Chapter 19 Financing and Valuation 495
bre44380_ch19_491-524.indd 495 09/30/15 12:07 PM
Review of Assumptions
In order to discount the perpetual crusher’s cash flows at Sangria’s WACC, you need to
assume that
∙ The project’s business risks are the same as those of Sangria’s other assets and remain so
for the life of the project.
∙ The project supports the same fraction of debt to value as in Sangria’s overall capital
structure, which remains constant for the life of the project.
You can see the importance of these two assumptions: If the perpetual crusher had greater
business risk than Sangria’s other assets, or if the acceptance of the project would lead to a
permanent, material change in Sangria’s debt ratio, then Sangria’s shareholders would not be
content with a 12.4% expected return on their equity investment in the project.
But users of WACC need not worry about small or temporary fluctuations in debt ratios.
Nor should they be misled by the immediate source of financing. Suppose that Sangria
decides to borrow $12.5 million to get a quick start on construction of the crusher. This does
not necessarily change Sangria’s long-term financing targets. The crusher’s debt capacity is
only $5 million. If Sangria decides for convenience to borrow $12.5 million for the crusher,
then sooner or later it will have to borrow $12.5 – $5 = $7.5 million less for other projects.
We have illustrated the WACC formula only for a project offering perpetual cash flows.
But the formula works for any cash-flow pattern if the firm adjusts its borrowing to maintain
a constant debt ratio over time.^3 When the firm departs from this borrowing policy, WACC is
only approximately correct.
Mistakes People Make in Using the Weighted-Average Formula
The weighted-average formula is very useful but also dangerous. It tempts people to make
logical errors. For example, manager Q, who is campaigning for a pet project, might look at
the formula
WACC = rD(1 − Tc) D__
V+ rE __E
V(^3) We can prove this statement as follows. Denote expected after-tax cash flows (assuming all-equity financing) as C 1 , C 2 , . . . , CT. With
all-equity financing, these flows would be discounted at the opportunity cost of capital r. But we need to value the cash flows for a
firm that is financed partly with debt.
Start with value in the next to last period: VT – 1 = DT – 1 + ET – 1. The total cash payoff to debt and equity investors is the cash flow
plus the interest tax shield. The expected total return to debt and equity investors is
Expected cash payoff in T = CT + TcrDDT – 1 (1)
= VT – 1 (^) ( 1 + rD _____ (^) VDT^ –^1
T – 1
- rE _VET^ –^1
T – 1
(^) ) (2)
Assume the debt ratio is constant at L = D/V. Equate (1) and (2) and solve for VT – 1:
VT – 1 = (^) 1 + (1 − ___T CT
c)rD L + rE (1 − L)
= __1 + WACCCT
The logic repeats for VT – 2. Note that the next period’s payoff includes VT – 1:
Expected cash payoff in T − 1 = CT – 1 + TcrDDT – 2 + VT – 1
= VT – 2 (^) ( 1 + rD _____DVT^ –^2
T – 2 - rE EV_T^ –^2
T – 2
(^) )
VT – 2 = ___ CT^ –^1 + VT^ –^1
1 + (1 − Tc)rDL + rE(1 − L)
= CT__^ –^1 + VT^ –^1
1 + WACC
= __CT^ –^1
1 + WACC - ____CT
(1 + WACC)^2
We can continue all the way back to date 0:
V 0 =^ Σ (^) tT = 1 ___Ct
(1 + WACC)t