DISCOUNTED CASH FLOW VALUATION
A.
Valuation steps
1.
2.
3.
B.
C.
Forecast future free cash flows
Determine required rate of return (discount rate)
Find present value of cash flows
Valuation formulas
1.
n CF
t
Finite period: PV  
t
t 1 1  k 
2.
Infinite period: PV 
CF1
kg
Sources of risk or uncertainty
1.
2.
3.
Free cash flow
Required rate of return
Growth rate
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D.
Applications of valuation
1.
2.
3.
4.
Bonds and stocks
Capital budgeting
Leasing
Mergers and acquisitions
Free Cash Flow (FCF):
 Total after-tax cash flow generated by the firm that is available for distribution to all
providers of the company’s capital:
o Shareholders
o Creditors
 The after-tax cash flow that would be available to firm’s shareholders if firm had no
debt
 Measure of cash produced by the business activities and determined before financing;
therefore not affected by the firm’s financial structure
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Defining the Free Cash Flow:
Profit after taxes
Accounting measure of firm profitability; not a cash flow.
+ After-tax net interest payments
[interest*(1-T)]
Ignore financing expense; want to measure cash produced
by business activity of the firm
= NOPAT
Net operating profit after tax
+ Depreciation
Noncash expense
-Increase in operating current
assets
Increase in working capital is a cash drain on firm
+ Decrease in operating current
assets
Decrease in working capital provides cash back to firm
+ Increase in operating current
liabilities
Increase in sales-related current liabilities provides cash
to firm
-Decrease in operating current
liabilities
Decrease in sales-related current liabilities is a cash drain
on firm
-Increase in fixed assets at cost
A use of cash which reduces firm’s free cash flow
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Enterprise Value of the Firm:
 The present value of the firm’s future anticipated free cash flows
 Weighted Average Cost of Capital (WACC) is appropriate discount rate
o k  wd k d 1  T   w p k p  ws k s (d= debt, p=pfd. stock, and s=common stock)
 Projected free cash flow stream is cut off at a finite horizon time and a terminal value
is substituted for the cash flows that will occur beyond that time
Estimating the terminal value: This can be done using the Gordon (constant growth) model
or market multiples
 To use the Gordon model, you must estimate g, the annual constant long term
growth rate after period t, where g < k:
TVt 
CFt 1  g 
kg
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CAPITAL BUDGETING CONCEPTS
 Methods of evaluating projects
1.
Net Present Value (NPV)
n CF
t (where the initial cash flow is usually negative)
 
t
t  0 1  k 
2.
Internal Rate of Return (IRR)
n
CFt
 CF0

t
t 1 1  IRR 
3.
Modified Internal Rate of Return (MIRR)
n
nt
 CFt 1  k 
t 1
 CF0
n
1  MIRR 
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4.
Payback
= Year before full recovery + (Uncovered cost at start of year/Cash flow during year)
ex: CF0 = -2,000, CF1 = 1,800, CF2 = 500:
Payback = 1 

200
 1.4 years
500
In capital budgeting, you compute the incremental free cash flows (the cash flows available to
the investors):
Changes in operating cash flow
-Changes in capital spending
-Changes in net working capital
=Changes in free cash flow
1. Operating Cash Flow
 Revenues
 Operating costs (Be sure to include effects on revenues and operating costs in other
parts of the company and incremental overhead or administrative costs)
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 Taxes (Include the tax effects of depreciation but not depreciation itself)
2. Investment (Capital Expenditures)
 Purchases and sales of assets
 Include any tax effects of sales
 Opportunity cost of assets already owned that are employed
3. Changes in net working capital include
 Sales and purchases on credit (accounts receivable and payable)
 Changes in inventories of materials and finished goods
 Reserves of cash
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TAXES AND CAPITAL BUDGETING
 Taxes are the part of capital budgeting that makes things complicated.
 Because of tax laws, we have to worry about whether certain effects are taxable and how
much tax they incur.
 One example is depreciation, which is a charge to earnings (a quasi-expense), but not an
actual cash flow.
 Another example is the sale of an asset. Whenever you sell an asset, you pay taxes on any
"profit" from the sale. Uncle Sam defines profit as:
 Profit = Selling Price - Book Value (where Book Value = Installed Cost of Asset Accumulated Depreciation)
Ex: If you sell an asset for $10,000, the book value is $6,000, and your tax rate is 40%
then: Profit = $10,000-$6,000=$4,000 and your net cash inflow is:
$10,000-.40($4,000)=$8,400.
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A Typical Profile of Cash Flows for a Project:
Initial outlays or cash flows
Purchase and installation of
assets
Intermediate cash flows
Revenues minus expenses
net of tax effects
Terminal cash flows
Proceeds from sale of assets net
of tax effects
Changes in net working capital
Changes in net working
capital
Costs of clean up or disposal
net of tax effects
Changes in overhead
expenses net of tax effects
Recovery of working capital
Training expenses net of tax
effects
Sale or disposal of replaced
assets net of tax effects
Depreciation tax shields
Most projects usually exhibit a normal cash flow pattern, meaning that the initial cash flow is
negative, followed by a series of cash inflows. A nonnormal cash flow pattern is one in which an
initial negative cash flow is followed by a series of inflows and outflows.
Note about net working capital:
Changes in net working capital frequently accompany capital expenditure decisions. The
recovery of working capital in the terminal cash flow occurs because at the end of the project’s
life the need for increased net working capital investment is assumed to end.
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Always ask the "with vs. without" question!
 The "with vs. without" rule says to always ask whether a particular cash flow is different
with versus without the project. If the answer is "yes" then include it in your project
analysis; otherwise leave it out. Typical items that do not get included are sunk costs and
overhead expenses. However, incremental overhead expenses would be included.
Things to keep in mind when computing incremental cash flows:
 Include changes, not levels, of net working capital
 Include the recovery of net working capital at the termination of a project
 Ignore costs that are not incremental (i.e., sunk costs and pre-committed expenditures)
 Ignore financing cash flows such as interest payments and dividends
 Include only overhead costs that are incremental to the project
 Include the opportunity cost of owned assets that are employed in a project
 Include the tax effects of the sale of assets
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 Include effects on the sales and costs of production of related products or services of the
company
 Ignore depreciation charges, but include the tax effects of depreciation
 Treat inflation consistently (i.e., discount nominal cash flows by nominal discount rates)
Inflation adjustments
1.
2.
Real versus nominal cash flows
Real versus nominal discount rates
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COMPUTING THE DISCOUNT RATE
1. If the project is a scale expansion of the existing business, then the WACC is usually sufficient:
WACC  w dk d 1  T  w pk p  w sk s (d= debt, p=pfd. stock, and s=common stock)
2. If the risk of the project is different from the risk of the firm then you should use a risk-adjusted
discount rate (RADR). One way of doing this is with the CAPM:
 Assign a beta to the project
 Establish risk classes within the firm and assign betas accordingly
 Look at companies with similar projects (may need to unlever beta--see
M&A discussion)
 Use CAPM to compute the discount rate:
k i  k RF  i (k M  k RF )
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OTHER PROJECT RISK ISSUES
1. Stand-alone risk: measures the risk the project would have it if were the firm's only asset. It is
measured by the variability of the asset's expected return.
 Sensitivity Analysis
 Simulation
 CV as a measure of risk:
 NPV
ENPV 
2. Within-firm risk: reflects the effects of a project on the firm's risk, and it is measured by the
project's effect on the firm's earnings variability.
3. Market risk: reflects the effects of a project on the riskiness of stockholders, assuming they hold
diversified portfolios. It is measured by the project's effect on the firm's beta coefficient.
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