Finance 7311
Note on Value of Firm
Definitions:
EBIT = earnings before interest & taxes
Tc = corporate tax rate
V = value of firm (assets)
E = value of equity
D = value of debt (thus: V = D + E)
Re = required equity return
Rd = required debt return
WACC = weighted average cost of capital
Ra = asset cost of capital (= Re when D = 0)
CF = cash flows
recall: for a perpetuity, PV = CF/R
Cash flow concepts:
1. Free cash flows to all equity firm:
EBIT(1-Tc) + depreciation - additional investment - NWC
2. Free cash flows to firm: same as to all
equity firm
3. Free cash flows to S/H:
Net Income + Depreciation - Additional Investment - NWC
+ Debt
3 equivalent evaluation methods:
(For simplicity, assume depreciation =
Additional Investment & NWC = 0)
1. PV of CF's to all equity firm at Ra
+ PV(tax shield)
Note: If the firm is all equity, then Re = Ra. In this case Re
is an 'unlevered' cost of equity. When there is debt in the firm
Re is a 'levered' cost of equity, which is higher.
a. CF's(all equity firm) = EBIT * (1 - Tc)
b. PV(tax shield) = Tc*D (if perpetuity)
V = [EBIT*(1 - Tc)] / Ra + Tc*D (perpetuity)
Vl = Vu + PV(tax shield)
The value of the 'levered' firm, Vl, is equal to the value of
the 'unlevered' firm, Vu, plus the present value of the tax
savings associated with debt. We can then find the value of
equity as follows: E = V - D
If the cash flows are not a perpetuity, then the above
equation for V would be replaced with an infinite sum.
Note: In an all equity firm WACC = Ra = Re.
2. PV of CF's to firm at WACC
CF's to firm = EBIT * (1 - Tc)
V = [EBIT * (1 - Tc)] / WACC (perpetuity)
and: E = V - D
If the cash flows are not a perpetuity, then the above
equation would be replaced with an infinite sum.
note: here WACC < Ra < Re
The values obtained in methods 1 & 2 should be identical.
In method 1 the present value of the tax savings associated with
debt are accounted for separately, while in method 2 they are
accounted for in the discount rate, WACC. The numerators are the
same in each.
3. PV of CF's to S/H's at 'levered' Re (PV of dividends)
E = [CF's to Equity] / Re (perpetuity)