BM410: Investments
Equity Valuation 2:
Calculating Intrinsic Value
Objectives
 B. Understand how to calculate intrinsic
value, using the four key methods
 C. Understand how to present intrinsic
value in your company report
A. Review the Importance of
Intrinsic Value
 What is intrinsic value?
 The present value of a firm’s cash flows discounted
by the firm’s required rate of return
 In an efficient market, what should the relationship be
between a firm’s intrinsic value and market value?
 In a truly efficient market, the intrinsic value should
equal its market value
 What happens if it doesn’t?
 There are opportunities for profit
Intrinsic Value (continued)
 How do you determine Intrinsic Value?
• It is a value assigned by the analyst
• It is based on specific theories and assumptions
• Analysts use specific models for estimation
• Lots of models exist, but remember, they are
proxies for reality – not reality
Intrinsic Value (continued)
 What happens if the intrinsic value is greater
than the market price (and your intrinsic value
is correct)?
• Intrinsic Value > Market Price
• Buy
• Intrinsic Value < Market Price
• Sell or Short Sell
• Intrinsic Value = Market Price
• Hold or Fairly Priced or valued
Questions
 Do you understand the importance of intrinsic
value?
B. Understand how to calculate
Intrinsic Value
• For the purposes of your company report, we
will cover the following topics:
1.
2.
3.
4.
5.
6.
Discount Rate
Discount Dividend Models
Internal Rate of Return (IRR)
Present Value of Free Cash Flows to Equity
Present Value of Operating Free Cash Flows
Relative Valuation Models
1. Discount Rate
 What is the discount rate?
• It is the rate of return required by investors to
compensate them for the risk of the firm
 What is the theory behind the discount rate?
• The CAPM Model
• This is one method broadly used by
practitioners to determine a company’s required
rate of return. This is the rate that is used to
determine the company’s cost of equity.
• What is the formula?
• K = rf + beta (risk premium)
Discount Rate (continued)
 What are the discount rates components?
• The nominal risk-free interest rate
• The risk premium (rM - rf )
• If the market is efficient, over time, the return
earned by investors should compensate them for
the risk of the investment.
 How is it used?
• It is used to discount all future cash flows to
determine the present value of future dividends.
• We use it to determine what the appropriate
discount rate is for our company
Discount Rate (continued)
 Where do you get the risk free rate?
• Generally, the risk-free rate is considered the rate
on a 3 month or 1 year US Treasury bill that you
expect to receive over the life of the investment
 Where do you get the beta?
• The easiest method is to get it from Bloomberg.
You type your company ticker [equity] and BETA.
Then make sure the index is appropriate for your
company.
Discount Rate (continued)
 What about the time frame?
• You get to pick. If you think the next 3 years is
more consistent with the past, choose a longer time
period. If it is more consistent with the most recent
period, choose a shorter time period. The minimum
period is 60 observations.
 What is the adjusted beta?
• Beta is volatile depending on the time period.
Companies such as Bloomberg calculate an
adjusted beta, which is 2/3 the calculated beta and
1/3 the market beta of 1. It tends to lower the beta
and hence reduce the discount rate, more consistent
with actual results
2. Dividend Discount Models (DDMs)
 What are DDM’s?
• Models which take into account discounting
expected future cash flows to gain a reference for
the value of a company
 How do they work?
• DDM’s determine the firm’s value by taking the
present value of all future cash flows (dividends and
the eventual sale of equity)
Dividend Discount Models (continued)
 How do you determine the final sale price of the stock?
• Remember the PE is the price divided by EPS.
Therefore, the future value of the stock is the
estimated PE in the future times the estimated EPS
• You calculate the 2006 EPS. Multiply the 2006
EPS estimate by your estimated 2006 PE ratio to
get the price of the stock
 So instead of guessing the future price, you guess the
future PE? Any hints?
• A good starting point is calculating your harmonic
mean PE for your last 5 years (positive PE’s only).
The formula is:
• (5/[(1/PE1)+(1/PE2)+(1/PE3)+(1/PE4)+ (1/PE5)])
Dividend Discount Models (continued)
What next?
• Find the present value of the future cash flows
(dividends) for the next three years and the forecast
sale price by discounting them by the discount rate
calculated above.
• This will give you an intrinsic value at your
estimated discount rate.
