (Vtxa). For a company with debt (D) and equity (E), this relationship is 
as follows:
 
V
V
D
E
u
txa
+
=
+

(10.1)
A second result of Modigliani and Miller’s work is that the total risk of the 
company’s assets, real and financial, must equal the total risk of the financial 
claims against those assets. Thus, in equilibrium, the blended cost of capital for 
operating assets (ku), which we call the unlevered cost of equity) and financial 
assets (ktxa) must equal the blended cost of capital for debt (kd) and equity (ke):
 
V
V k
V
V k
D
V k
E
V k
u
u
txa
txa
d
e
+
=
+

(10.2)
In the corporate-finance literature, academics combine Modigliani and 
Miller’s two equations to solve for the cost of equity (ke) in order to demon-
strate the relationship between leverage and the cost of equity. Appendix C 
algebraically rearranges Equation 10.2 to solve for the most flexible version of 
the levered cost of equity:
 
k
k
D
E k
k
V
E
k
k
e
u
u
d
txa
u
txa
=
+
−
(
) −
−
(
)
(10.3)
As this equation indicates, the cost of equity depends on the unlevered cost of 
equity, or the cost of equity when the company has no debt, plus a premium 
for leverage, less a reduction for the tax deductibility of debt. Note that when 
a company has no debt (D = 0) and subsequently no tax shields (Vtxa = 0), ke 
equals ku. This is why ku is referred to as the unlevered cost of equity.
Unfortunately, ku cannot be observed directly. In fact, none of the variables 
on the left side of Equation 10.2 can be observed directly. Only the values on 
the right—that is, those related to debt and equity—can be estimated using