198  Frameworks for Valuation
market data. Because there are so many unknowns and only one equation, we 
must impose additional restrictions to build a usable relationship between the 
levered (ke) and unlevered (ku) cost of equity.
If you believe the company will manage its debt-to-value ratio to a target 
level (the company’s debt will grow with the business), then the value of the 
tax shields will track the value of the operating assets. Thus, the risk of tax 
shields will mirror the risk of operating assets (ktxa = ku). Setting ktxa equal to 
ku, Equation 10.3 can be simplified as follows:
 
k
k
D
E k
k
e
u
u
d
=
+
−
(
) 
(10.4)
The unlevered cost of equity can now be reverse engineered using the ob-
served cost of equity, the cost of debt, and the market debt-to-equity ratio. 
(Appendix C shows some alternative versions for deriving ku from ke.)
Valuing Tax Shields and Other Capital Structure Effects
To complete an APV valuation, forecast and discount capital structure side 
effects such as tax shields, security issuance costs, and distress costs. Since 
GlobalCo has only a small probability of default, we estimated the company’s 
future interest tax shields using the company’s expected interest payments 
and marginal tax rate (see Exhibit 10.16). To calculate the expected interest 
payment in year 1, multiply the prior year’s debt of $250 million by the in-
terest rate of 4.0 percent. This results in an expected interest payment of $10 
million. Next, multiply the expected interest payment by the marginal tax rate 
of 20 percent, for an expected interest tax shield of $2 million in year 1. To 
determine the continuing value of interest tax shields beyond year 3, use a 
growth perpetuity based on interest tax shields in the continuing-value year, 
the unlevered cost of capital, and growth in NOPAT.
A company with significant leverage may not be able to fully use the tax 
shields (it may not have enough profits to shield). If there is a significant 
EXHIBIT 10.16  GlobalCo: Forecast of Interest Tax Shields
$ million
Forecast year
Prior-year 
net debt1
Interest rate, 
%
Expected 
interest 
payment
Marginal 
tax rate, 
%
Interest 
tax shield
Year 1
250.0
4.0
10.0
20.0
2.0
Year 2
270.0
4.0
10.8
20.0
2.2
Year 3
285.4
4.0
11.4
20.0
2.3
Continuing-value forecast
294.0
4.0
11.8
20.0
2.4
1 Total debt net of excess cash.

Capital Cash Flow Model  199
14 The Tax Cuts and Jobs Act of 2017 placed additional restrictions on the deductibility of interest, even for 
profitable companies. Only value interest tax shields if they meet deductibility guidelines.
probability of default, you must model expected tax shields, rather than the 
calculated tax shields based on promised interest payments.14 To do this, re-
duce each promised tax shield by the cumulative probability of default.
Capital Cash Flow Model
When a company actively manages its capital structure to a target debt-to-
value level, both free cash flow (FCF) and the interest tax shield (ITS) should 
be discounted at the unlevered cost of equity, ku, such that enterprise value 
equals the sum of discounted cash flows plus the sum of discounted interest 
tax shields:
V
k
k
t
u
t
t
t
u
t
t
=
+
+
+
=
∞
=
∞
∑
∑
FCF
ITS
(
)
(
)
1
1
1
1
In 2002, Richard Ruback of the Harvard Business School argued that there 
is no need to separate free cash flow from tax shields when both flows are 
discounted by the same cost of capital.15 He combined the two flows and 
named the resulting cash flow (i.e., FCF plus interest tax shields) capital cash 
flow (CCF):
V
k
t
t
u
t
t
=
(
) =
+
+
=
∞
∑
PV Capital Cash Flow
FCF
ITS
(
)
1
1
Given that Ruback’s assumptions match those of the weighted average 
cost of capital, the capital cash flow and WACC-based valuations will lead 
to identical results. In fact, we have now detailed three distinct but identical 
valuation methods created solely around how they treat tax shields: WACC 
(tax shield valued in the cost of capital), APV (tax shield valued separately), 
and CCF (tax shield valued in the cash flow).
Although free cash flow and capital cash flow lead to the same result when 
debt is proportional to value, we believe FCF models are superior to CCF 
models. By keeping NOPAT and FCF independent of leverage, it is easier to 
evaluate the company’s operating performance over time and against com-
petitors. A clean measure of historical operating performance leads to better 
forecasts.
15 R. S. Ruback, “Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows,” Financial Manage-
ment (Summer 2002): 85–103.