Security II. Selection
B. Firm Valuation and Equity Valuation
Three Approaches to DCF Valuation
There are three ways to implement this model in practice:
Dividend Discount Model,
Equity Valuation (FCFE),
Firm Valuation (FCFF).
The basic ingredients are always of the same type,
Existing cash flows,
Growth rates,
Discount rates,
A terminal value.
The key error to avoid is mismatching cash flows, growth rates and discount rates.
For example, discounting cash flows to equity at the weighted average
cost of capital will bias the estimated value of equity upward.
Cash Flows, Growth and Discount Rates
Dividend discount Model
Existing cash flow: current dividend
Growth rate: growth in equity earnings (net income).
growth rate = (retention ratio) x (return on equity)
Discount rate: cost of equity
Equity Valuation
Existing cash flow: FCFE = net income
- capital expenditures
+ Depreciation
- change in working capital
- net payments of debt principal
Growth rate: growth in equity earnings (net income).
growth rate = (retention ratio) x (return on equity)
Discount rate: cost of equity
Firm Valuation
Existing cash flow: FCFF = operating income
- taxes on operating income
+ Depreciation
- capital expenditures
- change in working capital
Growth rate: growth in operating income
growth rate = (reinvestment rate) x (return on capital)
Discount rate: WACC
Cash Flows and Discount Rates
You are analyzing a company with the following cash flows for the next five
years,
The cost of equity is 13.625% and the firm can borrow long term at 10% (the tax
rate for the firm is 50%).
The current market value of equity is $1,073 and the value of debt outstanding is
$800.
Equity vs. Firm Valuation
Method Discount 1: FCFE at the cost of equity
Cost of equity = 13.625%,
Value of equity = 50/1.13625 + 60/1.136252 + 68/1.136253 +
76.2/1.136254 + (83.49 + 1603)/1.136255 = $1073.
Method 2: Discount FCFF at the cost of capital
Cost of debt = 10% x (1-0.50) = 5%
WACC = 13.625% x (1073/1873) + 5% x (800/1873) = 9.94%
Value of firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 +
(123.49 + 2363)/1.09945 = $1873
Value of equity = value of firm value of debt
= $1873 - $800 = $1073
Error 1: Discount FCFE at the cost of capital
Value of equity = $1248
Value of equity is overstated by $175
Error 2: Discount FCFF at the cost of equity
Value of firm = $1613
Value of equity = $1613 - $800 = $813
Value of equity is understated by $260
Error 3:
Discount FCFF at WACC, but forget to subtract out the debt
Value of equity = $1873
Value of equity is overstated by $800
Linking FCFE and FCFF
Two basic FCF definitions:
FCFE = NI capex + dep OWC NPDP
(1)
FCFF = NOPAT capex + dep OWC
(2)
We have that:
NI = (1 t) (oper income + non operating income interest)
(3)
Plug (3) into (1), this gives:
FCFE = NOPAT capex + dep OWC
NPDP + (non operating income)(1 t) interest (1 t)
Therefore
FCFE + NPDP + interest (1 t) = FCFF + AT non operating income
Firm Value and Equity Value
To get from firm value to equity value, which of the following would you need to
do?
Subtract the value of long-term debt
Subtract the value of all debt
Subtract the value of all non-equity claims in the firm
Doing so will give you a value of equity that is
Greater than the value you would get in an equity valuation?
Smaller than the value you would get in an equity valuation?
Equal to the value you would get in an equity valuation?