• Divide the present value by the current market price
and you will get the percentage of overvaluation or
(under-valuation)
• From this valuation point, you determine
whether the stock is attractive (buy) or not (hold
or sell)
Dividend Discount Models (continued)
 What are we assuming?
• We are assuming that the stock’s dividend growth
rate will be at a constant rate over time. Although
this may be unrealistic for fast-growing or cyclical
firms, DDM’s may be appropriate for some mature,
slower-growing firms. Two and three-growth stage
models can be used to modify this model as
alternative assumptions
 What factors will impact the dividend growth
rate?
• The dividend growth rate will be influenced by the
age of the industry life cycle, structural changes,
and economic trends
Problems with DDMs (continued)
What are our assumptions for DDMs?
• 1. Dividends grow at a constant rate
• This is rarely the case
• 2. The constant growth rate will continue for an
infinite period
• This is also rarely the case
• 3. The required rate of return (k) is greater than the
infinite growth rate (g). If g > k, the model become
meaningless because the denominator becomes
negative
• If you have this problem, you will need to
reduce g downward. Document this clearly in
your reports.
3. Internal Rate of Return
 What is the internal rate of return?
• It is the discount rate that equates the present value
of cash outflows for an investment with the present
value of its cash inflows.
• Theoretically, you compare your firm’s cost of
capital to the IRR
• Accept (reject) any investment proposal with
an IRR greater (less) than your cost of
capital
 What are my cash flows?
• Your dividends and your eventual sale of the shares
4. Free Cash Flow to the Firm (FCFF)
 What is the difference between cash flow and
free cash flow?
• Free cash flow recognizes that some investing and
financing activities are critical to the ongoing
success of the firm over an above net income and
depreciation. Free cash flow takes these additional
costs into account
 What is Free Cash Flows to the Firm (OFCF)?
• Cash flow available to the company’s suppliers of
capital after all direct operating costs (CGS, SG&A,
etc.) and necessary investments in working capital
and fixed capital.
Free Cash Flow to the Firm (continued)
 How do we calculate FCFF?
• FCFF is equal to:
EBIT (1-tax rate) + depreciation (non cash charges)
– capital expenditures – change in net working
capital + terminal value
• This is the cash flow generated by a company’s
operations and available to all who have provided
capital to the firm – both equity and debt.
Free Cash Flow to the Firm (continued)
What is the appropriate discount rate?
• Because we are dealing with the cash flow available
for all capital suppliers, we use the WACC, which
combines the company’s cost of equity and debt.
 Where do we find the cost of equity?
• The cost of equity was determined with the
calculation of the discount rate k.
 Where do you find the cost of debt?
• The cost of debt is the interest rate at which the
company borrows money from the financial
markets. As a proxy, you can use the imbedded cost
of debt you calculated for your latest year
(generally adding a 1-2.0% premium)
Free Cash Flow to the Firm (continued)
 How do you calculate the weight for debt?
• Weight of Debt: LTD/Enterprise Value
 What is enterprise value?
• The enterprise value is the total market value of an
enterprise plus the value of its debt. It is a step
beyond market capitalization. It starts with market
capitalization, and then adds in preferred equity,
minority interest, and the market value of the firms
debt, then subtracts out the value of cash and cash
equivalents. It is a better statistic than market value
Free Cash Flow to the Firm (continued)
 How about the weight for equity?
• Weight of Equity: (1- Weight of Debt)
 What is the formula for the WACC?
• WACC = (Wd* Kd) (1-T) + (We * Ke)
Free Cash Flow to the Firm (continued)
 Once you have your operating free cash flows,
then what?
• 1. You assume a constant growth rate g for your
final cash flow, and discount that cash flow at
WACC-g
• 2. Sum your discounted cash flows and discount
them at your WACC to get your present value of the
firm’s operating Free Cash Flow
• 3. Subtract out your long-term debt to get the value
of your equity
• 4. Divide your firm value of equity by the number
of shares outstanding at your last forecast year
• 5. Compare your intrinsic value (per share) to your
current market price (per share)
5. Free Cash Flows to Equity (FCFE)
 What is free cash flow to equity?
• It is the cash flow available to the company’s
common equity holders after all payments to debt
holders, and after allowing for all operating
expenditures to maintain the firm’s asset base
Free Cash Flows to Equity (continued)
 What is our goal?
• To determine a value for the firm based on the free
cash flow available to equity shareholders after
payments to all other capital suppliers and after
providing for continued growth of the firm
 How is it calculated?
• Net Income + depreciation – capital expenditures
needed to achieve revenue forecast – change in net
working capital – principal debt repayments + new
debt + terminal value
• Remember that net working capital is current
assets less cash minus current liabilities less
notes payable and current portion of long-term
debt.
Free Cash Flows to Equity (continued)
 Once you have your free cash flows, then
what?
• 1. You discount your cash flows at your discount
rate k
• 2. You assume a constant growth rate g for your
final cash flow, and discount that cash flow at k-g
• 3. Sum your discounted cash flows to get your
present value of the firm’s equity
• 4. Divide the firm value by the number of shares
outstanding at your last forecast year
• 5. Compare your intrinsic value (per share) to your
current market price (per share)
Problems with PV Methods
 Any potential difficulties with these PV
calculations?
• These cash-flow techniques are very dependent on
two significant inputs:
• 1. The growth rate of cash flows g and
• 2. The estimate of the discount rate k.
• A small change in either input will have a
significant impact on the estimated value
• In addition, it is possible to derive intrinsic values
which are substantially above or below current
prices depending on how you adjust your estimated
inputs to the prevailing environment. Be careful!
6. Relative Valuation Methods
 What are relative valuation methods?
• Methods which provide information about how the
market is currently valuing stocks at several levels,
the market, industry, and comparative stocks in the
industry. These are often called “comps” or
“comparables”
 What is relative fair value?
• It is the value of the company relative to other
similar stocks, or stocks in the same market or
industry
 Which relative valuation methods are used most often?
• Generally, the most used in the industry is Price
Earnings. However, Price to Sales, Price to Book,
Dividend Yield, and Price to Cash Flow are also
Relative Valuation Methods (continued)
 How do you use relative valuation methods?
• You compare your company’s valuation ratio to the
market, industry, its history, or other companies
• If you notice a change in relative valuation, i.e. it is
cheaper (expensive) than it has been historically, it
may signal it may be a buy (sell) assuming no other
major changes in the company and industry
 In the Apple case, we used price earnings relative to
the market. Can we use price earnings relative to the
industry?
• Yes, although it is harder to find good forecast data
on the industry, as most industry indices do not
have forecasts.
Relative Valuation Methods (continued)
 How do I determine my buy and sell range?
• This is one of the most difficult challenges of being
an analyst. Here is where the art comes in!
• Look to company history.
• If the company has traditionally traded in a
tight range, the likelihood is that it will
continue
• If your company is volatile, it will be more
difficult and you will need to make the best
decision you can
• Use wisdom and judgment
• Determine whether you think it’s a buy, sell
or hold, then set your relative value
consistent with that view
Relative Valuation Methods (continued)
 How do you calculate relative valuation, say,
for example, relative PE?
• 1. Calculate your PE for your company
historically, and for your forecast period
• 2. Calculate your PE for the market/industry
historically, and for the forecast period
• 3. Calculate the relative PE (i.e. the company PE /
market PE) for all periods
Relative Valuation Methods (continued)
• 4. Determine what you consider to be a fair relative
PE range, i.e. at what relative PE would you buy the
stock, and at what relative PE would you sell the
stock
• 5. Calculate your buy and sell ranges using the
formula: relative PE range * market PE * firm EPS
= Price
Problems with Relative
Valuation Methods
 When is it most appropriate to use RVM?
• When you have a good set of comparables, i.e.
industries/companies in terms of size and risk
• When the aggregate market is not at a valuation
extreme, i.e. it is neither over or undervalued
 When are they inappropriate?
• When you have poor comparables or the current
market level is at extremes.
• If you compare the value of a company to the
very overvalued market, you might believe it is
cheap. However, you may be wrong as company
may be fully valued and the benchmark, the
market, is overvalued.
Summary
Intrinsic Value Calculations
 The next step is to summarize your intrinsic
calculations thus far.
• Take and average of the values calculated from the
Dividend Discount Model, Free Cash Flows From
Equity and Operating Cash Flow and compare
(divide into) with the current market price.
• This will let you know if the company’s stock is
over- or undervalued on a percentage basis
• If you have any models in which the intrinsic values
are negative, try to understand the problem (it is
generally because your g > k--see me), but
generally disregard that model
Review of Objectives
A. Do you understand the importance of
intrinsic value?
B. Do you understand how to calculate intrinsic
value, using the four key methods discussed?
C. Do you know how to present intrinsic value
in your company report?